System Identification

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System identification uses observations of a system, often alongside controlled inputs, to infer how it changes over time and how it will respond to new conditions. Approaches range from ARX and state-space or subspace methods to sparse equation discovery with SINDy, Koopman operators, neural ODEs, and physics-structured models such as Hamiltonian networks; Bayesian and active-learning methods help choose experiments and quantify uncertainty. These tools support prediction and control in settings including robotics, industrial processes, physical experiments, and systems observed through video. A central challenge is that accurate prediction on observed data does not guarantee that the underlying laws or parameters are identifiable, especially with sparse, noisy, partial, or weakly excited observations.

Latest papers

157 papers19 papers in the last four weeks, down 10% on the four weeks before. 0.1% of all new papers.

Apr 7, 2026

Optimal Centered Active Excitation in Linear System Identification

We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.

Kaito Ito, Alexandre Proutiere

Department of Information Physics and Computing, The University of Tokyo, Tokyo 113-8654, Japan · Division of Decision and Control Systems, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm 114 28, Sweden

Sample Complexity Active Learning System Identification

Apr 7, 2026

Robust Learning of Heterogeneous Dynamic Systems

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the problem of learning shared patterns from multiple heterogeneous dynamic systems. In this article, we propose a novel distributionally robust learning approach for modeling heterogeneous ODE systems. Specifically, we construct a robust dynamic system by maximizing a worst-case reward over an uncertainty class formed by convex combinations of the derivatives of trajectories. We show the resulting estimator admits an explicit weighted average representation, where the weights are obtained from a quadratic optimization that balances information across multiple data sources. We further develop a bi-level stabilization procedure to address potential instability in estimation. We establish rigorous theoretical guarantees for the proposed method, including consistency of the stabilized weights, error bound for robust trajectory estimation, and asymptotical validity of pointwise confidence interval. We demonstrate that the proposed method considerably improves the generalization performance compared to the alternative solutions through both extensive simulations and the analysis of an intracranial electroencephalogram data.

Shuoxun Xu, Zijian Guo, Brooke R. Staveland +2

University of California at Berkeley · Zhejiang University · University of California at San Francisco

Dynamical Systems Robust Estimation System Identification Distributionally Robust Optimization

Apr 6, 2026

A Robust SINDy Autoencoder for Noisy Dynamical System Identification

Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a library of candidate functions. Therefore, it relies on the assumption that the dynamics are sparsely represented in the coordinate system used. To address this limitation, one seeks a coordinate transformation that provides reduced coordinates capable of reconstructing the original system. Recently, SINDy autoencoders have extended this idea by combining sparse model discovery with autoencoder architectures to learn simplified latent coordinates together with parsimonious governing equations. A central challenge in this framework is robustness to measurement error. Inspired by noise-separating neural network structures, we incorporate a noise-separation module into the SINDy autoencoder architecture, thereby improving robustness and enabling more reliable identification of noisy dynamical systems. Numerical experiments on the Lorenz system show that the proposed method recovers interpretable latent dynamics and accurately estimates the measurement noise from noisy observations.

Kairui Ding

Department of Mathematics, Columbia University

Nonlinear System Identification System Identification Sparse Identification of Nonlinear Dynamics Latent Dynamics Modeling Autoencoders

Apr 2, 2026

Learning interacting particle systems from unlabeled data

Learning the potentials of interacting particle systems is a fundamental task across various scientific disciplines. A major challenge is that unlabeled data collected at discrete time points lack trajectory information due to limitations in data collection methods or privacy constraints. We address this challenge by introducing a trajectory-free self-test loss function that leverages the weak-form stochastic evolution equation of the empirical distribution. The loss function is quadratic in potentials, supporting parametric and nonparametric regression algorithms for robust estimation that scale to large, high-dimensional systems with big data. Systematic numerical tests show that our method outperforms baseline methods that regress on trajectories recovered via label matching, tolerating large observation time steps. We establish the convergence of parametric estimators as the sample size increases, providing a theoretical foundation for the proposed approach.

Viska Wei, Fei Lu

Department of Applied Mathematics and Statistics and Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA. · Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA.

System Identification Nonlinear System Identification

Mar 28, 2026

Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networks

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet when system parameters must be inferred from data, recent neural approaches offer flexibility at the cost of physical guarantees: Neural ODEs provide flexible trajectory approximation but may violate physical invariants, while energy preserving architectures do not natively represent dissipation essential to real-world systems. We introduce Lie Generator Networks (LGN), which learn a structured generator A and compute trajectories directly via matrix exponentiation. This shift from integration to exponentiation preserves structure by construction. By parameterizing A = S - D (skew-symmetric minus positive diagonal), stability and dissipation emerge from the underlying architecture and are not introduced during training via the loss function. LGN provides a unified framework for linear conservative, dissipative, and time-varying systems. On a 100-dimensional stable RLC ladder, standard derivative-based least-squares system identification can yield unstable eigenvalues. The unconstrained LGN yields stable but physically incorrect spectra, whereas LGN-SD recovers all 100 eigenvalues with over two orders of magnitude lower mean eigenvalue error than unconstrained alternatives. Critically, these eigenvalues reveal poles, natural frequencies, and damping ratios which are interpretable physics that black-box networks do not provide.

Shafayeth Jamil, Rehan Kapadia

Department of Electrical and Computer Engineering, University of Southern California

Structure-Preserving Neural Networks Dynamical Systems System Identification

Mar 21, 2026

Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms

Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics. This paper introduces a framework for jointly learning the state, dynamics, and parameters of filtering algorithms in data assimilation through a process we refer to as auto-differentiable filtering. The framework leverages a theoretically motivated loss function that enables learning from partial, noisy observations via gradient-based optimization using auto-differentiation. We further demonstrate how several well-known data assimilation methods can be learned or tuned within this framework. To underscore the versatility of auto-differentiable filtering, we perform experiments on dynamical systems spanning multiple scientific domains, such as the Clohessy-Wiltshire equations from aerospace engineering, the Lorenz-96 system from atmospheric science, and the generalized Lotka-Volterra equations from systems biology. Finally, we provide guidelines for practitioners to customize our framework according to their observation model, accuracy requirements, and computational budget.

Melissa Adrian, Daniel Sanz-Alonso, Rebecca Willett

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 · Department of Statistics, The University of Chicago, Chicago, IL 60637 · Department of Computer Science, The University of Chicago, Chicago, IL 60637 +1

Data Assimilation State Space Models System Identification

Mar 21, 2026

Swim2Real: VLM-Guided System Identification for Sim-to-Real Transfer

We present Swim2Real, a pipeline that calibrates a 16-parameter robotic fish simulator from swimming videos using vision-language model (VLM) feedback, requiring no hand-designed search stages. Calibrating soft aquatic robots is particularly challenging because nonlinear fluid-structure coupling makes the parameter landscape chaotic, simplified fluid models introduce a persistent sim-to-real gap, and controlled aquatic experiments are difficult to reproduce. Prior work on this platform required three manually tailored stages to handle this complexity. The VLM compares simulated and real videos and proposes parameter updates. A backtracking line search then validates each step size, tripling the accept rate from 14% to 42% by recovering proposals where the direction is correct but the magnitude is too large. Swim2Real calibrates all 16 parameters simultaneously, most closely matching real fish velocities across all motor frequencies (MAE = 7.4 mm/s, 43% lower than the next-best method), with zero outlier seeds across five runs. Motor commands from the trained policy transfer to the physical fish at 50 Hz, completing the pipeline from swimming video to real-world deployment. Downstream RL policies swim 12% farther than those from BayesOpt-calibrated simulators and 90% farther than CMA-ES. These results demonstrate that VLM-guided calibration can close the sim-to-real gap for aquatic robots directly from video, enabling zero-shot RL transfer to physical swimmers without manual system identification, a step toward automated, general-purpose simulator tuning for underwater robotics.

Kevin Qiu, Kyle Walker, Mike Y. Michelis +2

University of Warsaw · IDEAS NCBR · EPFL +2

Robot System Identification Sim-to-Real Transfer Underwater Robotics System Identification VLMs for Robotics

Mar 21, 2026

Achieving $\widetilde{O}(1/ε)$ Sample Complexity for Bilinear Systems Identification under Bounded Noises

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows marginally stable dynamics with polynomial mean-square state growth. We prove that the diameter of the feasible parameter set shrinks with sample complexity

\widetilde{\mathcal O}(1/ε)

where

ε

is the estimation error. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.

Hongyu Yi, Chenbei Lu, Jing Yu

Department of Electrical and Computer Engineering, University of Washington, Seattle, WA, USA. · Cornell University AI for Science Institute, Cornell University, Ithaca, NY, USA.

Parameter Estimation Uncertainty Quantification Sample Complexity System Identification

Mar 17, 2026

IRIS: A Real-World Benchmark for Inverse Recovery and Identification of Physical Dynamic Systems from Monocular Video

Unsupervised physical parameter estimation from video lacks a common benchmark: existing methods evaluate on non-overlapping synthetic data, the sole real-world dataset is restricted to single-body systems, and no established protocol addresses governing-equation identification. This work introduces IRIS, a high-fidelity benchmark comprising 240 real-world videos captured at 4K resolution and 60fps, spanning both single- and multi-body dynamics with independently measured ground-truth parameters and uncertainty estimates. Each dynamical system is recorded under controlled laboratory conditions and paired with its governing equations, enabling principled evaluation. A standardized evaluation protocol is defined encompassing parameter accuracy, identifiability, extrapolation, robustness, and governing-equation selection. Multiple baselines are evaluated, including a multi-step physics loss formulation and four complementary equation-identification strategies (VLM temporal reasoning, describe-then-classify prompting, CNN-based classification, and path-based labelling), establishing reference performance across all IRIS scenarios and exposing systematic failure modes that motivate future research. The dataset, annotations, evaluation toolkit, and all baseline implementations are publicly released.

Rasul Khanbayov, Mohamed Rayan Barhdadi, Erchin Serpedin +1

Hamad Bin Khalifa University · Texas A&M University

Parameter Identifiability System Identification Inverse Dynamics Inverse Problems

Mar 16, 2026

Discovery of interaction and diffusion kernels in particle-to-mean-field multi-agent systems

We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a priori knowledge of the underlying interaction structure. Starting from a discrete stochastic binary-interaction model, we formulate the inverse problem as a sequence of sparse regression tasks in structured finite-dimensional spaces spanned by compactly supported basis functions, such as piecewise linear polynomials. In particular, we assume that pairwise interactions between agents are not directly observed and that only limited trajectory data are available. To address these challenges, we propose two complementary identification strategies. The first based on random-batch sampling, which compensates for latent interactions while preserving the statistical structure of the full dynamics in expectation. The second based on a mean-field approximation, where the empirical particle density reconstructed from the data defines a continuous nonlocal regression problem. Numerical experiments demonstrate the effectiveness and robustness of the proposed framework, showing accurate reconstruction of both interaction and diffusion kernels even from partially observed. The method is validated on benchmark models, including bounded-confidence and attraction-repulsion dynamics, where the two proposed strategies achieve comparable levels of accuracy.

Giacomo Albi, Alessandro Alla, Elisa Calzola

Department of Computer Science, University of Verona, Verona, Italy · Department of Mathematics, La Sapienza University of Rome, Rome, Italy

System Identification

Mar 15, 2026

Coordinate-Independent Robot Model Identification

Robot model identification is commonly performed by least-squares regression on inverse dynamics, but existing formulations measure residuals directly in coordinate force space and therefore depend on the chosen coordinate chart, units, and scaling. This paper proposes a coordinate-independent identification method that weights inverse-dynamics residuals by the dual metric induced by the system Riemannian metric. Using the force--velocity vector--covector duality, the dual metric provides a physically meaningful normalization of generalized forces, pulling coordinate residuals back into the ambient mechanical space and eliminating coordinate-induced bias. The resulting objective remains convex through an affine-metric and Schur-complement reformulation, and is compatible with physical-consistency constraints and geometric regularization. Experiments on an inertia-dominated Crazyflie--pendulum system and a drag-dominated LandSalp robot show improved identification accuracy, especially on shape coordinates, on both downsampled and full datasets.

Yanhao Yang, Ross L. Hatton

Collaborative Robotics and Intelligent Systems (CoRIS) Institute at Oregon State University, Corvallis, OR USA

Robot Dynamics Identification Robot System Identification System Identification Inverse Dynamics

Mar 15, 2026

Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention

Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of candidate functions chosen via available domain knowledge. In contrast, deep learning can demonstrably model systems of broad complexity with high fidelity, but black-box function approximation typically fails to yield explicit descriptive or disentangled representations revealing the structure of a system. We develop a novel identifiability theorem, leveraging causal representation learning, to uncover disentangled representations of system parameters without structural assumptions. We derive a graphical criterion specifying when system parameters can be uniquely disentangled from raw trajectory data, up to permutation and diffeomorphism. Crucially, our analysis demonstrates that global causal structures provide a lower bound on the disentanglement guarantees achievable when considering local state-dependent causal structures. We instantiate system parameter identification as a variational inference problem, leveraging a sparsity-regularised transformer to uncover state-dependent causal structures. We empirically validate our approach across four synthetic domains, demonstrating its ability to recover highly disentangled representations that baselines fail to recover. Corroborating our theoretical analysis, our results confirm that enforcing local causal structure is often necessary for full identifiability.

Markus W. Baumgartner, Anson Lei, Joe Watson +1

Applied Artificial Intelligence Lab, Oxford Robotics Institute, Oxford, UK

System Identification Parameter Identifiability Causal Representation Learning Causal Structure Learning

Mar 12, 2026

Flowcean - Model Learning for Cyber-Physical Systems

Effective models of Cyber-Physical Systems (CPS) are crucial for their design and operation. Constructing such models is difficult and time-consuming due to the inherent complexity of CPS. As a result, data-driven model generation using machine learning methods is gaining popularity. In this paper, we present Flowcean, a novel framework designed to automate the generation of models through data-driven learning that focuses on modularity and usability. By offering various learning strategies, data processing methods, and evaluation metrics, our framework provides a comprehensive solution, tailored to CPS scenarios. Flowcean facilitates the integration of diverse learning libraries and tools within a modular and flexible architecture, ensuring adaptability to a wide range of modeling tasks. This streamlines the process of model generation and evaluation, making it more efficient and accessible.

Maximilian Schmidt, Swantje Plambeck, Markus Knitt +4

Hamburg University of Technology, Hamburg, Germany · Fraunhofer — Center for Maritime Logistics and Services CML, Hamburg, Germany · OFFIS — Institute for Information Technology, Oldenburg, Germany

Cyber-Physical Systems System Identification Automated Machine Learning

Mar 11, 2026

JEDI: Jointly Embedded Inference of Neural Dynamics

Animal brains flexibly and efficiently achieve many behavioral tasks with a single neural network. A core goal in modern neuroscience is to map the mechanisms of the brain's flexibility onto the dynamics underlying neural populations. However, identifying task-specific dynamical rules from limited, noisy, and high-dimensional experimental neural recordings remains a major challenge, as experimental data often provide only partial access to brain states and dynamical mechanisms. While recurrent neural networks (RNNs) directly constrained neural data have been effective in inferring underlying dynamical mechanisms, they are typically limited to single-task domains and struggle to generalize across behavioral conditions. Here, we introduce JEDI, a hierarchical model that captures neural dynamics across tasks and contexts by learning a shared embedding space over RNN weights. This model recapitulates individual samples of neural dynamics while scaling to arbitrarily large and complex datasets, uncovering shared structure across conditions in a single, unified model. Using simulated RNN datasets, we demonstrate that JEDI accurately learns robust, generalizable, condition-specific embeddings. By reverse-engineering the weights learned by JEDI, we show that it recovers ground truth fixed point structures and unveils key features of the underlying neural dynamics in the eigenspectra. Finally, we apply JEDI to motor cortex recordings during monkey reaching to extract mechanistic insight into the neural dynamics of motor control. Our work shows that joint learning of contextual embeddings and recurrent weights provides scalable and generalizable inference of brain dynamics from recordings alone.

Anirudh Jamkhandi, Ali Korojy, Olivier Codol +2

Mila - Quebec AI Institute · Université de Montréal

Latent Dynamics Modeling Dynamical Systems Recurrent Neural Networks System Identification

Mar 10, 2026

A neural operator for predicting vibration frequency response curves from limited data

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via machine learning has great potential to accelerate design iteration and make testing workflows more efficient. However, dynamical systems are conventionally difficult to solve via machine learning methods without using physics-based regularizing loss functions. To properly perform this forecasting task, a structure that has an inspectable physical obedience can be devised without the use of regularizing terms from first principles. The method employed in this work is a neural operator integrated with an implicit numerical scheme. This architecture enables operators to learn of the underlying state-space dynamics from limited data, allowing generalization to untested driving frequencies and initial conditions. This network can infer the system's global frequency response by training on a small set of input conditions. As a foundational proof of concept, this investigation verifies the machine learning algorithm with a linear, single-degree-of-freedom system, demonstrating implicit obedience of dynamics. This approach demonstrates 99.87% accuracy in predicting the Frequency Response Curve (FRC), forecasting the frequency and amplitude of linear resonance training on 7% of the bandwidth of the solution. By training machine learning models to internalize physics information rather than trajectory, better generalization accuracy can be realized, vastly improving the timeframe for vibration studies on engineered components.

D. Bluedorn, A. Badawy, B. E. Saunders +2

Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA. · Knight Foundation School of Computing and Information Science, Florida International University, Miami, FL 33199, USA. · Sandia National Laboratories, Albuquerque, NM 87123, USA.

Neural Surrogate Modeling Neural Operators Structural Mechanics System Identification

Mar 9, 2026

Unified Structural-Hydrodynamic Modeling of Underwater Underactuated Mechanisms and Soft Robots

Underwater robots are widely deployed for ocean exploration and manipulation. Underactuated mechanisms are advantageous in aquatic environments because reducing actuator count lowers motor-leakage risk while introducing inherent mechanical compliance. However, accurate modeling of underwater underactuated and soft robotic systems remains challenging, as it requires identifying high-dimensional structural and hydrodynamic parameters. In this work, we propose a trajectory-driven global optimization framework for unified structural-hydrodynamic modeling of underwater multibody systems. Inspired by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the proposed approach simultaneously identifies coupled elastic, damping, and distributed hydrodynamic parameters through trajectory-level matching between simulated and experimental motion. This enables high-fidelity reproduction of underactuated mechanisms and compliant soft robotic systems in underwater environments, using as little as a single video recording. We first validate the framework on a link-by-link underactuated multibody mechanism, demonstrating accurate identification of distributed hydrodynamic coefficients, with normalized end-effector position error below 5% across multiple trajectories, initial conditions, and both active-passive and fully passive configurations. The modeling strategy is further validated on an asymmetric octopus-inspired soft arm, confirming its effectiveness for compliant soft robotic systems. Finally, eight identified arms are assembled into a swimming octopus robot, where the unified parameter set enables realistic whole-body behavior without additional retuning. These results demonstrate the scalability and transferability of the proposed structural-hydrodynamic modeling framework across underwater underactuated and soft robotic systems.

Chenrui Zhang, Yiyuan Zhang, Yunfei Ye +3

Department of Mechanical Engineering and Advanced Robotics Centre, National University of Singapore, Singapore. · Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore.

Robot System Identification Underwater Robotics System Identification Soft Robotics

Mar 6, 2026

MOSIV: Multi-Object System Identification from Videos

We introduce the challenging problem of multi-object system identification from videos, for which prior methods are ill-suited due to their focus on single-object scenes or discrete material classification with a fixed set of material prototypes. To address this, we propose MOSIV, a new framework that directly optimizes for continuous, per-object material parameters using a differentiable simulator guided by geometric objectives derived from video. We also present a new synthetic benchmark with contact-rich, multi-object interactions to facilitate evaluation. On this benchmark, MOSIV substantially improves grounding accuracy and long-horizon simulation fidelity over adapted baselines, establishing it as a strong baseline for this new task. Our analysis shows that object-level fine-grained supervision and geometry-aligned objectives are critical for stable optimization in these complex, multi-object settings. The source code and dataset will be released.

Chunjiang Liu, Xiaoyuan Wang, Qingran Lin +9

CMU · Georgia Tech · Harvard +4

System Identification Materials Property Prediction Inverse Problems

Mar 5, 2026

Random Dot Product Graphs as Dynamical Systems: Limitations and Opportunities

Can we learn the differential equations governing the evolution of a temporal network? We investigate this within Random Dot Product Graphs (RDPGs), where each network snapshot is generated from latent positions evolving under unknown dynamics. We identify three fundamental obstructions: gauge freedom from rotational ambiguity in latent positions, realizability constraints from the manifold structure of the probability matrix, and trajectory recovery artifacts from spectral embedding. We develop a geometric framework based on principal fiber bundles that formalizes these obstructions. We characterize invisible dynamics as exactly the skew-symmetric generators, and show the realizable tangent space has dimension

nd - d(d-1)/2

. An holonomy dichotomy emerges: polynomial dynamics have commuting generators, stationary eigenvectors, and trivial holonomy, making gauge alignment purely statistical; Laplacian dynamics satisfy a non-commutativity criterion producing nontrivial holonomy, with curvature weighted by

1/(λ_ι+ λ_γ)

linking gauge sensitivity to the spectral gap. In

d=2

this yields full restricted holonomy

\mathrm{SO}(2)

; for

d \ge 3

generic full

\mathrm{SO}(d)

remains conjectural. Cram'er--Rao lower bounds reveal that the same spectral gap controlling curvature and injectivity simultaneously controls Fisher information, so geometric and statistical difficulty are inextricable. We prove an identifiability principle: symmetric dynamics cannot absorb skew-symmetric gauge contamination, so dynamics structure can resolve gauge ambiguity. We demonstrate this constructively with anchor-based alignment and a UDE pipeline recovering vector fields from noisy graph sequences. Yet finite-sample interactions between noise, gauge, and dynamics expressiveness remain beyond the asymptotic theory. We frame this gap as an open challenge.

Giulio Valentino Dalla Riva

Latent Dynamics Modeling Dynamic Graph Learning System Identification Latent Variable Models

Mar 2, 2026

Using the SEKF to Transfer NN Models of Dynamical Systems with Limited Data

Data-driven models of dynamical systems require extensive amounts of training data. For many practical applications, gathering sufficient data is not feasible due to cost or safety concerns. This work uses the Subset Extended Kalman Filter (SEKF) to adapt pre-trained neural network models to new, similar systems with limited data available. Experimental validation across damped spring and continuous stirred-tank reactor systems demonstrates that small parameter perturbations to the initial model capture target system dynamics while requiring as little as 1% of original training data. In addition, finetuning requires less computational cost and reduces generalization error.

Joshua E. Hammond, Tyler A. Soderstrom, Brian A. Korgel +1

McKetta Department of Chemical Engineering, The University of Texas at Austin, 200 East Dean Keeton St., Stop C0400, Austin, 78712, TX, United States · Energy Institute, The University of Texas at Austin, 2304 Whitis Ave., Stop C2400, Austin, 78712, TX, United States · Texas Materials Institute, The University of Texas at Austin, 204 E. Dean Keeton St., Stop C2201, Austin, 78712, TX, United States +2

System Identification Neural Surrogate Modeling

Feb 26, 2026

Latent Matters: Learning Deep State-Space Models

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics of observed sequence data. They are often trained by maximising the evidence lower bound. However, as we show, this does not ensure the model actually learns the underlying dynamics. We therefore propose a constrained optimisation framework as a general approach for training DSSMs. Building upon this, we introduce the extended Kalman VAE (EKVAE), which combines amortised variational inference with classic Bayesian filtering/smoothing to model dynamics more accurately than RNN-based DSSMs. Our results show that the constrained optimisation framework significantly improves system identification and prediction accuracy on the example of established state-of-the-art DSSMs. The EKVAE outperforms previous models w.r.t. prediction accuracy, achieves remarkable results in identifying dynamical systems, and can furthermore successfully learn state-space representations where static and dynamic features are disentangled.

Alexej Klushyn, Richard Kurle, Maximilian Soelch +2

Technical University of Munich · AWS AI Labs · Machine Learning Research Lab, Volkswagen Group, Munich +1

State Space Models Latent Dynamics Modeling Variational Autoencoders System Identification State Representation Learning

Feb 25, 2026

Dual-Regime Hybrid Aerodynamic Modeling of Winged Blimps With Neural Mixing

Winged blimps operate across distinct aerodynamic regimes that cannot be adequately captured by a single model. At high speeds and small angles of attack, their dynamics exhibit strong coupling between lift and attitude, resembling fixed-wing aircraft behavior. At low speeds or large angles of attack, viscous effects and flow separation dominate, leading to drag-driven and damping-dominated dynamics. Accurately representing transitions between these regimes remains a fundamental challenge. This paper presents a hybrid aerodynamic modeling framework that integrates a fixed-wing Aerodynamic Coupling Model (ACM) and a Generalized Drag Model (GDM) using a learned neural network mixer with explicit physics-based regularization. The mixer enables smooth transitions between regimes while retaining explicit, physics-based aerodynamic representation. Model parameters are identified through a structured three-phase pipeline tailored for hybrid aerodynamic modeling. The proposed approach is validated on the RGBlimp platform through a large-scale experimental campaign comprising 1,320 real-world flight trajectories across 330 thruster and moving mass configurations, spanning a wide range of speeds and angles of attack. Experimental results demonstrate that the proposed hybrid model consistently outperforms single-model and predefined-mixer baselines, establishing a practical and robust aerodynamic modeling solution for winged blimps.

Xiaorui Wang, Hongwu Wang, Yue Fan +2

The authors are with the Robotics and Control Laboratory, School of Advanced Manufacturing and Robotics, and the State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing, 100871, China

Vehicle Dynamics System Identification Physics-Informed ML

Feb 22, 2026

Vid2Sid: Videos Can Help Close the Sim2Real Gap

Calibrating a robot simulator's physics parameters (friction, damping, material stiffness) to match real hardware is often done by hand or with black-box optimizers that reduce error but cannot explain which physical discrepancies drive the error. When sensing is limited to external cameras, the problem is further compounded by perception noise and the absence of direct force or state measurements. We present Vid2Sid, a video-driven system identification pipeline that couples foundation-model perception with a VLM-in-the-loop optimizer that analyzes paired sim-real videos, diagnoses concrete mismatches, and proposes physics parameter updates with natural language rationales. We evaluate our approach on a tendon-actuated finger (rigid-body dynamics in MuJoCo) and a deformable continuum tentacle (soft-body dynamics in PyElastica). On sim2real holdout controls unseen during training, Vid2Sid achieves the best average rank across all settings, matching or exceeding black-box optimizers while uniquely providing interpretable reasoning at each iteration. Sim2sim validation confirms that Vid2Sid recovers ground-truth parameters most accurately (mean relative error under 13% vs. 28--98%), and ablation analysis reveals three calibration regimes. VLM-guided optimization excels when perception is clean and the simulator is expressive, while model-class limitations bound performance in more challenging settings.

Kevin Qiu, Yu Zhang, Marek Cygan +1

University of Warsaw · IDEAS NCBR · EPFL +1

Robot System Identification Robot Dynamics Identification System Identification Sim-to-Real Transfer VLMs for Robotics

Feb 20, 2026

PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

Real physical systems are dissipative -- a pendulum slows, a circuit loses charge to heat -- and forecasting their dynamics from partial observations is a central challenge in scientific machine learning. We address the position-only (q-only) problem: given only generalized positions~

q_t

at discrete times (momenta~

p_t

latent), learn a structured model that (a)produces stable long-horizon forecasts and (b)recovers physically meaningful parameters when sufficient structure is provided. The port-Hamiltonian framework makes the conservative-dissipative split explicit via $\dot{x}=(J-R)\nabla H(x)$ , guaranteeing $dH/dt\le 0$ when $R\succeq 0$ . We introduce PHAST (Port-Hamiltonian Architecture for Structured Temporal dynamics), which decomposes the Hamiltonian into potential $V(q)$ , mass

M(q)

, and damping~

D(q)

across three knowledge regimes (KNOWN, PARTIAL, UNKNOWN), uses efficient low-rank PSD/SPD parameterizations, and advances dynamics with Strang splitting. Across thirteen q-only benchmarks spanning mechanical, electrical, molecular, thermal, gravitational, and ecological systems, PHAST achieves the best long-horizon forecasting among competitive baselines and enables physically meaningful parameter recovery when the regime provides sufficient anchors. We show that identification is fundamentally ill-posed without such anchors (gauge freedom), motivating a two-axis evaluation that separates forecasting stability from identifiability.

Shubham Bhardwaj, Chandrajit Bajaj

Department of Computer Science, Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, USA

Time Series Forecasting Port-Hamiltonian Systems Hamiltonian Neural Networks Nonlinear System Identification System Identification Parameter Identifiability

Feb 19, 2026

Variational Grey-Box Dynamics Matching

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems and real-world weather forecasting demonstrate that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

Gurjeet Sangra Singh, Frantzeska Lavda, Giangiacomo Mercatali +1

Physics-Informed Generative Modeling System Identification Flow Matching

Feb 18, 2026

System Identification under Constraints and Disturbance: A Bayesian Estimation Approach

We introduce a Bayesian system identification (SysID) framework for jointly estimating robot's state trajectories and physical parameters with high accuracy. It embeds physically consistent inverse dynamics, contact and loop-closure constraints, and fully featured joint friction models as hard, stage-wise equality constraints. It relies on energy-based regressors to enhance parameter observability, supports both equality and inequality priors on inertial and actuation parameters, enforces dynamically consistent disturbance projections, and augments proprioceptive measurements with energy observations to disambiguate nonlinear friction effects. To ensure scalability, we derive a parameterized equality-constrained Riccati recursion that preserves the banded structure of the problem, achieving linear complexity in the time horizon, and develop computationally efficient derivatives. Simulation studies on representative robotic systems, together with hardware experiments on a Unitree B1 equipped with a Z1 arm, demonstrate faster convergence, lower inertial and friction estimation errors, and improved contact consistency compared to forward-dynamics and decoupled identification baselines. When deployed within model predictive control frameworks, the resulting models yield measurable improvements in tracking performance during locomotion over challenging environments.

Sergi Martinez, Steve Tonneau, Carlos Mastalli

Robot Motor Intelligence (RoMI) Lab, Heriot-Watt University, U.K. · Informatics School, University of Edinburgh, U.K.

Robot System Identification System Identification Robot Dynamics Identification Robot State Estimation

Feb 17, 2026

Uniform error bounds for quantized dynamical models

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.

Abdelkader Metakalard, Fabien Lauer, Kevin Colin +1

CRAN, SYNALP · ∗Universit´e de Lorraine, CNRS, CRAN, F-54000 Nancy, France · ∗∗Universit´e de Lorraine, CNRS, LORIA, F-54000 Nancy, France +2

System Identification Generalization Bounds Low-Bit Quantization Statistical Learning Theory

Dec 15, 2025

Adaptive digital twins for predictive decision-making: Online Bayesian learning of transition dynamics

This work shows how adaptivity can enhance value realization of digital twins in civil engineering. We focus on adapting the state transition models within digital twins represented through probabilistic graphical models. The bi-directional interaction between the physical and virtual domains is modeled using dynamic Bayesian networks. By treating state transition probabilities as random variables endowed with conjugate priors, we enable hierarchical online learning of transition dynamics from a state to another through effortless Bayesian updates. We provide the mathematical framework to account for a larger class of distributions with respect to the current literature on digital twins. To compute dynamic policies with precision updates we solve parametric Markov decision processes through reinforcement learning. The proposed adaptive digital twin framework enjoys enhanced personalization, increased robustness, and improved cost-effectiveness. We assess our approach on a case study involving structural health monitoring and maintenance planning of a railway bridge.

Eugenio Varetti, Matteo Torzoni, Marco Tezzele +1

MOX – Dipartimento di Matematica, Politecnico di Milano, Milan, 20133, Italy · Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, 20133, Italy · Mathematics Department, Emory University, Atlanta, 30322, GA, United States

System Identification Digital Twins Adaptive Learning

Dec 5, 2025

Symmetric Linear Dynamical Systems are Learnable from Few Observations

We consider the problem of learning the parameters of a

N

-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time

T

. We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices using only

T=\mathcal{O}(\log N)

observations, irrespective of whether the matrix is sparse or dense. This estimator is based on the method of moments and does not rely on problem-specific regularization. This is especially important for applications such as structure discovery.

Minh Vu, Andrey Y. Lokhov, Marc Vuffray

Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Dynamical Systems Parameter Estimation Stochastic Linear Dynamical Systems System Identification

Nov 12, 2025

When is a System Discoverable from Data? Discovery Requires Chaos

The deep learning revolution has enabled major AI advances in physical sciences, particularly in discovering dynamical systems from observational data. Yet the reliability of learned surrogates and symbolically discovered models is often undermined by non-uniqueness: models may fit observed trajectories perfectly, but lack genuine predictive power. We show that chaos, despite its association with unpredictability, is often what makes governing equations discoverable. We prove that the classical Lorenz system is analytically discoverable and verify experimentally that for many systems out-of-domain generalization emerges precisely at chaos onset. Conservative systems, by contrast, are inherently non-discoverable from data alone. The prevalence of chaotic systems in benchmarks may have inadvertently obscured this limitation. These findings help explain why AI excels at weather forecasting, yet struggles in many engineering applications: the systems most amenable to discovery (chaotic ones) are often least amenable to control.

Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3

University of Cambridge · LMU Munich and Munich Center for Machine Learning (MCML) · IBM Research

Dynamical Systems Nonlinear System Identification System Identification Chaotic Dynamical Systems

Sep 21, 2025

Data-efficient Kernel Methods for Learning Hamiltonian Systems

Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from trajectory data. We present two approaches: a 2-step method that reconstructs trajectories before learning the Hamiltonian, and a 1-step method that jointly infers both. Across several benchmark systems, including mass-spring dynamics, a nonlinear pendulum, and the Henon-Heiles system, we demonstrate that our framework achieves accurate, data-efficient predictions and outperforms 2-step kernel-based baselines, particularly in scarce-data regimes, while preserving the Hamiltonian structure. Moreover, we prove a priori error estimates, ensuring reliability of the learned models. We also provide a more general, problem-agnostic numerical framework that goes beyond Hamiltonian systems and can be used for data-driven learning of arbitrary dynamical systems.

Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi +2

Department of Computing and Mathematical Sciences, Caltech, CA, USA. · Beyond Limits, CA, USA. · The Alan Turing Institute, London, UK. +1

Dynamical Systems Nonlinear System Identification System Identification Kernel Methods Hamiltonian Dynamics