Latent Dynamics Modeling

Follow this topic Ask about this topic

Momentum

35 papers in the last four weeks, up 483% on the four weeks before. 0.3% of all new papers.

Jul 13Week of Sep 28

Latest papers 172

May 25, 2026cs.LG

Autoregression-Free Neural Operators for Time-Dependent PDEs

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon prediction through autoregressive rollout directly in high-dimensional physical field spaces, where each predicted state is recursively fed back as the input for the next step. Although effective for short-term prediction, this autoregressive rollout and the lack of continuous-time modeling lead to progressive error accumulation over long-horizon rollouts. In this work, we propose Autoregression-Free Neural Operators (AFNO), which map the time evolution of PDEs into a latent space and model continuous-time vector fields within it. AFNO uses flow matching to learn the latent vector field, thereby enabling continuous evolution over extended horizons, avoiding autoregressive rollout and capturing dynamics under varying parameter configurations through explicit conditioning on physical parameters. Theoretical analysis and extensive experiments on six PDEs demonstrate that AFNO improves long-horizon prediction stability and consistently reduces rollout errors compared with the baselines.

Jiaquan Zhang, Caiyan Qin, Haoyu Bian +7

School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China · School of Robotics and Advanced Manufacture, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China · School of Mathematical Sciences, Capital Normal University, Beijing 100048, China +3

Latent Dynamics Modeling PDE Operator Learning Spatiotemporal Forecasting

May 25, 2026cs.LG

UWM-JEPA: Predictive World Models That Imagine in Belief Space

World models for partially observed environments must imagine multiple compatible hidden futures and steer between them under counterfactual actions. Joint Embedding Predictive Architectures (JEPAs) do this in latent space, but a vector-valued latent has no internal structure for carrying the belief over hidden continuations through blind rollout. We introduce the Unitary World Model JEPA (UWM-JEPA), a JEPA world model with a density-matrix latent on a joint system-environment space and a learned unitary predictor. The construction preserves the joint-state spectrum exactly during rollout, so the predictor itself cannot dissipate the represented uncertainty. On a hidden-velocity indicator task requiring five-step forward simulation under a given action sequence with the target observation masked, UWM-JEPA reaches 0.77 accuracy and degrades monotonically as actions are perturbed; a parameter-matched LSTM-JEPA trained under the same counterfactual-target objective and action head collapses to majority-class accuracy (0.53) under every action condition. Under blind rollout, UWM-JEPA loses fewer than ten points of probe R^2 at short horizons while vector-latent baselines lose forty-one and sixty-eight; both nevertheless tie on a held-out context probe, locating the separation in the predictor rather than the encoder. Action sensitivity itself requires training against counterfactual rather than teacher-forced targets, a finding that applies beyond the unitary parameterisation. For JEPA world models to imagine under partial observability, latent geometry and predictor dynamics matter, not frozen context-encoding capacity alone.

Santosh Kumar Radha, Oktay Goktas

AgentField AI, Toronto, Canada

World Model Learning Latent Dynamics Modeling Joint-Embedding Predictive Architecture Action-Conditioned World Models

May 23, 2026cs.LG

Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting

Time series driven by unobserved latent states frequently exhibit abrupt jump discontinuities whose timing and magnitude cannot be predicted from observed history alone. Classical jump-diffusion models offer a principled mathematical framework but assume rigid parametric forms, while recent neural jump models operate on fully observed trajectories without inferring the hidden states that govern the dynamics. We propose \textit{Deep ZakaiJ}, a latent-state model for partially observed jump-diffusion systems that embeds the Zakai nonlinear filtering equation into a neural encoder--decoder architecture. The encoder recursively updates a belief over the latent state via Strang splitting into three interpretable substeps: prior propagation, diffusion innovation, and jump innovation, yielding a differentiable, first-order-accurate approximation of the exact filtering evolution. The decoder is a structured jump-diffusion model explicitly conditioned on the filtered belief, preserving the separation between continuous dynamics and discontinuous shocks. On synthetic, financial, and oceanographic datasets, \textit{Deep ZakaiJ} improves distributional forecasts while remaining competitive in point accuracy, achieving calibrated predictive intervals and recovering interpretable latent structure in synthetic and qualitative case studies.

Yan Leng, Thibaut Mastrolia, Hao Wang

University of Texas at Austin · University of California, Berkeley

Stochastic Differential Equations Latent Dynamics Modeling Time Series Forecasting Probabilistic Time Series Forecasting

May 22, 2026cs.LG

Learning partially observed systems with neural Hamiltonian ordinary differential equations

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially observed settings, where some state variables are completely unobserved and must be inferred without direct supervision. Here, we present neural Hamiltonian ordinary differential equations (NHODE), a framework that combines Hamiltonian neural networks (HNNs) with neural ordinary differential equations (neural ODEs) to learn partially observed dynamical systems from data. The Hamiltonian structure enforces energy conservation by construction, while the neural ODE framework enables a flexible training procedure that allows the loss to be defined only on observed variables. We also incorporate additional physical constraints through symmetry-aware coordinate transformations and separable energy formulations. The framework is evaluated on systems of increasing complexity, from linear and nonlinear mass-spring systems to the chaotic three-body problem. Across all examples, increasing the amount of embedded physical structure improves the accuracy and long-horizon stability of the predictions. Even in the most challenging regimes, the NHODE framework captures both observed and latent dynamics, whereas purely data-driven baselines become unstable.

Sunniva Meltzer, Sølve Eidnes, Alexander Johannes Stasik

Department of Mathematics and Cybernetics, SINTEF Digital, Norway · Department of Physics, University of Oslo, Norway · Department of Data Science, Norwegian University of Life Science, Norway

Dynamical Systems Latent Dynamics Modeling Nonlinear System Identification Hamiltonian Neural Networks Physics-Informed ML Neural ODEs+1

May 22, 2026cs.LG

Learning Individual Dynamics from Sparse Cross-Sectional Snapshots

Predicting how a dynamical unit evolves over time - how an individual ages, an epidemic spreads, or a physical system degrades - typically requires dense longitudinal tracking. When only extremely sparse or entirely cross-sectional data is available, inferring individualized, continuous-time trajectories is fundamentally ill-posed. Existing methods force a strict compromise: sequence models (e.g. latent ODEs) require dense longitudinal data, while cross-sectional methods (e.g. optimal transport, flow matching-based) map aggregate populations, losing individual dynamics. In this paper, we demonstrate that this dichotomy can be broken. We introduce CADENCE, a principled probabilistic framework that recovers continuous individual trajectories from isolated snapshots by anchoring latent dynamics to static, individual-level contexts. We provide novel identifiability guarantees for single-timepoint trajectory inference. By combining a score-based spatial encoder (bijective Probability Flow ODE) to eliminate diffeomorphic ambiguities with a Soft Mixture-of-Experts (SMoE) router, we show that individual dynamical parameters and routing function are jointly identifiable. Across a suite of benchmarks spanning physical systems to real-world biological data, CADENCE, trained strictly on extremely sparse snapshots with context structure, matches or exceeds the performance of state-of-the-art sequential models trained on dense, full-trajectory data.

Christian Lagemann, Kai Lagemann, Steven L. Brunton +1

Statistics and Machine Learning, German Center for Neurodegenerative Diseases (DZNE), Bonn, Germany · MediaTek Research, London, United Kingdom · Department of Mechanical Engineering & AI Institute in Dynamic Systems, University of Washington, Seattle, United States +1

Parameter Identifiability Latent Dynamics Modeling Trajectory Prediction

May 21, 2026cs.LG

Dreaming Smoothly and Sample Efficiently with Gradient Penalized Latent Dynamics

Model-based reinforcement learning improves sample efficiency by learning a world model. However, existing latent world models such as DreamerV3 do not explicitly enforce local smoothness in their learned transition dynamics, leaving a useful inductive bias for transition dynamics learning unexploited. We propose GPLD, a gradient-penalized latent dynamics regularizer for DreamerV3 that applies a row-wise Jacobian penalty to the posterior latent distribution to encourage locally smooth transition learning. We show that this penalty can be interpreted as the continuous-latent analog of finite-difference smoothing of transition laws in discrete embedded-state MDPs, and estimate it efficiently using Hutchinson-style stochastic probes. Empirically, across DeepMind Control proprioceptive tasks, GPLD improves aggregate sample efficiency, with particularly strong gains on higher-complexity locomotion environments. On more challenging quadruped tasks, GPLD reaches high-return behavior earlier and exhibits more consistent late-stage learning over longer horizons. Explicit local smoothness regularization is a simple and effective way to improve latent world models for smooth continuous control environments. Code for GPLD is available at github.com/romils9/gpld-mbrl .

Romil V. Sonigra, P. R. Kumar

Texas A&M University · Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843

Latent Dynamics Modeling Jacobian Regularization Latent World Models Sample-Efficient RL Model-Based RL

May 21, 2026cs.CV

EMMA: Extracting Multiple physical parameters from Multimodal Data

We introduce EMMA, a physics-informed multimodal framework that recovers all identifiable dynamical parameters of a system directly from raw video, audio, and image-based time-series observations. Unlike prior video-only approaches that struggle with occluded states, hidden actuation inputs, or assumptions about known initial conditions and coordinate frames, EMMA performs joint inference of explicit parameters, implicit dynamical components, and calibration invariants within a unified continuous-time model. EMMA leverages a Liquid Time-Constant (LTC) network to learn latent dynamics from heterogeneous modalities while a physics-constrained loss enforces consistency with the governing differential equations. A unified feature pipeline enables consistent alignment across video trajectories, acoustic signatures, and chart-derived measurements, allowing EMMA to estimate parameters under forced, implicit, and multivariate dynamics without requiring segmentation masks, differentiable rendering, or specialized sensors. Across 100+ scenarios including five standard dynamical benchmarks (75 Delfys videos), real-world rover and quadrotor systems with hidden inputs, and simulation-chart case studies spanning biological and chaotic systems, EMMA delivers robust multi-parameter recovery and significantly outperforms existing single-modality and equation-discovery baselines. Our results establish EMMA as a general, scalable solution for physics-consistent model extraction from opportunistic multimodal data. Code and data are available at: https://github.com/ImpactLabASU/EMMA-CVPR2026

Farhat Shaikh, Ayan Banerjee, Sandeep Gupta

IMPACT Lab, School of Computing & Augmented Intelligence (SCAI) Arizona State University, Tempe, AZ

Parameter Estimation Latent Dynamics Modeling System Identification Physics-Informed ML Multimodal Sensor Fusion

May 21, 2026cs.LG

From Snapshots to Trajectories: Learning Single-Cell Gene Expression Dynamics via Conditional Flow Matching

Single-cell RNA sequencing (scRNA-seq) provides high-dimensional profiles of cellular states, enabling data-driven modeling of cellular dynamics over time. In practice, time-resolved scRNA-seq is collected at only a few discrete time points as unpaired snapshot populations, leaving substantial temporal gaps. This motivates trajectory inference at unmeasured time points. Existing methods mainly follow two directions, optimal-transport (OT) alignment provides distribution-level matching between observed snapshots, while continuous-time generative models support forecasting via learned dynamics. However, two challenges remain: (i) unpaired snapshots render local transitions between adjacent time points ambiguous, leading to unstable supervision; and (ii) long-horizon prediction relies on repeated integration, where small modeling errors compound and cause distribution drift. To address these challenges, we propose single-cell Flow Matching (scFM), a latent generative framework based on coupling-conditioned flow matching. First, we compute entropically regularized OT couplings between adjacent snapshots and use them to construct soft, weighted flow-matching targets for learning time-dependent velocity fields. Second, we learn bidirectional velocity fields and leverage their consistency to refine couplings and improve temporal coherence under sparse supervision. Third, we introduce distribution-level alignment and latent dynamic regularization to anchor long rollouts and mitigate drift. Experiments on real-world time-series scRNA-seq datasets show that scFM consistently improves distributional prediction performance for both temporal interpolation and extrapolation. Moreover, scFM yields more accurate trajectory reconstruction and temporally coherent visualizations where intermediate time points are absent, indicating a more faithful recovery of underlying temporal gene expression dynamics.

Siyu Pu, Qingqing Long, Xiaohan Huang +7

Computer Network Information Center, Chinese Academy of Sciences · University of California, Los Angeles

Latent Dynamics Modeling Conditional Flow Matching Single-Cell Transcriptomics

May 21, 2026cs.LG

ChronoMedicalWorld: A Medical World Model for Learning Patient Trajectories from Longitudinal Care Data

Long-horizon clinical simulation -- predicting how a patient's physiology evolves over years under specified interventions -- is central to chronic-disease care, yet existing electronic health record (EHR) models are predominantly discriminative, and general-purpose large language models drift under repeated interventions. We propose the \textbf{ChronoMedicalWorld Model (CMWM)}, an action-conditioned latent world-model framework for learning patient trajectories from longitudinal care data. CMWM couples a joint-embedding state encoder with a wide action encoder that admits both structured intervention indicators and free-text communication embeddings, and trains a recurrent latent transition module under a six-term objective: next-observation supervision, next-latent prediction, SIGReg latent regularisation, and three physiology-aware shape priors (slope, continuity, large-jump penalty). A closed-loop rollout-prefix protocol matches training to deployment, so the model is optimised against the same multi-step error it exhibits at inference. As a concrete case study, we instantiate CMWM for annual estimated glomerular filtration rate (eGFR) trajectory forecasting in chronic kidney disease (CKD). On a 2{,}232-patient nephrology cohort, the CKD instantiation achieves a dynamic-50% history rollout test mean absolute error (MAE) of 7.384 and root-mean-square error (RMSE) of 10.256, against 7.964 and 11.069 for a tuned GPT-5.5 structured-prompting baseline (

-7.28\%

MAE,

-7.35\%

RMSE), with the gain dominated by the dialogue portion of patient--health-coach communication. The framework is not CKD-specific: its architecture, loss design, and training protocol apply to any chronic condition that can be cast as periodic clinical state interleaved with structured and conversational interventions.

Jiangyuan Wang, Xuyong Chen, Junwei He +3

Beijing KidneyTec Medical Technology Co., Ltd., Beijing, China

Latent Dynamics Modeling Healthcare Action-Conditioned World Models Clinical Outcome Prediction Latent World Models Longitudinal EHR Modeling

May 20, 2026cs.CV

Latent Dynamics for Full Body Avatar Animation

Pose-driven full-body avatars built on neural rendering produce high-quality novel views of a captured subject. Yet loose clothing and other dynamic elements deform in ways pose alone cannot explain: the same pose can correspond to many different states, because their motion depends on history, inertia, and contact. Explicit simulation and layered-garment methods can model such dynamics, but they require either a dedicated garment template, which raw multi-view capture does not naturally provide, or a test-time physics simulator with non-trivial runtime cost. A parallel line of work learns data-driven clothing avatars that avoid explicit garment layers. These methods add an auxiliary latent for variation beyond pose; at inference, they fix it, regress it from pose, or retrieve it from training data, without explicitly modeling how the latent evolves with its own dynamics. Additionally, even in everyday motion with loose clothing, existing architectures often struggle to capture fine-grained detail, producing blurry renderings and temporal artifacts. We augment a pose-conditioned 3D Gaussian avatar with a transformer-based decoder and a dynamics residual latent that captures temporal appearance and geometry variation beyond the driving signals. At inference, a learned latent dynamics model evolves the residual latent from a short pose history and the previous latent state. The model decomposes each update into driving, restoring, and dissipative forces, producing temporally coherent, history-dependent rollouts with negligible added cost. Different initial conditions yield diverse yet plausible motion trajectories, and the force decomposition exposes controls such as stiffness. Across nine captured sequences of everyday motion with diverse loose garments, quantitative metrics and a perceptual user study show improved animation quality over recent data-driven baselines.

Shichong Peng, Chengxiang Yin, Fei Jiang +7

Simon Fraser University, Canada · Codec Avatars Lab, Meta, USA

Latent Dynamics Modeling Human Motion Generation 3D Avatar Generation Human Avatar Animation

May 20, 2026cs.LG

Modeling Temporal scRNA-seq Data with Latent Gaussian Process and Optimal Transport

Single-cell RNA sequencing provides insights into gene expression at single-cell resolution, yet inferring temporal processes from these static snapshot measurements remains a fundamental challenge. Current approaches utilizing neural differential equations and flows are sensitive to overfitting and lack careful considerations of biological variability. In this work, we propose a generative framework that models population trends using a latent heteroscedastic Gaussian process (GP) approximated by Hilbert space methods. To address the absence of genuine cell trajectories, we leverage an optimal transport (OT) objective that aligns generated and observed population distributions. Our method explicitly captures biological heterogeneity by incorporating cell-specific latent time and cell type conditioning to disentangle temporal asynchrony and trajectories to different cell types. We demonstrate state-of-the-art performance on complex interpolation and extrapolation benchmarks and introduce a novel gradient-based strategy for inferring perturbation trajectories.

Mehmet Yigit Balik, Harri Lähdesmäki

Department of Computer Science, Aalto University, Espoo, Finland.

Latent Dynamics Modeling Conditional Generative Modeling Single-Cell Transcriptomics Gaussian Process Regression

May 20, 2026math.OC

Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics

Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and control settings. We present a weak-form latent-space reduced-order modeling framework for accelerating gradient-based PDE-constrained optimization. The proposed approach builds on Weak-form Latent Space Dynamics Identification (WLaSDI), which compresses high-dimensional solution trajectories into a low-dimensional latent representation and identifies parametric latent dynamics using weak-form system identification. By avoiding explicit numerical differentiation of training trajectories, the weak-form improves robustness to noisy data and yields more reliable surrogate dynamics for optimization. We formulate the resulting reduced PDE-constrained optimization problem and derive both direct-sensitivity and adjoint-based gradient expressions for the learned latent dynamics, enabling scalable gradient evaluation with respect to design parameters. The framework is demonstrated on three time-dependent benchmark problems: thermal radiative transfer for optimal hohlraum design, the two-stream instability Vlasov-Poisson system, and the inviscid Burgers equation. Across these examples, WLaSDI produces accurate optimal designs, remains robust under noisy training data, and delivers substantial computational savings, including speedups of up to five orders of magnitude relative to full-order optimization. These results demonstrate that weak-form latent dynamics provide an efficient and noise-robust surrogate foundation for gradient-based optimization of complex time-dependent PDE systems.

April Tran, Terry Haut, David Bortz +1

Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA · Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, 94550, CA, USA

Latent Dynamics Modeling PDE Surrogate Modeling System Identification Reduced-Order Modeling Constrained Optimization

May 18, 2026cs.LG

L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting

Mainstream methods for multivariate time-series forecasting largely follow the Direct-Mapping paradigm. They learn a unified mapping from history to the future in the observation space to fit value-level dependencies. However, real-world systems often undergo distribution shifts and regime changes. In such cases, a unified mapping can exhibit response lag around turning points, causing error accumulation within the switching window and reducing forecasting reliability. To address this issue, we propose L-Drive, a change-aware forecasting framework. L-Drive introduces a Latent-Context, to explicitly characterize high-level dynamics evolving over time, and uses gating to modulate increment representations. This provides more timely change cues and improves adaptation to changing segments. In addition, it incorporates patch-shared relative positional basis functions to strengthen intra-segment structural modeling and reduce overfitting caused by absolute-position memorization. Extensive experiments validate the effectiveness of L-Drive and show a better overall trade-off between forecasting accuracy and computational efficiency.

Fan Zhang, Shijun Chen, Hua Wang

Shandong Technology and Business University, Yantai, Shandong, China · Ludong University, Yantai, Shandong, China

Multivariate Time Series Forecasting Latent Dynamics Modeling Time Series Forecasting Non-Stationary Time Series Forecasting Temporal Distribution Shift

May 16, 2026cs.CV

Factorized Latent Dynamics for Video JEPA: An Empirical Study of Auxiliary Objectives

Joint-Embedding Predictive Architectures (JEPA) are a promising framework for self-supervised video representation learning, yet the behavior of auxiliary objectives in small-scale Video-JEPA training is not well characterized. We report a small-scale empirical study of 18 auxiliary objective variants for Video-JEPA across two pretraining regimes: single-dataset (UCF-101) and mixed-dataset (UCF-101 + Something-Something V2 + ImageNet-100). We evaluate frozen representations on three complementary benchmarks: Diving-48 (fine-grained motion), SomethingSomething V2 (temporal reasoning), and ImageNet-100 (appearance). Our experiments suggest that many auxiliary objectives exhibit capacity trade-offs: gains on one downstream capability often coincide with degradation on another. We then study FWM-HW-LD (Factorized World-Model with Hard-Region-Weighted Latent Dynamics), a training-time objective that separates the latent representation into appearance and dynamics subspaces and applies hard-region weighting to both JEPA prediction errors and latent dynamics errors. In our mixed-dataset setting, FWM-HW-LD improves ImageNet-100 by +5.92 and SSv2 by +3.21 percentage points relative to the reference baseline, while remaining within 0.30 percentage points on Diving-48. These results indicate that latent factorization is a useful direction for studying auxiliary-objective trade-offs in Video-JEPA.

Santosh Premi

Disentangled Representation Learning Latent Dynamics Modeling Joint-Embedding Predictive Architecture Video Action Recognition Video Representation Learning

May 15, 2026cs.LG

Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure

Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and physics-aware modeling are inherently coupled. We study this problem for latent port-Hamiltonian systems, a structured class encompassing both conservative and dissipative dynamics. We propose a two-stage identify-then-project framework. First, a contrastive teacher learns continuous-time latent dynamics from partial observations. Then, a student projects the identified teacher representation and dynamics onto a port-Hamiltonian submanifold via a learned affine chart, yielding a physically consistent realization. As a conceptual counterfactual, we also consider a single-stage variant that jointly learns latent identification and port-Hamiltonian structure, but find it to be less reliable, motivating the proposed two-stage teacher-student framework. We show theoretically that affine projection is the natural bridge between the affine gauge of contrastive latent identification and the port-Hamiltonian systems. Empirically, we demonstrate that the proposed two-stage approach preserves the teacher's dynamics while enforcing physical structure, and performs more reliably than the single-stage alternative, particularly in dissipative regimes and high-dimensional visual settings.

Peilun Li, Kaiyuan Tan, Daniel Moyer +1

Department of Computer Science Vanderbilt University Nashville, TN 37235

Contrastive Learning Latent Dynamics Modeling System Identification Physics-Informed ML State Representation Learning Port-Hamiltonian Systems+1

May 15, 2026cs.LG

Hypothesis-driven construction of mesoscopic dynamics

Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including global well-posedness, asymptotic stability, unique factorization identifiability, and discrete energy dissipation, applicable to all spatio-temporal evolution equations within this hypothesis class prior to all learning stages. Data from each problem instance is then used to guide the identification of members within our hypothesis class, giving rise to accurate, robust and interpretable dynamical models. We empirically validate this framework on both data from continuum PDE models as a check, and on data arising from microscopic chain models for which exact meso-scale models are unknown. The proposed approach not only acts as an effective dynamics learner, but also offers vital interpretable diagnostics of the underlying physics.

Zhuoyuan Li, Aiqing Zhu, Qianxiao Li

Institute for Functional Intelligent Materials, National University of Singapore · Department of Mathematics, National University of Singapore

Latent Dynamics Modeling Nonlinear System Identification Physics-Informed ML

May 15, 2026cs.LG

Ada-Diffuser: Latent-Aware Adaptive Diffusion for Decision-Making

Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are fundamental to environment transitions, reward structures, and high-level agent behavior. Explicitly modeling these hidden processes is essential for both precise dynamics modeling and effective decision-making. In this paper, we propose a unified framework that explicitly incorporates latent dynamic inference into generative decision-making from minimal yet sufficient observations. We theoretically show that under mild conditions, the latent process can be identified from small temporal blocks of observations. Building on this insight, we introduce Ada-Diffuser, a causal diffusion model that learns the temporal structure of observed interactions and the underlying latent dynamics simultaneously, and furthermore, leverages them for planning and control. With a modular design, Ada-Diffuser supports both planning and policy learning tasks, enabling adaptation to latent variations in dynamics, rewards, and latent actions. Experiments on simulated control and robotic benchmarks demonstrate its effectiveness in accurate latent inference and adaptive policy learning.

Fan Feng, Selena Ge, Minghao Fu +6

University of California San Diego · MBZUAI · Carnegie Mellon University +2

Latent Action Learning Latent Dynamics Modeling Diffusion-Based Planning Diffusion Policy Model-Based RL

May 15, 2026cs.LG

From Observed Viability to Internal Predictive Approximation: A Single-Subject Latent-Space Analysis of Gait Dynamics Under Occlusal Constraint

Understanding adaptive biomechanical systems requires distinguishing observable performance, static multivariate representation, longitudinal displacement, and internal approximation of observed change. This study introduces Level 5, which examines whether the M1-M2 transformation observed in a single-subject gait dataset can be approximated within a selected PCA representation. Gait was recorded with instrumented insoles in a participant with Parkinson's disease under six occlusal observational probes during two sessions eleven weeks apart. A simplified feed-forward neural network was trained to approximate M2 PC1-PC2 coordinates from M1 coordinates, occlusal-probe descriptors, and the longitudinal-transition indicator. In the core analysis aligned with Level 4, the model preserved the Euclidean centroid-displacement hierarchy dOC3 < dONL < dOC2.5. In the extended six-probe analysis, it preserved the broad structure of the exploratory ordering. Held-out M2 and leave-condition-out analyses provided internal tests beyond the full-dataset fit, while a within-session analysis described probe positions relative to ONL. The term predictive is used only in a restricted methodological sense. The model does not provide prospective clinical prediction, patient-level forecasting, or generalization to unseen individuals. Occlusal conditions are treated as observational probes applied during measurement, not as continuous causal drivers of longitudinal evolution. The findings are exploratory, retrospective, representation dependent, and non causal. They do not establish causal occlusal effects, validated viability thresholds, therapeutic superiority, distinct physiological states, or generalizable predictive validity.

Jacques Raynal, Pierre Slangen, Elsa Raynal +1

Laboratory of Bioengineering and Nanosciences (LBN), University of Montpellier, France · 2EuroMov Digital Health in Motion, University of Montpellier, IMT Mines Alès, Alès, France · 3Certified Sophrologist and Dental Assistant, Sensorimotor Practice, Montpellier, France +1

Latent Dynamics Modeling Gait Analysis Parkinson's Disease

May 14, 2026cs.LG

Toward World Modeling of Physiological Signals with Chaos-Theoretic Balancing and Latent Dynamics

Physiological time series signals reflect complex, multi-scale dynamical processes of the human body. Existing modeling studies focus on static tasks such as classification, event forecasting, or short-horizon next step prediction, while long-horizon signal-level forecasting and predictive nature of physiological signals remain underexplored. We introduce NormWear-2, a world model that encodes both multivariate physiological signals and clinical intervention variables into a shared latent space and models their joint temporal evolution as a dynamical system. Our approach combines inference from prior pre-trained knowledge (intuition) with instant non-parametric latent state transition adaptation (insight), enabling coherent forecasting across multiple temporal scales, conditioned on heterogeneous clinical interventions. During the pretraining phase, we find that chaos-theoretic balancing of dynamical regime diversity yields more robust representations, with a smaller balanced corpus outperforming one twice its size and capturing bifurcation regimes. We evaluate the world model performance across diverse real-world physiological datasets spanning heterogeneous temporal resolutions and intervention regimes, covering daily life, point-of-care, and clinical settings, including fitness planning, hemodialysis, diabetes management, and surgical monitoring. These evaluation datasets comprise records from 8,026 subjects, spanning study durations from 3.2 hours for high-resolution signal data to 2.3 years for longitudinal clinical biomarker tracking. NormWear-2 achieves the best overall forecasting performance across time, frequency, and latent representation domains, with significant improvements over state-of-the-art time series foundation models, while maintaining competitive downstream representation quality, providing a step toward general-purpose world models for physiological signals.

Yunfei Luo, Xi Chen, Yuliang Chen +8

University of California San Diego · Dartmouth College · Amazon Web Services +3

Multivariate Time Series Forecasting World Model Learning Latent Dynamics Modeling Time Series Forecasting

May 14, 2026cs.RO

Learning Cross-Coupled and Regime Dependent Dynamics for Aerial Manipulation

Accurate dynamics models are critical for aerial manipulators operating under complex tasks such as payload transport. However, modeling these systems remains fundamentally challenging due to strong quadrotor-manipulator coupling, delayed aerodynamic interactions, and regime-dependent dynamics variations arising from payload changes and manipulator reconfiguration. These effects produce residual dynamics that are simultaneously cross-coupled, history-dependent, and nonstationary, causing both analytical models and purely offline learned models to degrade during deployment. To address these challenges, we propose a structured encoder-decoder framework for adaptive residual dynamics learning in aerial manipulators. The proposed nonlinear latent encoder captures cross-variable coupling and temporal dependencies from state-input histories, while a lightweight linear latent decoder enables online adaptation under regime-dependent nonstationary dynamics. The linear-in-parameter decoder structure permits closed-form Bayesian adaptation together with consistency-driven covariance inflation, enabling rapid and stable adaptation to both transient and slowly varying dynamics changes while remaining compatible with real-time model predictive control (MPC). Experimental results on a real aerial manipulation platform demonstrate improved residual prediction accuracy, faster adaptation under changing operating conditions, and enhanced MPC-based trajectory tracking performance. These results highlight the importance of jointly modeling coupled temporal dynamics and deployment-time nonstationarity for reliable aerial manipulation.

Rishabh Dev Yadav, Samaksh Ujjawal, Sihao Sun +2

Department of Computer Science, The University of Manchaster, U.K. · Department of Cognitive Robotics, Delft University of Technology, Netherlands · International Institute of Information Technology Hyderabad. +1

Aerial Robotics Online System Identification Latent Dynamics Modeling Residual Dynamics Learning Aerial Manipulation

May 14, 2026cs.LG

DRL-STAF: A Deep Reinforcement Learning Framework for State-Aware Forecasting of Complex Multivariate Hidden Markov Processes

Forecasting multivariate hidden Markov processes is challenging due to nonlinear and nonstationary observations, latent state transitions, and cross-sequence dependencies. While deep learning methods achieve strong predictive accuracy, they typically lack explicit state modeling, whereas Hidden Markov Models (HMMs) provide interpretable latent states but struggle with complex nonlinear emissions and scalability. To address these limitations, we propose DRL-STAF, a Deep Reinforcement Learning based STate-Aware Forecasting framework that jointly predicts next-step observations and estimates the corresponding hidden states for complex multivariate hidden Markov processes. Specifically, DRL-STAF models complex nonlinear emissions using deep neural networks and estimates discrete hidden states using reinforcement learning, reducing the reliance on predefined transition structures and enabling flexible adaptation to diverse temporal dynamics. In particular, DRL-STAF mitigates the state-space explosion encountered by typical multivariate HMM-based methods. Extensive experiments demonstrate that DRL-STAF outperforms HMM variants, standalone deep learning models, and existing DL-HMM hybrids in most cases, while also providing reliable hidden-state estimates.

Manrui Jiang, Jingru Huang, Yong Chen +1

Department of Industrial Engineering, Tsinghua University, Beijing 100084, China · Department of Industrial and Systems Engineering, University of Iowa, Iowa City, IA 52242, USA.

Multivariate Time Series Forecasting Reinforcement Learning Latent Dynamics Modeling Sequence Modeling Hidden Markov Models

May 14, 2026math.NA

Wavelet-Based Observables for Koopman Analysis: An Extended Dynamic Mode Decomposition Framework

We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm. We then construct closed-form expressions of the action of the Koopman semigroup and its resolvent in terms of these observables. To approximate the action of Koopman semigroup numerically, we combine Extended Dynamic Mode Decomposition (EDMD) with the proposed wavelet-based observables leading to the Wavelet Dynamic Mode Decomposition via Continuous Wavelet Transform (cWDMD) algorithm. We validate our theoretical results on two numerical examples.

Cankat Tilki, Serkan Gugercin

Department of Mathematics, Virginia Tech, Blacksburg, VA - 24061.

Dynamical Systems Koopman Operator Learning Latent Dynamics Modeling Wavelet Methods Dynamic Mode Decomposition

May 13, 2026cs.AI

Why We Need World Models for AGI: Where LLMs Fail and How World Models May Outperform

Large language models achieve strong performance in language generation and knowledge-intensive tasks, yet remain limited in settings requiring causal reasoning, persistent state tracking, and long-horizon planning. We argue that these limitations may arise from an objective-level mismatch between sequence prediction and reasoning over latent environment dynamics. To formalize this distinction, we introduce Latent Dynamics Inference (LDI), a conceptual perspective that interprets language and multimodal observations as partial evidence of underlying transition dynamics. To empirically investigate this perspective, we introduce Flux, a sequential reasoning environment specified entirely through natural-language rules. As a proof-of-concept case study, the rules are first compiled into an explicit state-transition simulator, illustrating that structured latent transition dynamics can, in some cases, be operationally extracted from textual rule descriptions. This enables a controlled comparison between the LLMs operating purely over textual observations and reinforcement-learning agents trained directly within the extracted latent state space. Within this case study, agents operating with explicit access to the latent state space exhibit substantially more stable behavior in long-horizon gameplay, achieving an aggregate win rate of approximately 79% versus 11% for LLMs. Qualitative analysis further reveals failure modes consistent with unstable persistent state tracking, including invalid actions, state-tracking errors, and short-horizon reasoning failures. The complete implementation of the Flux environment available at https://github.com/FeisalAlaswad/FLUX-RL-Agent Within the evaluated setting, these results suggest that strong sequence prediction alone may struggle to support robust long-horizon dynamic reasoning without mechanisms for persistent state tracking and transition modeling

Feisal Alaswad, Batoul Aljaddouh, Maher Alrahhal +2

Department of Computing Technologies SRM Institute of Science and Technology Kattankulathur 603203, Tamil Nadu, India · Bio-Sensing and Bio-Sensors Group Smart Automation and Communication Technologies Research Institute of Sciences and Engineering University of Sharjah, UAE · Department of Computer Engineering College of Computing and Informatics University of Sharjah, UAE

Latent Dynamics Modeling Long-Horizon Agent Evaluation Causal Reasoning in Language Models Causal Reasoning Latent World Models

May 12, 2026cs.RO

Support-Safe Variational Hybrid Filtering for Contact-Mode and Sparse-Law Recovery

Contact-rich robot dynamics are hybrid: a single observation can match several latent states and contact regimes (free, impact, stick--slip). A standard amortized filter that places no probability on a feasible contact transition will permanently lose the branch the robot actually follows. We introduce VHYDRO, a variational hybrid dynamics learner that prevents this branch loss. At each step, VHYDRO mixes the learned proposal with a feasible transition law before sampling and importance weighting, ensuring that every transition retained by the model-feasible carrier remains covered. VHYDRO jointly infers a continuous latent state and a discrete contact mode, and fits a sparse port-Hamiltonian law to each recovered regime. On top of this, three guarantees connect: support coverage stabilizes filtering, the stabilized filter concentrates the discrete contact posterior on coherent regimes, and mode-pure segments admit sparse port-Hamiltonian recovery. The recovery error separates cleanly into filtering, derivative, mode-impurity, and physics-residual parts. Three empirical findings track the same mechanism. Under heavy occlusion the support-safe filter stays usable while a non-defensive proposal collapses. On ManiSkill demonstrations and on four Sawyer/BridgeData task families the discrete state forms temporally coherent contact-regime segments that the discrete state yields a stronger joint profile across ARI, change-point F1, and segment purity than post-hoc and mode-free baselines. On hybrid systems with known equations the mode-conditioned sparse fit recovers the active physical terms; purely predictive baselines do not.

Marios Papamichalis, Regina Ruane

Human Nature Lab, Yale University, New Haven, CT 06511 · Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, 3733 Spruce Street, Philadelphia, PA 19104-6340

Latent Dynamics Modeling System Identification Robot State Estimation

May 11, 2026cs.LG

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators

Long-horizon forecasting of time-dependent partial differential equations (PDEs) is critical for characterizing the sustained evolution of physical systems. While neural operators have emerged as efficient surrogates, they typically learn implicit finite-time transitions from discrete observations. When deployed autoregressively, such propagators often suffer from rapid error accumulation and dynamic drift. To address this, we propose a neural forecasting framework that reformulates PDE rollout as learning a Structured Spectral Propagator (SSP) in a propagation-oriented latent space. Following an analysis-propagation-synthesis design, our framework: (i) maps physical states into a shared, time-consistent spatial representation; (ii) projects this space into a compact propagation state to isolate recurrent dynamics from fine-grained spatial details, thereby decoupling reconstruction fidelity from rollout regularity; and (iii) evolves retained spectral modes using a frequency-conditioned linear backbone complemented by a nonlinear spectral closure to account for truncated interactions. This explicit structuring endows the propagator with a strong inductive bias for coherent modal evolution. Extensive experiments demonstrate that SSP significantly outperforms state-of-the-art baselines, reducing relative

L_2

errors by up to 48.9% and exhibiting improved stability in temporal extrapolation beyond the supervised horizon.

Xiaoxiao Lu, Ye Yuan, Jiahao Shi

School of AIA, Huazhong University of Science and Technology

Latent Dynamics Modeling PDE Surrogate Modeling PDE Operator Learning Spatiotemporal Forecasting Spectral Methods

May 9, 2026cs.LG

Event Fields: Learning Latent Event Structure for Waveform Foundation Models

We propose a new class of waveform foundation models that departs from conventional sequence based representations by modeling physiological time series as realizations of latent event processes. Rather than treating signals as collections of local tokens or patches, our approach assumes that clinically meaningful structure arises from temporally extended, interacting events whose boundaries and dynamics are not directly observed. To capture this structure, we introduce a self supervised learning framework that enforces consistency across stochastic segmentations and time frequency projections of the same waveform, encouraging representations that are invariant to signal level perturbations while preserving event level organization. The resulting model combines a segmentation aware encoder with a latent interaction operator that captures dependencies among inferred events, and naturally extends to multimodal settings by aligning modalities through shared event representations. Across a range of physiological benchmarks, including arrhythmia classification, hemodynamic prediction, and waveform retrieval, the proposed method improves performance, robustness, and label efficiency relative to strong sequence based baselines. These results suggest that shifting from signal centric to event centric representations provides a more appropriate inductive bias for modeling physiological dynamics and offers a complementary path to scaling foundation models in healthcare.

Li Na, Yuanyun Zhang, Shi Li

University of Science and Technology of China · Columbia University

Irregular Time-Series Modeling Latent Dynamics Modeling Self-Supervised Time Series Representation Learning Time-Series Foundation Models

May 9, 2026cs.LG

FLUX: Geometry-Aware Longitudinal Flow Matching with Mixture of Experts

Many biological systems evolve through continuous local dynamics while switching between latent regimes defined by learning, stimulus context, internal state, or developmental stage. These processes are often observed only as unpaired longitudinal snapshots: the same cells, neurons, or animals are not tracked as matched trajectories, even though population states are sampled across successive stages. This creates two coupled challenges. First, trajectories must respect curved low-dimensional manifolds embedded in high-dimensional biological measurements. Second, the model must identify when the transport mechanism itself changes. We introduce FLUX (FLow matching for Unpaired longitudinal data with miXture-of-experts), a geometry-aware longitudinal flow-matching framework for joint transport modeling and unsupervised regime discovery. FLUX learns a data-dependent metric from pooled labeled and unlabeled observations, uses that metric to construct geometry-aware conditional paths between adjacent marginals, and decomposes the resulting velocity field into sparse expert vector fields selected by a Straight-Through Gumbel-Softmax router. Across manifold controls, a regime-switching Lorenz system, widefield cortical calcium imaging during associative learning, and embryoid body single-cell differentiation, FLUX reconstructs longitudinal transport while recovering interpretable regime structure. Ablations show that mixture-of-experts routing alone is insufficient: FLUX without geometric learning can fit local transport but fails or weakens regime discovery when regimes are encoded in local dynamics. These results suggest that geometry-aware velocity decomposition provides a general strategy for discovering latent biological state transitions from unpaired longitudinal snapshots.

Josue Ortega Caro, Yongxu Zhang, Hannah M Batchelor +3

Yale University

Dynamical Systems Flow Matching Latent Dynamics Modeling Mixture of Experts Regime-Switching Dynamical Systems

May 7, 2026stat.ML

End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems

Learning identifiable representations in deep generative models remains a fundamental challenge, particularly for sequential data with regime-switching dynamics. Existing approaches establish identifiability under restrictive assumptions, such as stationarity or limited emission models, and typically rely on variational autoencoder (VAE) estimators, which introduce approximation gaps that limit the recovery of the latent structure. In this work, we address both the theoretical and practical limitations of this setting. First, we establish identifiability of a broad class of recurrent nonlinear switching dynamical systems under flexible assumptions, significantly extending prior results. Second, we introduce

Ω

SDS, a flow-based estimator that enables exact likelihood optimization using expectation-maximisation. Through empirical validation on both synthetic and real-world data, our results demonstrate that

Ω

SDS achieves improved disentanglement compared to VAE-based estimators and more accurate forecasting of underlying dynamics.

Carles Balsells-Rodas, Zhengrui Xiang, Xavier Sumba +1

Imperial College London

Dynamical Systems Latent Variable Models Latent Dynamics Modeling Regime-Switching Dynamical Systems Nonlinear System Identification

May 7, 2026cs.LG

Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations

In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert principle, which governs the motion of dynamical systems, is preserved by construction in the absence of external forces. This allows learning physically consistent models that overcome erroneous drift in the system's energy, thereby providing stable long-term predictions. At the core of our approach lie linear operators for Gaussian process conditioning, constructed from discrete forced Euler-Lagrange equations and variational discretization schemes. Thereby and unlike prior work, the method enables learning dynamics from discrete position snapshots, i.e., without access to a system's velocities or momenta. This is particularly relevant for a large class of practical scenarios where only position measurements are available, for instance, in motion capture or visual servoing applications. We demonstrate the data-efficiency and generalization capabilities of the LGPs in various synthetic and real-world case studies, including a real-world soft robot with hysteresis. The experimental results underscore that the LGPs learn physically consistent dynamics with uncertainty quantification solely from sparse positional data and enable stable long-term predictions.

Jan-Hendrik Ewering, Kathrin Flaßkamp, Niklas Wahlström +2

Leibniz Universität Hannover · Saarland University · Uppsala University

Latent Dynamics Modeling Physics-Informed ML Gaussian Process Regression Data-Efficient Learning

May 7, 2026cs.AI

HaM-World: Soft-Hamiltonian World Models with Selective Memory for Planning

World models enable model-based planning through learned latent dynamics, but imagined rollouts become unstable as the planning horizon grows or the dynamics distribution shifts. We argue that this instability reflects two missing structures in planner-facing latents: history-conditioned memory for approximate Markov completeness, and geometric organization that separates configuration, momentum, and task semantics. We propose HaM-World (HMW), a structured world model that decomposes the latent state into a canonical (q, p) subspace and a context subspace c, while using Mamba selective state-space memory as the history-conditioned input to the same latent dynamics. Within this interface, (q, p) evolves through an energy-derived Hamiltonian vector field plus learnable residual/control dynamics, while c captures semantic, dissipative, and non-conservative factors. This gives the planner a single latent state shared by dynamics prediction, reward/value estimation, imagined rollouts, and CEM action search. On four DeepMind Control Suite tasks, HaM-World reaches the highest Avg. AUC (117.9, +9.5%), reduces long-horizon rollout error to 45% of a strong baseline model, and wins 11/12 k in {3,5,7} MSE cells. Under 12 OOD perturbations spanning dynamics shifts, action delay, and observation masking, HaM-World achieves the highest return in every condition, with average OOD-return gains of 10.2% on Finger Spin and 13.6% on Reacher Easy. Mechanism diagnostics further show bounded action-free Hamiltonian-energy drift, structured energy variation under policy rollouts, and coherent control-induced energy transfer, supporting the intended Soft-Hamiltonian dynamics design.

Haoyun Tang, Haodong Cui, Keyao Xu +2

1Xi’an Jiaotong University · 2Huazhong University of Science and Technology · 3Nankai University +1

World Model Learning Latent Dynamics Modeling World Model-Based Planning Hamiltonian Neural Networks Model-Based Planning Hamiltonian Dynamics

May 4, 2026stat.ML

Online Generalised Predictive Coding

This paper introduces an extension of generalised filtering for online applications. Generalised filtering refers to data assimilation schemes that jointly infer latent states, learn unknown model parameters, and estimate uncertainty in an integrated framework -- e.g., estimate state and observation noise -- at the same time (i.e., triple estimation). This framework appears across disciplines under different names, including variational Kalman-Bucy filtering in engineering, generalised predictive coding in neuroscience, and Dynamic Expectation Maximisation (DEM) in time-series analysis. Here, we specialise DEM for ``online'' data assimilation, through a separation of temporal scales. We describe the variational principles and procedures that allow one to assimilate data in a way that allows for a slow updating of parameters and precisions, which contextualise fast Bayesian belief updating about the dynamic hidden states. Using numerical studies, we demonstrate the validity of online DEM (ODEM) using a non-linear -- and potentially chaotic -- generative model, to show that the ODEM scheme can track the latent states of the generative process, even when its functional form differs fundamentally from the dynamics of the generative model. Framed from a neuro-mimetic predictive coding perspective, ODEM offers a biologically inspired solution to online inference, learning, and uncertainty estimation in dynamic environments.

Mehran H. Z. Bazargani, Szymon Urbas, Adeel Razi +2

Insight Research Ireland Centre, UCD, Dublin, Ireland. · UCD School of Mathematics and Statistics, UCD, Belfield, Dublin, Ireland. · Turner Institute for Brain and Mental Health, School of Psychological Sciences, Monash University, Melbourne, Victoria, Australia. +5

Parameter Estimation Latent Dynamics Modeling Predictive Coding Data Assimilation Expectation-Maximization

May 4, 2026cs.LG

Closed-Loop CO2 Storage Control With History-Based Reinforcement Learning and Latent Model-Based Adaptation

Closed-loop management of geological CO2 storage requires control policies that adapt to uncertain reservoir behavior while relying on observations that are realistically available during operation. This work formulates CO2 injection and brine-production control as a partially observable sequential decision problem and studies deployable deep reinforcement-learning controllers trained with high-fidelity reservoir simulation. We first compare privileged-state, well-only, history-conditioned, masking-curriculum, and asymmetric teacher-student model-free policies in order to quantify the value of temporal well-response information and training-time privileged simulator states. We then evaluate a latent model-based adaptation pipeline that reuses nominal latent dynamics and retunes controllers under known injector failure, leakage-induced dynamics and reward shift, and compartmentalized reservoir connectivity. The results show that history-conditioned policies recover nearly all of the privileged-state performance while using only deployable well-level information, and that latent model-based retuning outperforms direct model-free retuning under the same scenario-specific real-simulator budget in the abnormal operating cases. The proposed framework therefore provides a simulator-budget-aware alternative to repeated online history matching and re-optimization for closed-loop CO2 storage control.

Sofianos Panagiotis Fotias, Vassilis Gaganis

School of Mining and Metallurgical Engineering, National Technical University of Athens, Athens 157 73, Greece · Institute of Geoenergy, Foundation for Research and Technology, Chania, 73100, Greece

RL Control Latent Dynamics Modeling Partially Observable RL Model-Based RL

May 1, 2026q-bio.QM

A Universal Space of Brain Dynamics for Unveiling Cognitive Transitions and Individual Differences

Representing dynamical systems through data-driven universal spaces has proven effective; however, achieving this universality for human brain activity remains a significant challenge, further aggravated by diverse cognitive states and individual subjects. Recognizing that spatial properties reflect physical wiring while temporal properties reflect brain function, we develop Universal Brain Dynamics (UBD) to construct a universal space tailored to brain activity and quantify corresponding dynamics using a model-derived Jacobian matrix. Crucially, we validate UBD's universality by accurately predicting functional magnetic resonance imaging (fMRI) signals (Pearson's r > 0.9) across eight states and 963 subjects in the Human Connectome Project (HCP). Through evaluating resting-state fMRI represented within UBD, we gain insight into how infra-slow fluctuation (ISF) underpins brain activity. Furthermore, we reveal a new perspective on structure-function coupling (SFC) by analyzing the temporal sequence of brain dynamics. Extending UBD to task-evoked states, we derive brain dynamics across various cognitive conditions, elucidating the neural mechanisms driving cognitive transitions at a finer granularity. For individual differences, we compare brain dynamics across subjects to identify the neural underpinnings of these variations. Our findings suggest that synergistically integrating spatial and temporal properties of brain activity establishes a universal space for its unfolding, enabling the precise numerical analysis of underlying neural mechanisms across varying conditions.

Ronghua Zheng, Chengyuan Qian, Weiyang Ding

Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, China. · Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, China.

Latent Dynamics Modeling

May 1, 2026cs.AI

Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling

World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning. However, current world model research is often dominated by three partially separated routes: 2D video-generative models that emphasize visual future synthesis, 3D scene-centric models that emphasize spatial reconstruction, and JEPA-like latent models that emphasize abstract predictive representations. While each route has made important progress, they still struggle to provide physically reliable, action-controllable, and long-horizon stable predictions for embodied decision making. In this paper, we argue that the bottleneck of world models is no longer only whether they can generate realistic futures, but whether those futures are physically meaningful and useful for action. We propose \emph{Hamiltonian World Models} as a physically grounded perspective on world modeling. The key idea is to encode observations into a structured latent phase space, evolve the latent state through Hamiltonian-inspired dynamics with control, dissipation, and residual terms, decode the predicted trajectory into future observations, and use the resulting rollouts for planning. We discuss how Hamiltonian structure may improve interpretability, data efficiency, and long-horizon stability, while also noting practical challenges in real-world robotic scenes involving friction, contact, non-conservative forces, and deformable objects.

Sen Cui, Jingheng Ma

Tsinghua University

Latent Dynamics Modeling World Models World Model-Based Planning Model-Based Planning Hamiltonian Dynamics Embodied World Models

Apr 30, 2026cs.RO

RopeDreamer: A Kinematic Recurrent State Space Model for Dynamics of Flexible Deformable Linear Objects

The robotic manipulation of Deformable Linear Objects (DLOs) is a fundamental challenge due to the high-dimensional, non-linear dynamics of flexible structures and the complexity of maintaining topological integrity during contact-rich tasks. While recent data-driven methods have utilized Recurrent and Graph Neural Networks for dynamics modeling, they often struggle with self-intersections and non-physical deformations, such as tangling and link stretching. In this paper, we propose a latent dynamics framework that combines a Recurrent State Space Model with a Quaternionic Kinematic Chain representation to enable robust, long-term forecasting of DLO states. By encoding the DLO as a sequence of relative rotations (quaternions) rather than independent Cartesian positions, we inherently constrain the model to a physically valid manifold that preserves link-length constancy. Furthermore, we introduce a dual-decoder architecture that decouples state reconstruction from future-state prediction, forcing the latent space to capture the underlying physics of deformation. We evaluate our approach on a large-scale simulated dataset of complex pick-and-place trajectories involving self-intersections. Our results demonstrate that the proposed model achieves a 40.52% reduction in open-loop prediction error over 50-step horizons compared to the state-of-the-art baseline, while reducing inference time by 31.17%. Our model further maintains superior topological consistency in scenarios with multiple crossings, proving its efficacy as a compositional primitive for long-horizon manipulation planning.

Tim Missal, Lucas Domingues, Berk Guler +3

Technical University of Darmstadt · School of Electrical and Computer Engineering, Universidade Estadual de Campinas (UNICAMP), Brazil · Instituto de Pesquisas Eldorado, Brazil +5

Latent Dynamics Modeling Robotic Manipulation State Space Models

Apr 28, 2026cs.LG

Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Space Models

Model-Based Reinforcement Learning distinguishes between physical dynamics models operating on proprioceptive inputs and latent dynamics models operating on high-dimensional image observations. A prominent latent approach is the Recurrent State Space Model used in the Dreamer family. While epistemic uncertainty quantification to inform exploration and mitigate model exploitation is well established for physical dynamics models, its transfer to latent dynamics models has received limited scrutiny. We empirically demonstrate that latent transitions are biased toward well-represented regions of latent space, exhibiting an attractor behavior that can deviate from true environment dynamics. As a result, discrepancies in environment dynamics may not manifest in latent space, undermining the reliability of epistemic uncertainty estimates. Because these attractors often lie in high-reward regions, latent rollouts systematically overestimate predicted rewards. Our findings highlight key limitations of epistemic uncertainty estimation in latent dynamics models and motivate more critical evaluation of this method.

Julia Berger, Bernd Frauenknecht, Sebastian Trimpe +1

1RWTH Aachen University

Uncertainty Quantification Latent Dynamics Modeling Latent World Models Model-Based RL Epistemic Uncertainty

Apr 26, 2026q-bio.NC

Integrative neurocybernetic modeling in the era of large-scale neuroscience

Large-scale neuroscience is generating rich datasets across animals, brain areas and behavioral contexts, yet our modeling efforts remains fragmented across isolated experiments. We argue that understanding behavior requires integrative neurocybernetic models: understandable dynamical models that capture the closed-loop coupling of brain, body and environment, treat the brain as a controller pursuing latent objectives, represent structured variation across scales, and scale to heterogeneous datasets. Such models shift the goal from predicting neural recordings in isolation to inferring the organizing principles that govern neural and behavioral dynamics. We outline a practical route toward this goal by combining nonlinear state-space models and meta-dynamical extensions with scalable inference, knowledge distillation, mixed open- and closed-loop training, and connectomics-informed architectures. By pooling complementary constraints from recordings, behavior, perturbations and anatomy, integrative neurocybernetic models can provide statistical amplification, few-shot generalization, and mechanistic insight into shared dynamical structure, individual variation, and the control objectives that govern behavior. This agenda offers a model-centric path from fragmented data to a mechanistic science of how brains produce behavior.

Il Memming Park, Ayesha Vermani, Gonzalo G. de Polavieja +11

Champalimaud Centre for the Unknown, Champalimaud Foundation, Lisbon, Portugal · Harvard University, Cambridge, MA, USA · Yale University, New Haven, CT, USA +3

Computational Cognitive Modeling Latent Dynamics Modeling

Apr 24, 2026cs.LG

Beyond Patient Invariance: Learning Cardiac Dynamics via Action-Conditioned JEPAs

Self-supervised learning in healthcare has largely relied on invariance-based objectives, which maximize similarity between different views of the same patient. While effective for static anatomy, this paradigm is fundamentally misaligned with clinical diagnosis, as it mathematically compels the model to suppress the transient pathological changes it is intended to detect. We propose a shift towards Action-Conditioned World Models that learn to simulate the dynamics of disease progression, or Event-Conditioned. Adapting the LeJEPA framework to physiological time-series, we define pathology not as a static label, but as a transition vector acting on a patient's latent state. By predicting the future electrophysiological state of the heart given a disease onset, our model explicitly disentangles stable anatomical features from dynamic pathological forces. Evaluated on the MIMIC-IV-ECG dataset, our approach outperforms fully supervised baselines on the critical triage task. Crucially, we demonstrate superior sample efficiency: in low-resource regimes, our world model outperforms supervised learning by over 0.05 AUROC. These results suggest that modeling biological dynamics provides a dense supervision signal that is far more robust than static classification. Source code is available at https://github.com/cljosegfer/lesaude-dynamics

Jose Geraldo Fernandes, Luiz Facury, Pedro Robles Dutenhefner +1

Department of Computer Science Universidade Federal de Minas Gerais Belo Horizonte, Brazil

Latent Dynamics Modeling Healthcare Electrocardiography Self-Supervised Time Series Representation Learning World Models Action-Conditioned World Models+2

Apr 22, 2026cs.LG

Early Detection of Latent Microstructure Regimes in Limit Order Books

Limit order books can transition rapidly from stable to stressed conditions, yet standard early-warning signals such as order flow imbalance and short-term volatility are inherently reactive. We formalise this limitation via a three-regime causal data-generating process (stable

\to

latent build-up

\to

stress) in which a latent deterioration phase creates a prediction window prior to observable stress. Under mild assumptions on temporal drift and regime persistence, we establish identifiability of the latent build-up regime and derive guarantees for strictly positive expected lead-time and non-trivial probability of early detection. We propose a trigger-based detector combining MAX aggregation of complementary signal channels, a rising-edge condition, and adaptive thresholding. Across 200 simulations, the method achieves mean lead-time

+18.6 \pm 3.2

timesteps with perfect precision and moderate coverage, outperforming classical change-point and microstructure baselines. A preliminary application to one week of BTC/USDT order book data shows consistent positive lead-times while baselines remain reactive. Results degrade in low signal-to-noise and short build-up regimes, consistent with theory.

Prakul Sunil Hiremath, Vruksha Arun Hiremath

Department of Computer Science and Engineering Visvesvaraya Technological University, Belagavi · Department of Business Administration K.L.E. Society’s College of Business Administration

Quantitative Finance Latent Dynamics Modeling Change-Point Detection Algorithmic Trading

Apr 20, 2026cs.LG

AC-SINDy: Compositional Sparse Identification of Nonlinear Dynamics

We present AC-SINDy, a compositional extension of the Sparse Identification of Nonlinear Dynamics (SINDy) framework that replaces explicit feature libraries with a structured representation based on arithmetic circuits. Rather than enumerating candidate basis functions, the proposed approach constructs nonlinear features through compositions of linear functions and multiplicative interactions, yielding a compact and scalable parameterization and enabling sparsity to be enforced directly over the computational graph. We also introduce a formulation that separates state estimation from dynamics identification by combining latent state inference with shared dynamics and multi-step supervision, improving robustness to noise while preserving interpretability. Experiments on nonlinear and chaotic systems demonstrate that the method recovers accurate and interpretable governing equations while scaling more favorably than standard SINDy.

Peter Racioppo

Independent Researcher Los Angeles, CA 90731

Latent Dynamics Modeling Sparse Identification of Nonlinear Dynamics Nonlinear System Identification Symbolic Regression

Apr 20, 2026cs.RO

HALO: Hybrid Auto-encoded Locomotion with Learned Latent Dynamics, Poincaré Maps, and Regions of Attraction

Reduced-order models are powerful for analyzing and controlling high-dimensional dynamical systems. Yet constructing these models for complex hybrid systems such as legged robots remains challenging. Classical approaches rely on hand-designed template models (e.g., LIP, SLIP), which, though insightful, only approximate the underlying dynamics. In contrast, data-driven methods can extract more accurate low-dimensional representations, but it remains unclear when stability and safety properties observed in the latent space meaningfully transfer back to the full-order system. To bridge this gap, we introduce HALO (Hybrid Auto-encoded Locomotion), a framework for learning latent reduced-order models of periodic hybrid dynamics directly from trajectory data. HALO employs an autoencoder to identify a low-dimensional latent state together with a learned latent Poincaré map that captures step-to-step locomotion dynamics. This enables Lyapunov analysis and the construction of an associated region of attraction in the latent space, both of which can be lifted back to the full-order state space through the decoder. Experiments on a simulated hopping robot and full-body humanoid locomotion demonstrate that HALO yields low-dimensional models that retain meaningful stability structure and predict full-order region-of-attraction boundaries.

Blake Werner, Sergio A. Esteban, Massimiliano De Sa +2

Caltech, Pasadena, CA, USA · NC State University, Raleigh, NC, USA

Dynamical Systems Humanoid Robot Locomotion Latent Dynamics Modeling Reduced-Order Modeling

Apr 17, 2026cs.LG

Geometric regularization of autoencoders via observed stochastic dynamics

Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a long-standing problem: local-chart methods like ATLAS suffer from exponential landmark scaling and per-step reprojection, while autoencoder alternatives leave tangent-bundle geometry poorly constrained, and the errors propagate into the learned drift and diffusion. We observe that the ambient covariance~

Λ

already encodes coordinate-invariant tangent-space information, its range spanning the tangent bundle. Using this, we construct a tangent-bundle penalty and an inverse-consistency penalty for a three-stage pipeline (chart learning, latent drift, latent diffusion) that learns a single nonlinear chart and the latent SDE. The penalties induce a function-space metric, the

ρ

-metric, strictly weaker than the Sobolev

H^1

norm yet achieving the same chart-quality generalization rate up to logarithmic factors. For the drift, we derive an encoder-pullback target via Itô's formula on the learned encoder and prove a bias decomposition showing the standard decoder-side formula carries systematic error for any imperfect chart. Under a

W^{2,\infty}

chart-convergence assumption, chart-level error propagates controllably to weak convergence of the ambient dynamics and to convergence of radial mean first-passage times. Experiments on four surfaces embedded in up to

201

ambient dimensions reduce radial MFPT error by

50

--

70\%

under rotation dynamics and achieve the lowest inter-well MFPT error on most surface--transition pairs under metastable Müller--Brown Langevin dynamics, while reducing end-to-end ambient coefficient errors by up to an order of magnitude relative to an unregularized autoencoder.

Sean Hill, Felix X. -F. Ye

Department of Mathematics and Statistics, University at Albany, SUNY

Latent Dynamics Modeling Autoencoders Manifold Learning

Mar 13, 2026cs.LG

Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs

Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable. The problem becomes even more severe when the model must also predict beyond the training time range. Existing methods usually cannot handle parameter generalization and temporal extrapolation at the same time. Standard parameterized models treat time as just another input and therefore fail to capture intrinsic dynamics, while recent continuous-time latent methods often rely on expensive test-time auto-decoding for each instance, which is inefficient and can disrupt continuity across the parameterized solution space. To address this, we propose Disentangled Latent Dynamics Manifold Fusion (DLDMF), a physics-informed framework that explicitly separates space, time, and parameters. Instead of unstable auto-decoding, DLDMF maps PDE parameters directly to a continuous latent embedding through a feed-forward network. This embedding initializes and conditions a latent state whose evolution is governed by a parameter-conditioned Neural ODE. We further introduce a dynamic manifold fusion mechanism that uses a shared decoder to combine spatial coordinates, parameter embeddings, and time-evolving latent states to reconstruct the corresponding spatiotemporal solution. By modeling prediction as latent dynamic evolution rather than static coordinate fitting, DLDMF reduces interference between parameter variation and temporal evolution while preserving a smooth and coherent solution manifold. As a result, it performs well on unseen parameter settings and in long-term temporal extrapolation. Experiments on several benchmark problems show that DLDMF consistently outperforms state-of-the-art baselines in accuracy, parameter generalization, and extrapolation robustness.

Zhangyong Liang, Huanhuan Gao

National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, PR China · School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China

Latent Dynamics Modeling PDE Solving PDE Surrogate Modeling Physics-Informed ML

Mar 12, 2026cs.AI

Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reformulated as a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.

David Baumgartner, Eliezer de Souza da Silva, Iñigo Urteaga

Department of Computer Science, Norwegian University of Science and Technology, Norway · BCAM — Basque Center for Applied Mathematics, Spain · Department of Informatics Engineering, University of Coimbra, Portugal +2

Normalizing Flows Latent Dynamics Modeling Time-Series Anomaly Detection

Mar 12, 2026cs.RO

Learn Structure, Adapt on the Fly: Multi-Scale Residual Learning and Online Adaptation for Aerial Manipulators

Autonomous Aerial Manipulators (AAMs) are inherently coupled, nonlinear systems that exhibit nonstationary and multiscale residual dynamics, particularly during manipulator reconfiguration and abrupt payload variations. Conventional analytical dynamic models rely on fixed parametric structures, while static data-driven model assume stationary dynamics and degrade under configuration changes and payload variations. Moreover, existing learning architectures do not explicitly factorize cross-variable coupling and multi-scale temporal effects, conflating instantaneous inertial dynamics with long-horizon regime evolution. We propose a predictive-adaptive framework for real-time residual modeling and compensation in AAMs. The core of this framework is the Factorized Dynamics Transformer (FDT), which treats physical variables as independent tokens. This design enables explicit cross-variable attention while structurally separating short-horizon inertial dependencies from long-horizon aerodynamic effects. To address deployment-time distribution shifts, a Latent Residual Adapter (LRA) performs rapid linear adaptation in the latent space via Recursive Least Squares, preserving the offline nonlinear representation without prohibitive computational overhead. The adapted residual forecast is directly integrated into a residual-compensated adaptive controller. Real-world experiments on an aerial manipulator subjected to unseen payloads demonstrate higher prediction fidelity, accelerated disturbance attenuation, and superior closed-loop tracking precision compared to state-of-the-art learning baselines, all while maintaining strict real-time feasibility.

Samaksh Ujjawal, Naveen Sudheer Nair, Shivansh Pratap Singh +3

1Robotics Research Center, IIIT Hyderabad, India. · Department of Computer Science, University of Manchester, UK. · 3Newcastle University, UK.

Aerial Robotics Test-Time Adaptation Latent Dynamics Modeling Residual Learning Adaptive Control Multiscale Time-Series Modeling

Feb 27, 2026cs.CV

Accelerating Masked Image Generation by Learning Controlled Latent Dynamics

Masked Image Generation Models (MIGMs) have achieved great success, yet their efficiency is hampered by the multiple steps of bi-directional attention. In fact, there exists notable redundancy in their computation: when sampling discrete tokens, the rich semantics contained in the continuous features are lost. Some existing works attempt to cache the features to approximate future features. However, they exhibit considerable approximation error under aggressive acceleration settings. We attribute this to their limited expressivity and the failure to account for sampling information. To fill this gap, we propose learning a lightweight model that incorporates both previous features and sampled tokens, and regresses the average velocity field of feature evolution. The model has moderate complexity that suffices to capture the subtle dynamics while keeping lightweight compared to the original base model. We apply our method to two representative MIGMs and tasks. In particular, on the state-of-the-art Lumina-DiMOO, it achieves over 4x acceleration of text-to-image generation while maintaining quality, significantly pushing the Pareto frontier of masked image generation. The code and model weights are available at https://github.com/Kaiwen-Zhu/MIGM-Shortcut.

Kaiwen Zhu, Quansheng Zeng, Yuandong Pu +9

Shanghai Jiao Tong University Shanghai, China · Shanghai AI Laboratory Shanghai, China · Shanghai Innovation Institute Shanghai, China +6

Latent Dynamics Modeling T2I Generation Masked Image Modeling

Feb 4, 2026cs.CL

Textual Planning with Explicit Latent Transitions

Planning requires a transition model that predicts how each action changes the current state. When a large language model (LLM) plays this role, every next state is generated token by token, which makes searching over many possible futures slow and expensive. Existing alternatives either still query an LLM at every step or require a symbolic model of the domain. We propose EmbedPlan, a transition model built on frozen text embeddings: it embeds natural language descriptions of the state and the action with a frozen LLM, predicts the embedding of the next state with a lightweight learned network, and returns the closest real state. Because this network can be trained on top of any encoder, EmbedPlan also provides a controlled way to compare text representations for learning transitions. We evaluate it on 9 classical planning domains, under six settings that hold out progressively more of the data, from transitions to entire domains, and against baselines ranging from predicting no change to learning symbolic action rules. On planning problems seen during training, EmbedPlan almost always ranks the true next state among its top five guesses, still does so for most queries even when every observed state is a candidate, and retains 92-99% of its single-step accuracy when predicting several steps ahead from its own outputs. Given the same candidate states as GPT-5.4, it picks the true next state more often while taking about 0.17 ms per transition with cached embeddings. Accuracy is lower on unseen problems and near chance on unseen domains, and the controlled comparison traces this limit to the state representation rather than to the learned transition.

Eliezer Shlomi, Ido Levy, Eilam Shapira +6

Technion – Israel Institute of Technology, Haifa, Israel · IBM, Haifa, Israel.

Latent Dynamics Modeling LLM Planning Model-Based Planning

Dec 12, 2025cond-mat.stat-mech

Emergence of Nonequilibrium Latent Cycles in Unsupervised Generative Modeling

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two independently parametrized transition matrices, defining a Markov chain whose steady state is intrinsically out of equilibrium. Likelihood maximization drives this system toward nonequilibrium steady states with finite entropy production, reduced self-transition probabilities, and persistent probability currents in the latent space. These cycles are not imposed by the architecture but arise from training, and models that develop them reproduce the empirical distribution of data classes more faithfully, with a clear correlation between agreement with the data and entropy production. Compared with equilibrium approaches such as restricted Boltzmann machines, our model breaks the detailed balance between the forward and backward conditional transitions and relies on a log-likelihood gradient that depends explicitly on the last two steps of the Markov chain. Hence, this exploration of the interface between nonequilibrium statistical physics and modern machine learning suggests that introducing irreversibility into latent-variable models can improve the fidelity of the generated data distribution.

Marco Baiesi, Alberto Rosso

Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy · INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy · LPTMS, CNRS, Universit´e Paris-Saclay, 91405, Orsay, France

Latent Variable Models Latent Dynamics Modeling Markov Models Generative Modeling

Aug 23, 2025stat.ML

Neural Stochastic Differential Equations on Compact State Spaces: Theory, Methods, and Application to Suicide Risk Modeling

Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for EMA data, as it is irregularly sampled, noisy, and partially observed. But SDE-based models suffer from two key limitations. (a) These models often violate domain constraints, undermining scientific validity and clinical trust of the model. (b) Training is numerically unstable without ad hoc fixes (e.g. oversimplified dynamics) that are ill-suited for high-stakes applications. Here, we develop a novel class of expressive SDEs whose solutions are provably confined to a prescribed compact polyhedral state space, matching the domains of EMA data. In this work, (1) we show why chain-rule based constructions of SDEs on compact domains fail, theoretically and empirically; (2) we derive constraints on drift and diffusion for general and stationary SDEs so their solutions remain in the desired state space; and (3), we introduce a parameterization that maps arbitrary (neural or expert-given) dynamics into constraint-satisfying SDEs. On several real EMA datasets, including a large suicide-risk study, our parameterization improves forecasts and optimization dynamics over standard latent neural SDE baselines. These contributions pave the way for principled, trustworthy continuous-time models of suicide risk and other clinical time series and extend applications of SDE-based methods (e.g. diffusion models) to domains with hard state constraints.

Malinda Lu, Yue-Jane Liu, Matthew K. Nock +1

Wellesley College · Harvard University

Stochastic Differential Equations Latent Dynamics Modeling Mental Health Suicide Risk Modeling Clinical Risk Prediction

Feb 7, 2025cs.LG

Stochastic Optimal Control for Continuous-Time fMRI Representation Learning

Learning robust representations from functional magnetic resonance imaging (fMRI) is fundamentally challenged by the temporal irregularity and noise inherent in data from heterogeneous sources. Existing self-supervised learning (SSL) methods often discard critical temporal information by discretizing or averaging fMRI signals. To address this, we introduce a novel framework that reframes SSL as a Stochastic Optimal Control (SOC) problem. Our approach models brain activity as continuous-time latent dynamics, learning a robust representation of brain dynamics by optimizing a control policy that is agnostic to the temporal irregularity. This SOC framework naturally unifies masked autoencoding (MAE) and joint-embedding prediction (JEPA) to extract compact, control-derived representations. Furthermore, a simulation-free inference strategy ensures computational efficiency and scalability for large-scale fMRI datasets. Our model demonstrates state-of-the-art performance across diverse downstream applications, highlighting the potential of the SOC-based continuous-time representation learning framework.

Joonhyeong Park, Byoungwoo Park, Chang-Bae Bang +4

KAIST · Yonsei University · EverEx +1

Latent Dynamics Modeling Self-Supervised Time Series Representation Learning Predictive Representation Learning Medical Image Representation Learning

Oct 14, 2024eess.SY

Automated Discovery of Operable Dynamics from Videos

Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics, including a set of compact state variables that preserve the smoothness of the system dynamics and a differentiable vector field, directly from video without requiring prior domain-specific knowledge. The prominence and effectiveness of the proposed approach are demonstrated through both quantitative and qualitative analyses of a range of dynamical systems, including the identification of stable equilibria, the prediction of natural frequencies, and the detection of chaotic and limit cycle behaviors. The results highlight the potential of our data-driven approach to advance automated scientific discovery.

Kuang Huang, Dong Heon Cho, Boyuan Chen

Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, New York, 10027, NY, USA. · Department of Computer Science, Duke University, 308 Research Dr., Durham, 27705, NC, USA. · Department of Mechanical Engineering and Material Science, Duke University, 121 Hudson Hall, Durham, 27708, NC, USA. +1

Dynamical Systems Latent Dynamics Modeling System Identification Autonomous Scientific Discovery

Date pendingcs.CV

Self-Supervised Cardiac Phase Detection via Single-Parameter Latent Orbits

Accurate identification of end-diastole (ED) and end-systole (ES) in echocardiography underpins the quantification of ventricular function, yet manual selection of these key frames is subjective and introduces clinically significant inter-operator variability. Recent self-supervised methods either prescribe strict periodic trajectories or learn an unconstrained low-dimensional motion subspace from reconstruction or registration objectives. The former offers interpretability but imposes restrictive assumptions on temporal progression, whereas the latter leaves cardiac phase implicit and ED/ES must be recovered through post-hoc geometric processing of the learned trajectory. We translate the physiological observation that cardiac phase is a one-dimensional signal into a prior by constraining the latent motion component to a single-parameter latent orbit, i.e., a global linear trajectory in latent space indexed by a bounded scalar phase variable. Mapping this variable through a sinusoidal nonlinearity yields an oscillatory motion signal with consistent temporal ordering, enabling direct identification of ED and ES from the learned phase signal. This inductive bias allows the model to capture an interpretable representation of the cardiac cycle, while maintaining flexibility to capture irregular heartbeats. Trained on EchoNet-Dynamic without annotations, our minimal single-parameter cardiac phase model learns an effective latent orbit, significantly improves upon the previous state of the art in ED localisation and matches it in ES localisation while using a more constrained representation and fewer training epochs. This demonstrates that a principled physiological inductive bias can match or exceed the performance of more complex representations. Code is available at: https://github.com/BonniciJ/OrbitalEcho/

John Bonnici, Matthew Baugh, Aleksandra Kulbaka +3

Departament of Computing, Imperial College London, UK · Friedrich–Alexander University Erlangen–Nürnberg, DE · Ultromics Ltd, Oxford, UK

Latent Dynamics Modeling Self-Supervised Learning Echocardiography Ultrasound Imaging