Dynamics Models

Deterministic dynamics modeling of tendon-driven continuum robots remains challenging owing to uncertainties in material behavior, tendon transmission, friction, and contact. Measured joint configurations and nominal tendon commands do not fully characterize these internal mechanical factors, leaving uncertainty in the subsequent motion. We therefore develop a history-conditioned, physics-informed flow-matching framework for probabilistic dynamics prediction, using motion and actuation histories to predict the distribution of the next complete joint configuration. By recursively sampling next-step configurations under prescribed commands, the model predicts distributions of future whole-body motions. In simulation, scenario-specific models achieve five-second trajectory Energy Scores (lower is better) of 12.05 mm under internal friction variation and 9.29 mm under unobserved actuation disturbances. Relative to the conditional variational autoencoder and diffusion baselines, Flow attains lower Energy Scores and coverage closer to the nominal level in both scenarios. Ablations support history and structural conditioning in both scenarios. On the physical robot, predictions under two tendon-command profiles excluded from training capture the principal motion sequences, with five-second Energy Scores of 11.91 and 11.42 mm, lower than the compared baselines. The predicted-to-measured spread ratios are 1.65 and 1.22 (closer to 1 is better). These results support history-conditioned probabilistic dynamics prediction under incomplete mechanical observations.

This paper presents dynamics-relaxed model predictive control (DR-MPC), a novel MPC formulation for legged locomotion, and a tailored interior-point method (IPM) solver. The formulation combines online optimization feasibility by construction with a contact-aware input parameterization. DR-MPC moves the dynamics equality and affine input constraints into quadratic penalties and retains only nonempty box constraints. The resulting box-constrained quadratic program (QP) has a block-arrow Hessian that enables the state and affine-output directions to be eliminated through a Schur complement. The solver factors only the reduced control system after swing-force elimination and contact-aligned move blocking. For the evaluated implementations using the same DR-MPC formulation, our method achieves median end-to-end MPC speedups of $16.0\times$ over HPIPM and $4.4\times$ over OSQP, with comparable locomotion performance in simulation. DR-MPC achieves a median onboard MPC end-to-end time of $4.4$ ms and is validated on a Unitree Go1 quadruped. Open-source code will be made available after publication.

Monte Carlo Tree Search (MCTS) is a powerful framework for solving complex decision-making problems, yet it often relies on the assumption that the simulator and the real-world dynamics are identical. Although this assumption helps achieve the success of MCTS in games like Chess, Go, and Shogi, the real-world scenarios incur ambiguity due to their modeling mismatches in low-fidelity simulators. In this work, we present a new robust variant of MCTS that mitigates dynamical model ambiguities. Our algorithm addresses transition dynamics and reward distribution ambiguities to bridge the gap between simulation-based planning and real-world deployment. We incorporate a robust power mean backup operator and carefully designed exploration bonuses to ensure finite-sample convergence at every node in the search tree. We show that our algorithm achieves a convergence rate of $\mathcal{O}(n^{-1/2})$ for the value estimation at the root node, comparable to that of standard MCTS. Finally, we provide empirical evidence that our method achieves robust performance in planning problems even under significant ambiguity in the underlying reward distribution and transition dynamics.

The purpose of this paper is the identification of high-fidelity digital twin data models from numerical code outputs by non-intrusive techniques (i.e., not requiring Galerkin projection of the governing equations onto the reduced modes basis). In this paper the author defines the concept of the digital twin data model (DTM) as a model of reduced complexity that has the main feature of mirroring the original process behavior. The significant advantage of a DTM is to reproduce the dynamics with high accuracy and reduced costs in CPU time and hardware for settings difficult to explore because of the complexity of the dynamics over time. This paper introduces a new framework for creating efficient digital twin data models by combining two state-of-the-art tools: randomized dynamic mode decomposition and deep learning artificial intelligence. It is shown that the outputs are consistent with the original source data with the advantage of reduced complexity. The DTMs are investigated in the numerical simulation of three shock wave phenomena with increasing complexity. The author performs a thorough assessment of the performance of the new digital twin data models in terms of numerical accuracy and computational efficiency.

A finite-difference bowed-string model with implicitly resolved Stribeck friction is presented, with a regime diagnostic, the Schelleng bow-force limits on four strings, and a comparison of learned bow controllers. Implicit resolution is necessary, and quantitatively so: a lagged contact force cannot capture the string on a discrete grid, so no stick phase forms at any bow force. With friction, impedance and quality factor taken from published measurement rather than fitted, all four strings return a stick fraction of 89.1% against an ideal 90%. Schelleng's maximum bow force is recovered on every string. The minimum is not: it follows $Z v_b β^{-1}$ rather than the predicted $Z^2 v_b β^{-2}$, reducing both squared dependences to first powers. Six controllers at matched capacity, over four strings and twenty seeds each, place a gated recurrent network ahead of a feedforward one, by most under a mid-stroke disturbance. The feedforward network completes more strokes only from a start the model's own playability map places outside the Helmholtz region. A minimal gated variant fails because gates computed from the input alone cannot clear a latched state. Training loss selects neither the capacity nor the context length, and no learned controller improves on the lookup rule that generated its labels. That bound has a domain. Regressing the controller's score on the rule's gives a slope of 0.32, more than ten standard errors below unity, so the controller overtakes the rule where the rule fails and is bounded by it where it holds. Under a rigid finger stop the plant is provably invariant, so transfer loss between pitches belongs to the controller alone and is traced to one feature. A regime classifier without a stick test labels small-amplitude periodic slipping as Helmholtz motion, and a harmonicity measure rates a string the bow never grips above Helmholtz motion.

Railway engineers need simulation models that predict vehicle responses across operating scenarios that cannot be tested exhaustively. Agreement with representative measurements provides essential evidence, but calibration at a limited set of conditions does not guarantee accuracy elsewhere. We present a multifidelity railway-bogie response-correction method that treats multibody simulation histories as low-fidelity information and roller-rig measurements as high-fidelity evidence. This method combines an experiment-anchored fidelity assignment with physics-informed discrepancy learning for multichannel bogie-response histories. A time-delay neural network (TDNN) represents the condition-dependent simulation trend, and development-fitted amplitude alignment defines the low-fidelity baseline. A residual-correction network then models the reproducible response component not explained by this baseline and adds it to the baseline. An effective dynamic-balance equation constrains the learned discrepancy by representing differences in inertia, damping, stiffness, and external forcing between the simulated and physical systems. The training objective combines this constraint with residual matching, temporal smoothness, and a combined channel-2 acceleration loss selected using displacement-acceleration consistency evidence. For the evaluated reconstruction case, the corrected response gives a mean coefficient of determination of 0.8197, a mean normalized root-mean-square error (NRMSE) of 4.6055 %, and a mean normalized mean absolute error (NMAE) of 1.9297 %. These results provide initial evidence of accurate response prediction at the held-out 385 km/h condition.

Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback-Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

Accurate dynamic models play a central role in achieving reliable control of quadcopters. Classical system identification methods remain widely used, mainly because of their interpretability. However, they often fail to capture important nonlinear effects, especially in small-scale aerial platforms where such effects become more pronounced. Data-driven approaches offer a different perspective. They can represent complex nonlinear dynamics more effectively, but this comes at the cost of reduced interpretability and the absence of well-calibrated uncertainty estimates. In this work, we propose a framework that combines physics-based modeling with data-driven learning, while explicitly accounting for uncertainty. A physics-based model is first identified using the Prediction Error Method (PEM), which captures the main structure of the system. The remaining dynamics are then modeled using a Gaussian Process (GP), allowing the residual behavior to be learned directly from data. This separation makes it possible to distinguish between known physical effects and unmodeled dynamics. The proposed framework is validated on a Duckiedrone-like experimental setup. The results show that the PEM-GP model achieves prediction accuracy comparable to that of a Long Short-Term Memory (LSTM) network, while additionally providing calibrated uncertainty estimates. This combination improves model reliability and supports uncertainty-aware decision-making.

Simulation of admittance-type models requires physically consistent dynamic models that are rarely available for off-the-shelf, everyday objects, limiting the fidelity of haptic interfaces that rely on such simulations. This paper presents the first complete workflow for producing physically consistent models of large real-world objects with various constraints and mechanisms, guaranteeing physical consistency of inertia and friction parameters. The workflow separates each object and identifies the handle and body in two stages, requiring no torque sensors at hinges, axles, or other constrained joints. Models are produced for a heavy, closer-actuated door and a wheelbarrow, representing objects of differing constraint types and model complexity. The door is modeled using four-bar linkage kinematics and a fluid dynamics-based lumped parameter model including opening, backcheck, swing, and latch zones. The wheelbarrow is modeled as a rigid body with a spherical wheel and no slip during rolling. Handle estimation RMS errors were below 0.64 N and 0.042 Nm across both objects. Door body estimation had RMS error of 2.19 Nm and wheelbarrow body estimation had RMS error of 6.77 Nm.

A key obstacle to deploying reinforcement learning in real-world systems is hyperparameter selection, particularly when simulators are unavailable and online experimentation is costly. Prior work has proposed calibration models trained on offline data to approximate environment dynamics and enable offline hyperparameter selection, but these methods have so far been evaluated only in simple simulated settings. In this paper, we present the first application of calibration models in a real-world industrial setting: a municipal water treatment plant. We evaluate several calibration model approaches, including a k-nearest neighbors model with a Laplacian distance metric, on high-dimensional, non-stationary sensor data for nexting prediction tasks. Our results show that these models can generate realistic long-horizon rollouts and recover meaningful hyperparameter sensitivity trends. We further examine how calibration models scale to year-long datasets, how they support the selection of fine-tuning learning rates for pre-trained agents, and how robust they are under distribution shift. Overall, our findings provide a proof of concept for using offline dynamics models to support RL deployment in real-world environments, while highlighting important practical challenges for future work.

The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error. Forcing all sources into one black box makes mechanism attribution and constraint preservation unauditable; forcing every mechanism into one equation family discards mature domain solvers. We propose SD-GWM, a Structural Dynamics Graph World Model as an executable structural contract: nodes declare self-dynamics S, edges declare neighbor graph-coupled dynamics N---both fixed-form mechanism assets (rules, ODEs, solvers) calibrating only authorized parameters. An optional bounded residual R concentrates learnability, while a global projection maps states to feasibility, enforcing constraints without guaranteeing accuracy gains. On eight pre-registered research questions, SD-GWM delivers (i) heterogeneous integration: rules and solvers plug in natively; (ii) semantic fidelity: disabling R preserves source semantics bit-for-bit, with four theory properties under explicit proof/empirical boundaries; (iii) auditable governance: stepwise traces enable counterfactual fault localization (top-1 = 1.0) without post-hoc approximations. On a semi-synthetic flood testbed and USGS streamflow, SD-GWM reduces constraint violations to floating-point tolerance in analytical tests and to zero in semi-synthetic and real-data cases. Persistence matches SD-GWM in calm periods, but during a 254-day extreme-flood shift persistence and all neural baselines collapse (90-min RMSE 892-3007 cfs) while SD-GWM holds at 108 cfs (8-28x gain). The bounded residual cuts RMSE ~50% only under backbone bias. We position SD-GWM not as a universally superior forecaster, but as a verifiable substrate for auditable, constraint-safe spatiotemporal mining.

Accurate models of underwater vehicle motion are needed for autonomous execution of marine tasks like infrastructure inspection and scientific sampling. However, such motion is challenging to characterize using traditional physics-based methods. This paper presents a novel data-driven framework for learning stochastic underwater vehicle dynamics. Using Euler-Poincaré dynamics and the geometry of Lie groups, we develop a stochastic physics-informed neural network architecture that respects the physical and geometric constraints of underwater vehicles. Our approach leverages structure-preserving stochastic integration and builds upon moment matching and finite dimensional matching to ensure geometrically-consistent training. We evaluate our approach in simulation and on an underwater vehicle navigating dock pylons in a harbor environment. The results demonstrate that our method learns accurate and robust dynamics models, enabling safe model-based control in challenging marine environments.

Sim-to-real policies are designed under nominal dynamics, but target-system trials may yield only a few isolated one-step transitions. We study pre-execution certification of a fixed control sequence, such as an action chunk produced by a learned policy. If the sequence reaches an unobserved state-input region, the observations remain consistent with target systems whose trajectories separate along it by an arbitrarily large amount. Any deterministic certifier sound for all of them must then decline to certify or return a reachable tube with arbitrarily large projected width. For bounded smooth classes of the target-nominal model error, we derive a finite plan-dependent projected-width lower bound. These results expose a trilemma among uniform trajectory containment, finite projected width, and unrestricted model-error behavior beyond the observations. ForeReach requires a supplied componentwise Lipschitz bound on the model error. Observed transition pairs can refute this declaration but cannot establish it outside the observed locations. Conditional on a valid declaration, our method constructs a set-membership envelope for the model error, propagates a zonotopic reachable tube, and certifies only when propagation remains within the certification domain and every projected tube slice avoids the unsafe set. In two benchmark systems, calibration baselines may remain narrow after losing trajectory containment outside data support, whereas our method declines to certify unsupported sequences and recovers certification when relevant target data and sufficient obstacle clearance are available.

Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose MetaKoopman, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios, including snow, ice, and mixed-friction conditions, as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration, and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: https://mahmoud-selim.github.io/MetaKoopman/

We show how large-deviation statistics allows one to obtain reliable estimates of the multiplicity of stable fixed-points in a model of neural ordinary differential equations previously employed in computational tasks. The result is obtained by developing a suitable perturbative method in the amplitude of the disorder. It turns out that for not-too-large coupling strengths there are no qualitative differences between the symmetric case, when the dynamics is a purely gradient evolution, and the asymmetric case, when limit cycles and chaos can, in principle, arise. The selection of this specific model is dictated by pedagogical reasons, but we are confident that the approach can be extended to other many-degree-of-freedom dynamical models characterized by different classes of random coupling matrices.

We present a structured large-language-model-driven workflow for automated multi-variable control design from dynamic process models. The workflow decomposes the design task into constrained code-generation steps: plant-interface construction, normalization, manipulated-variable controlled-variable (MV-CV) pairing, controller specification, closed loop simulation, scenario generation, performance evaluation and Bayesian-optimization (BO) based tuning. Generated artifacts are executed and validated before downstream tasks proceed, and failed artifacts are repaired using validation feedback. The proposed approach is demonstrated on a nonlinear gas-preheater benchmark with coupled pressure and temperature dynamics. The generated workflow produces a physically consistent decentralized PI (proportional-integral) feedback-feedforward control structure and an executable tuning environment. Bayesian optimization reduces the closed loop performance objective, which aggregates set-point tracking and disturbance-rejection errors for the controlled variables, by approximately 26.5% relative to the initial controller generated by the workflow, mainly through improved pressure-loop transient performance. This figure quantifies the automated tuning stage rather than a comparison against a manually designed controller. The results demonstrate the feasibility of using structured large-language-model-based code generation to construct executable control-design workflows, while also highlighting the need for broader validation on larger plantwide-control benchmarks.

Multi-Robot Motion Planning in continuous environments, where robots must generate dynamically feasible, collision-free trajectories, is challenging due to the combinatorial growth of the joint trajectory space and the difficulty of enforcing dynamic feasibility and hard safety constraints. Recent approaches recast trajectory planning as probabilistic inference, sampling from a posterior over trajectories using diffusion models whose score functions are learned from demonstration data. While showing promising performance, these approaches are limited: they often rely on sizable demonstration datasets and struggle to rigorously enforce dynamics and hard safety constraints during sampling. To this end, we introduce Model-Based Diffusion Optimal Control (MDOC), a model-based diffusion planner that efficiently produces dynamically feasible trajectories without relying on data. Crucially, we show that MDOC's safety mechanism -- combining known dynamics models with Control Barrier Function-constrained projections -- naturally scales to multi-robot planning settings through Conflict-Based Search. Across simulation experiments, this integrated method consistently outperforms representative baseline planners in sample efficiency, geometric smoothness, and success rate, while reducing computation time and producing collision-free trajectories.

At the limit of handling, a stabilizing MPC depends on the yaw-rate reference it tracks and the stable-handling envelope it enforces, both operating-point-dependent and unknown a priori, so fixed or worst-case settings are either too conservative or unsafe. We learn this uncertainty with a conditional diffusion residual model and apply it to the controller's reference and constraints rather than its control law. Conditioned on the steering command, the model returns the residual's mean and a predictive spread: the mean re-sizes the tracked yaw reference, while the spread, propagated over the prediction horizon, tightens the stable-handling envelope through a one-sided chance back-off. Together these form the proposed diffusion-residual MPC (D-res), so caution is anticipated ahead of the tracking error rather than corrected after it by a high-gain loop. Because only two moments per command are needed, the generator is tabulated offline and the online controller adds a single table lookup to the baseline MPC, with no in-loop diffusion; it runs within the 100 Hz budget on an NVIDIA Jetson AGX Xavier (worst-case 4.08 ms per step). Across a 7-DOF model and high-fidelity CarMaker co-simulation spanning vehicle, tire, road, and maneuver diversity, D-res reduces peak side-slip where the fixed bicycle model is least accurate and restores directional stability on low-friction maneuvers, where the fixed reference over-commands the available grip.

Accurate dynamics modeling of Brushless DC (BLDC) motors is fundamental to high-performance robotic joint control. This paper presents a Physics-Informed Neural Network (PINN) with a deep residual (ResNet) backbone that learns a continuous-time surrogate of the full six-state BLDC motor dynamics. Given simulation time, applied three-phase voltages, and excitation parameters as inputs, the network directly predicts all motor state variables -- rotor angle, angular velocity, three-phase currents, and winding temperature -- while simultaneously satisfying the governing electromechanical and thermal ODEs through a composite physics-data loss. A curriculum scheduling strategy gradually activates the physics penalty to prevent premature convergence. Training runs are completed in under two minutes on a standard CPU. Crucially, once trained, PINN inference achieves latencies of 0.1--22, mu s per query, up to 118x faster than conventional ODE solvers, making it suitable for real-time observer and control applications.

Many phenomena of deep learning are dynamical: they concern not only which minima exist, but how gradient descent reaches, avoids, or selects among them. Edge-of-stability behavior, sharpness oscillations, catapult phases, balancing, and movement toward flatter representations are effects of the training map itself, and are poorly captured by the small-step gradient-flow limit. This paper studies fixed-step gradient descent as a discrete dynamical system in a hierarchy of exactly solvable models retaining basic structures of deep learning: depth, factorization, width, data coupling, activation, and stochasticity. The starting point is the balanced scalar reduction of a deep linear chain, giving a quartic loss and a cubic gradient map whose post-edge behavior is explicit. Under the natural large-depth scaling, this dynamics converges to a universal Ricker-type map. The edge of stability is therefore not a breakdown of optimization, but the first bifurcation of the training map. Embedding the scalar dynamics back into factored models turns these regimes into learning phenomena. Finite steps break conservation laws of gradient flow and contract factorization imbalance; residual oscillations move parameters toward flatter, more balanced representations. Wider linear networks produce a ladder of spectral edges, so the optimal learning rate can lie beyond the first edge. Data coupling, nonlinear activations, and stochastic targets preserve the same organizing principle: finite-step oscillations drive alignment, balancing, and representation selection. Thus the learning rate is not merely a numerical stability parameter. It is a structural parameter of the training dynamics, determining its attractors and shaping the representations gradient descent selects.

In this article, we present dynamic modeling, gait synthesis, and feedback control design for a modular novel subsurface robot, designed for human-free subsurface exploration and excavation. The subsurface propagator design is based on two major aspects: 1) anchor and propel movement like an earthworm and 2) excavation similar to tunnel boring machines. This design is decoupled into five separate modules: one drill head to excavate and create cavity for propagation, two modules to anchor the robot, and two modules to enable propagation of the body. In order to design a controller for each of the modules, dynamic models using the Euler-Lagrange framework are developed. These mathematical models are used as a baseline to design controlled decoupled operation of the different joint movements. The operation of robotic assembly is constructed via a centralized state machine for gait synthesis with integration of the designed feedback controller. The controllers are tested on the real robot geometry to aid sim-to-real integration: A physics-based Unity simulation using a CAD model of the robot and integration of the trained controller via ROS verifies the performance of the robot. The experimental results demonstrate that the proposed design, controllers and the gait synthesis strategy together are capable of anchoring the robot in place and creating an total advancement of 30,mm into the soil after completing 3 gait cycles.

Online latent state estimation constitutes a fundamental challenge within the artificial intelligence field, serving as a foundational tool for diverse applications, including sequential decision making, anomaly and change-point detection. In this paper, a novel online distributed sensing framework, where agents collaborate and exchange information to perform latent state estimation, is presented. The proposed estimator combines available partial domain knowledge with the representation capabilities of deep neural networks. In particular, the designed sensing framework incorporates prior estimates, optimized consensus weights, and Kalman-like recursive updates to perform decentralized inference, without relying on knowledge of noise statistics. Extensive experiments on linear, chaotic (Lorenz), and practical wireless tracking environments reveal that the proposed Covariance-Agnostic Neural Kalman Consensus Filter (CA-NKCF) outperforms traditional distributed Kalman and particle filters as well as purely model-free deep neural networks, exhibiting robustness even when the underlying motion and observation models are misspecified. It is also demonstrated that CA-NKCF's performance advantage remains stable across varying noise levels, random communication topologies, latent state dimensions, and observation clutter densities induced by scattering objects in wireless systems.

A companion study introduced joint durability into the dimensional design of the Theo Jansen walking linkage and found its classical "holy numbers" Pareto-dominated, but it modelled the revolute joints as ideal, clearance-free pins, so its wear figures were relative rankings, not a prediction of in-service degradation. Here we relax that idealization. We build a forward-dynamic model of the Jansen leg in which a revolute joint becomes a clearance joint with a continuous normal contact law (Lankarani-Flores, hysteresis-damped) and Ambrosio friction, integrated as a constraint-stabilized differential-algebraic system, and couple it to the Archard law in a wear->clearance->impact feedback loop. Three findings emerge. First, neglecting clearance underestimates the peak joint load: the clearance model gives a peak contact force of ~104 N at the load-bearing pin against ~48 N for the ideal joint (~2x amplification), rising to ~426 N when two joints carry clearance at once. Second, the coupling is strongly impact-sensitive--single trajectories are non-monotonic and can reverse the design ranking, a chaos consistent with the literature--so designs must be compared statistically; over an ensemble of 16 randomized phases the optimized joint is robustly more durable, with per-cycle wear ~9-7x lower (peak force ~4x lower) at one clearance joint and still ~1.7x lower on both with two (p<0.01 throughout). Third, the wear is strongly non-uniform--it concentrates on a ~10 deg load arc--so assuming uniform clearance growth underestimates local clearance growth by ~36x. The clearance-free durability advantage thus survives the chaotic, multi-joint, non-uniformly-worn coupling in the ensemble mean. We deliver the first clearance-coupled forward-dynamic model of the Jansen leg and specify a falsifiable protocol to test each prediction.

Accurate dynamics models are critical for informed decision-making in robotic systems, particularly for agile aerial vehicles operating under uncertainty. Neural network dynamics models are attractive for capturing complex nonlinear effects, but existing predictive approaches struggle with long-horizon forecasting because their autoregressive rollout mechanism amplifies errors over time. Joint Embedding Predictive Architectures (JEPAs) offer a compelling alternative by modeling dynamics in latent space, yet prior JEPA-style methods for robot navigation have been studied primarily for kinematic-level planning, with limited investigation in high-frequency control. In this work, we introduce the JEPA-style model for real-time quadrotor control. The proposed approach combines a latent dynamics model with a novel physics-inspired prober that maps frozen latents to interpretable state, enabling physically grounded long-horizon prediction. Additionally, we combine the learned model with a sampling-based optimal control solution to take advantage of its predictive capabilities for real-time control on embedded hardware. Finally, to reduce the dependence on expensive and unsafe real-world data collection, we develop a structured pipeline for automated dataset generation. Extensive open-loop and outdoor closed-loop experiments demonstrate accurate prediction, robust zero-shot sim-to-real transfer, and strong generalization across diverse operating conditions.

Machine learning models are increasingly used to model chemical process systems, yet they often lack principled uncertainty quantification and mechanisms to enforce physical constraints. We propose a probabilistic neural network framework that guarantees satisfaction of linear equality constraints within a given tolerance, while capturing aleatoric uncertainty. Compared to state-of-the-art methods, our formulation demonstrates improved predictive accuracy, uncertainty calibration, and adherence to constraints on reduced data. It also demonstrates competitive performance, but with significantly faster training times when evaluated on large data regimes. We evaluated this on two batch reactor case studies, enforcing mass balances.

In this paper, we present a fully discrete approach for the accurate and numerically efficient dynamical modeling and state estimation of continuum robots. The model is based on geometrically exact beams in a minimal, strain-based formulation and derived in the framework of Lie group variational integrators, allowing to preserve important geometric properties that we exploit to achieve high accuracy and numerical efficiency. We then propose a disturbance observer based on an extended Kalman filter formulation that reliably estimates system states as well as model uncertainties and external disturbances. Experiments on a real system validate the accuracy and efficiency of the proposed model and observer.

Modeling soft robot dynamics is challenging due to their continuum structure and typically nonlinear dynamics. Creating models based on first-order principles is typically time-demanding, and their expressiveness is limited, whereas data-driven models lack interpretability and physical consistency. This work aims to overcome these challenges by introducing a port-Hamiltonian Gaussian Process Regression framework for learning and simulating the dynamics of planar, rod-like soft robots. In detail, the proposed model integrates Cosserat rod theory and Hamiltonian physics with data-driven inference to preserve the system's energy structure while accurately learning the rod dynamics. Numerical simulations show that we can achieve accurate and energy-consistent representations of a rod-like soft robot, showing the potential for a robust and interpretable pathway for modeling complex continuum mechanics.

Learned dynamics models often answer global physical questions, such as fault severity or impact stiffness, by pooling a per-step feature sequence into one readout vector. This sequence-to-global interface creates an under-studied temporal credit problem: with only trajectory-level supervision, a model can predict accurately in training conditions while reading from abundant smooth correlates rather than the brief physical events that determine the target. We call this failure temporal credit dilution. It is not exposed by the training loss and is not removed by standard physics-informed residuals, because the error lies in where the global readout assigns functional credit. We introduce Credit-in-Event, an interface-level probe for measuring how much pooled credit lands on event steps, and prove in closed form that a pooled linear reader routes credit to a spurious background channel as the event fraction shrinks. We then propose CREST, a training-free and label-free readout that estimates a transient event core from learned features and re-anchors the pooled representation through event-versus-rest contrast. Across simulated gear and impact systems, recurrent and attention encoders, and public bearing vibration data, CREST reduces out-of-distribution error while restoring event credit. Ablations show that stable-step selection and receptive-field shrinking fail, confirming that the gain comes from event-core credit re-anchoring rather than a generic locality or stability prior.

Biophysical neuron models link measurements of neural activity to underlying cellular mechanisms. Yet, a central challenge is that the kinetics of many ion channels are poorly characterized, and practical simplifications -- omitting channels or reducing morphological detail -- introduce systematic gaps between model and biology. Bridging these gaps requires approaches that can flexibly discover unmodeled dynamics while preserving mechanistic interpretability. Here, we introduce a hybrid modeling framework that embeds neural ordinary differential equations into conductance-based biophysical models to capture unknown currents or mis-specified channel kinetics. By parameterizing the neural ODE in terms of voltage-dependent steady-state and time-constant functions, we recover interpretable gating dynamics directly from voltage recordings without assuming a functional form. We show that the hybrid model fits the gating kinetics of 2400 ion channel models and recovers unknown gating dynamics from single current-clamp recordings, generalizing to out-of-distribution stimulus regimes under realistic inputs and parameter misspecification. We also use our method to reduce a multicompartment model of a cortical neuron into a single-compartment hybrid model with a learned axial current, yielding up to an order of magnitude lower computational cost. Together, our results establish a plug-and-play framework for selectively replacing unknown components of conductance-based models with neural ODEs while preserving their mechanistic structure.

Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.

Many multivariate dynamical systems are observed only through trajectories, leaving the mechanisms governing their joint dynamics hidden. Existing approaches can impose interpretable dynamics or learn flexible state transitions, yet the resulting interaction structure is typically either specified in advance or left implicit within the learned dynamics. We introduce MF-Net, a recurrent dynamical model that represents all variables in a shared field state and updates this state through a learned relation law. Each variable carries a field component, and these components evolve jointly through a learnable mechanical transition. Here, mechanical refers to the relation-to-motion organization of the transition, where learned relations shape state-dependent flows, field responses, and motion tendencies that move the field state forward. The resulting structure is part of the rollout itself: learned relations influence how the field moves, and the same internal quantities support both forecasting and structural readout. Across known-law interaction systems, chaotic benchmarks, real neural recordings, and ecological time series, MF-Net achieves competitive short- and medium-horizon forecasting while retaining inspectable structural readout. On the 40-dimensional Lorenz--96 testbed, MF-Net achieves an eight-step $R^2$ of $0.798\pm0.018$; across five seeds, its learned relation matrix recovers the local coupling support with a local/nonlocal strength ratio of $19.80\pm1.00$ and Precision@$K$ of $1.000\pm0.000$. MF-Net provides a structure-readable dynamical modeling framework in which learned relations are trained through forward evolution and, on real data, interpreted as functional predictive couplings under appropriate observational limits.

Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, and control of model complexity. This paper proposes a Physics-Encoded Modular Hybrid Layer (PE-MHL) framework, in which a baseline physics-based model is incrementally refined through the addition of new sub-models, where each new component adds complexity while preserving what previous components have already learned. We establish a theoretical guarantee for this construction: with a least-squares initialization of each new sub-model, the training error is monotonically non-increasing in the number of sub-models and provably converges. Empirical evaluations on a nonlinear NARX benchmark and the Quanser Aero 2 platform demonstrate that PE-MHL outperforms equivalently sized monolithic networks in both accuracy and generalization, while also providing more stable training dynamics and better preservation of underlying data structures.

This paper examines three approaches for modeling the dynamics of a flexible-link 2-DoF robotic arm to address unmodeled dynamics not captured by rigid-body models. Two physics informed models combine rigid-body dynamics (RBD) formulations with a Gaussian Mixture Model (GMM) to capture residual model errors and linkage flexibility. A kinematics-based regression model serves as a purely data-driven baseline. Using an open-source dataset, torque predictions are first estimated using Ridge regression on kinematic features, while the physicsbased baseline is constructed from published specifications, and ordinary least-squares regression is subsequently used to estimate the same parameter set directly from data. Results show that the physics-based parameters yield the poorest accuracy, while regularized and least-squares estimators align more closely with measured torques. Residual analysis and error metrics highlight the limitations of purely parametric models for flexible-link systems and underscore the value of regularization and data-driven identification, supporting developments of semi-parametric residual learning methods.

Accurate prediction of polymerization dynamics is essential for process design, control, and optimization. Yet, purely mechanistic models require labor-intensive parameterization of partially characterized kinetics, while purely data-driven models demand large, diverse datasets that are costly to obtain, particularly in early-design stages. We propose a hybrid Neural Ordinary Differential Equation (NODE) framework for data-efficient modeling of free-radical polymerization. Using batch polymerization of methyl methacrylate (MMA) as a case study, the mechanistic mass balances are retained explicitly, and only the partially-characterized effective radical concentration governing monomer consumption is learned from data through a neural network surrogate, while established reactions such as initiator decomposition, propagation, and termination remain physically modeled. The hybrid NODE is evaluated against a discrete-time feedforward neural network and a purely data-driven NODE under sparse data conditions, with models trained on as few as ten measurements under both regular and irregular sampling. The hybrid NODE consistently achieves lower prediction errors and more physically consistent extrapolations than both purely data-driven baselines. In a generalization scenario with noisy data and unseen operating conditions, the hybrid NODE achieves an RMSE of 0.013, compared to 0.31 for the data-driven NODE and 0.68 for the discrete-time model, demonstrating that learning only a closure term rather than the full dynamics is sufficient for reliable prediction under limited data availability.

Machine learning (ML) is increasingly used for data-driven modeling of buildings to enable downstream tasks such as fault detection and diagnosis, and energy-efficient control. While recent work improves generalization across building characteristics, weather, and occupancy, generalization also depends on sufficient exploration of the control-driven system state space. Existing real-world datasets and simulation environments predominantly reflect stationary operation under fixed control policies, resulting in limited excitation and reduced robustness to unseen operating conditions. This paper introduces BuilDyn, a package based on BuilDa that enables customizable excitation strategies for control-oriented data generation. BuilDyn further supports sampling from representative building distributions and provides a Python interface for easy integration into machine learning pipelines. We demonstrate the benefits of BuilDyn by comparing the performance of data-driven ML models trained on non-excited and excited data for one building. With BuilDyn, we hope to advance scalable control-oriented modeling and support future directions such as transfer learning and building-specific foundation models.

In many industrial domains, the Functional Mock-up Interface (FMI) is used to exchange simulation models as Functional Mock-up Units (FMUs) across different partners using various modelling tools. This opens up the possibilities for simulation-based verification and validation using FMUs for ensuring reliable system behaviour. However, deriving effective test oracles for these simulation models remains challenging due to the absence of explicit expected outputs. This limits the applicability of conventional testing approaches, which require access to the internal workings of the systems. Metamorphic testing (MT) addresses this limitation by leveraging metamorphic relations (MRs), but extracting such relations from specifications remains largely a manual and error-prone process. To address this challenge, we propose an LLM-powered multi-agent workflow for specification-based metamorphic testing of FMU-based simulation models. The approach takes functional and interface specifications as input and orchestrates multiple agents to extract requirements and derive MRs. These MRs are expressed using Given-When-Then patterns to structure input conditions (Given), transformations (When), and expected output behaviours (Then). These relations are then used to generate metamorphic test cases, execute simulations, and evaluate output consistency across multiple sessions. We evaluate the approach on a Lube Oil Cooling system FMU, demonstrating its ability to automatically generate meaningful MRs and corresponding test cases. Preliminary results indicate that the proposed workflow can effectively support the systematic verification and validation of dynamic simulation models by reducing manual effort and improving test generation.

Developing dynamic models for tendon-driven continuum robots is challenging due to their nonlinear, high-dimensional, and friction-dominated dynamics. This paper presents a comparative study of data-driven system identification methods, including N4SID, ARX, and SINDYc, for modeling a tendon-actuated continuum robot with rolling joints developed at CERN. Despite the high number of joints of the robot, experimental analysis reveals that a two-degree-of-freedom dynamic model can accurately capture the system dynamics, owing to strong kinematic dependencies between the joints. The models are validated against experimental data, and used in the design of a model predictive controller, demonstrating their feasibility for real-time control.

Model merging enables the reuse of fine-tuned models without joint training or access to original data. Dynamic merging further improves flexibility by selectively activating task-relevant parameters and efficiently composing experts across multiple tasks. However, existing dynamic methods either maintain a full shared model with tiny experts or allocate excessive capacity to experts, leading to suboptimal accuracy--efficiency trade-offs. To address this, we propose DiDi-Merging, a slim dynamic merging framework that leverages differentiable rank allocation to balance shared and expert parameters. By formulating parameter budgeting as differentiable rank optimization in low-rank modules and introducing a data-free refinement step to recover task fidelity, DiDi-Merging matches prior dynamic baselines at only 1.24x the parameters of a single fine-tuned model and surpasses them at 1.4x, substantially more compact than methods requiring > 2x storage. DiDi-Merging applies across vision, language, and multimodal tasks.

Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often contain hierarchical annotations and known transition priors, existing UOT approximations rarely exploit this multiscale structure or prior knowledge. We introduce Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST-FM), a simulation-free framework that scales UOT by leveraging hierarchical data structure. MUST-FM further supports an optional supervised formulation that incorporates transition priors, such as cell lineages, to guide the learning of displacement fields and mass variations. Experiments show that MUST-FM reduces computational overhead while achieving robust and biologically meaningful trajectory inference, enabling dynamic modeling of atlas-scale single-cell datasets.

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.

Classical planners can effectively solve very large deterministic MDPs represented in STRIPS or PDDL where states are sets of atoms over objects and relations, and lifted action schemas add or delete these atoms. This compact representation yields strong search heuristics and provides an ideal setting for structural generalization, since lifted relations and action schemas give rise to infinitely many domain instances. A central challenge is to learn these relations and action schemas from data, and recent approaches have addressed this problem using different types of observations. In this work, we develop a novel neural network architecture for learning action schemas from traces where states are fully observed but action arguments are unobserved. The problem is a simplification but an important step towards learning planning domains from sequences of images and action labels, and we aim to solve this simplification in a nearly perfect manner. The challenge lies in learning the action schemas while simultaneously identifying the action arguments from observed state changes. Our approach yields a robust differentiable component that can then be integrated into larger neuro-symbolic models. We evaluate the architecture on various planning domains, where the learned lifted action schemas must recover the ground-truth structure. Additionally, we report experiments on robustness to observation noise and on a variation related to slot-based dynamics models.

Rich feature learning in tasks that unfold over time often requires the model to pass through bifurcations, constituting qualitative changes in the underlying model dynamics. We develop a local theory of gradient descent near these transitions through the empirical state-space neural tangent kernel (sNTK). Our central finding is that bifurcations both dominate and simplify learning dynamics: near bifurcations, we can reduce sNTK to a rank-one operator corresponding to learning in a classical normal form system, providing an analytically tractable description of the local learning geometry, even for high-dimensional recurrent systems. Concretely, we give a procedure for decomposing sNTK into bifurcation-relevant and residual channels, showing that near commonly codimension-1 bifurcations the relevant channel is a rank-one operator that is highly amplified. This amplification causes the bifurcation channel to dominate the full sNTK. Thus, bifurcations locally warp the learning landscape, funneling gradient descent into a few critical dynamical directions and making the nearby kernel and loss geometry predictable from classical normal forms. We illustrate this in a student-teacher recurrent neural network: the first learned bifurcation coincides with a sharp collapse in sNTK effective rank and the emergence of a dominant parameter direction whose restricted sNTK closely matches the landscape predicted by the scalar pitchfork normal form. Finally, we show that low-rank natural gradient methods resolve the resulting learning instability near bifurcations with very little overhead over SGD.

Over the years, research in system identification has provided a rich set of methods for learning dynamical models, together with well-established theoretical guarantees. In practice, however, the choice of model class, training algorithm, and hyperparameter tuning is still largely left to empirical trial-and-error, requiring substantial expert time and domain experience. Motivated by recent advances in agentic artificial intelligence, we present ASIA, a framework that delegates this iterative search to a large language model acting as an autonomous coding agent. Building on existing agentic platforms, ASIA closes the loop between hypothesis, implementation, and evaluation without human intervention, requiring only a plain-English description of the identification problem. We conduct an empirical study of ASIA on two system identification benchmarks and analyse the agent's search behaviour, the architectures and training strategies it discovers, and the quality of the resulting models. We also discuss the potential of the approach and its current limitations, including implicit test leakage, reduced methodological transparency, and reproducibility concerns.

Unlike most static material properties widely studied in the machine learning literature, ionic transport properties are inherently dynamic, making their fast and accurate prediction from static atomic structures challenging. The current standard approach, molecular dynamics (MD) simulations, suffers from prohibitively high computational cost. Recent autoregressive learning-based MD acceleration methods requiring sequential inference remain slow and prone to error accumulation; in contrast, existing non-autoregressive material property prediction models are less accurate because they fail to exploit dynamics. Moreover, existing methods typically benefit from datasets either with or without atomic trajectories, but not both. To overcome these limitations, we propose a non-autoregressive learning framework based on auxiliary modality learning, which treats atomic trajectories as an auxiliary modality during training but does not require them at inference. This enables the predictor to learn dynamics without sequential inference while benefiting from both types of datasets. As a result, our framework achieves over 200 times speedup compared to autoregressive models on the dataset with atomic trajectories while substantially reducing prediction error relative to non-autoregressive benchmarks across both types of datasets. Our code is available at https://github.com/jykim-git/MD.

Qualitative models provide crucial instruments for modelling complex biological systems. While advances in automated reasoning and symbolic encodings have enabled rigorous inference of these models from data, the process remains highly fragile. First, biological measurement errors inevitably propagate into formal model specifications. Second, when a specification becomes unsatisfiable, distinguishing between fundamental design flaws and minor technical errors is notoriously difficult. This uncertainty often leads to under-specification, as it is unclear which observations are still ``safe'' to incorporate. To overcome these challenges, we introduce a robust inference method based on weighted MaxSMT. By encoding uncertain biological observations as weighted soft constraints, our approach enables the solver to identify a model best reflecting the observations, even with some conflicting constraints. Our method allows for Boolean and multi-valued variable domains, alongside observations derived from discretisation (level constraints) and differential expression (ordering constraints). We show our approach can be used to successfully infer neural cell differentiation models from prior-knowledge networks with 200--1300 genes using ordering constraints on all included genes.

The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons $T$. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the $T$-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.

We propose a causal reasoning framework for creative robot tool use where a suitable tool for a task is correctly identified for use beyond its primary objectives. The proposed framework first discovers the causal relationships between the tool and the task by conducting simulated experiments in a dynamics model. We decouple the causal discovery problem into two complementary components: VLM-based feature suggestion and counterfactual tool generation via targeted geometric and physical feature perturbations. Then, novel objects are classified based on identified causal features, and the tool use skill is transferred via keypoint matching conditioned on the identified causal features. By reconstructing the task in a dynamics model, our approach grounds tool use in the physics of the problem. We illustrate our approach in reaching a distant object with different sticks, scooping candies from a bowl using diverse items, and using different boxes or crates as stepping platforms to retrieve an object from a high shelf. Our baseline comparisons show that identifying causal features and grounding them in physical tool properties leads to more reliable tool selection and stronger skill keypoint transfer.

This paper mainly studies the accurate height jumping control of wheeled-bipedal robots based on torque planning and energy consumption optimization. Due to the characteristics of underactuated, nonlinear estimation, and instantaneous impact in the jumping process, accurate control of the wheeled-bipedal robot's jumping height is complicated. In reality, robots often jump at excessive height to ensure safety, causing additional motor loss, greater ground reaction force and more energy consumption. To solve this problem, a novel wheeled-bipedal jumping dynamical model(W-JBD) is proposed to achieve accurate height control. It performs well but not suitable for the real robot because the torque has a striking step. Therefore, the Bayesian optimization for torque planning method(BOTP) is proposed, which can obtain the optimal torque planning without accurate dynamic model and within few iterations. BOTP method can reduce 82.3% height error, 26.9% energy cost with continuous torque curve. This result is validated in the Webots simulation platform. Based on the torque curve obtained in the W-JBD model to narrow the searching space, BOTP can quickly converge (40 times on average). Cooperating W-JBD model and BOTP method, it is possible to achieve the height control of real robots with reasonable times of experiments.

Model merging has attracted attention as an effective path toward multi-task adaptation by integrating knowledge from multiple task-specific models. Among existing approaches, dynamic merging mitigates performance degradation caused by conflicting parameter updates across tasks by flexibly combining task-specific parameters at inference time, thereby maintaining high performance. However, these methods require storing independent parameters for each task, resulting in prohibitive storage overhead. To address this issue, we first experimentally demonstrate that the fine-tuned weight increments (referred to as task vectors) exhibit an impulse-like activation pattern and high robustness to low-bit representations. Driven by this insight, we propose T-Switch, which decomposes task vectors into three compact components: a binary sparse mask, a sign vector, and a scalar scaling factor, achieving high-fidelity approximation at high compression ratios. We then introduce Auto-Switch, a training-free merging scheme that automatically composes task vectors via feature similarity retrieval. Building on this, we develop Auto-Switch, a training-free merging scheme that automatically assembles task vectors through feature similarity retrieval. Furthermore, to transform task vector sparsification and quantization from static rules to adaptive learning, we propose FlexSwitch, a learnable framework which jointly optimizes the compression strategy for each model unit via Learnable Gating Sparsification (LGS) and Bit-width Adaptive Selection (BAS), while employing the Sparsity-Aware Storage Strategy (SASS) to select the optimal storage encoding structure. Finally, by incorporating a K-Nearest Neighbor (KNN) inference scheme with a learnable low-rank metric, we present Auto-FlexSwitch, a dynamic model merging approach that supports highly efficient task vector compression.

In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performance for specific Bayesian model updating problems. However, a common challenge with these approaches lies in the fact that the embedded neural networks often necessitate retraining when faced with new tasks, a process that is time-consuming and significantly undermines the competitiveness of these methods. This paper introduces a newly developed adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo (AM-SGHMC) algorithm. The idea behind AM-SGHMC is to optimize the sampling strategy by training adaptive neural networks, and due to the adaptive design of the network inputs and outputs, the trained sampler can be directly applied to various Bayesian updating problems of the same type of structure without further training, thereby achieving meta-learning. Additionally, practical issues for the feasibility of the AM-SGHMC algorithm for structural dynamic model updating are addressed, and two examples involving Bayesian updating of multi-story building models with different model fidelity are used to demonstrate the effectiveness and generalization ability of the proposed method.

Tendon-Driven Continuum Robots (TDCRs) pose significant modeling and control challenges due to complex nonlinearities, such as frictional hysteresis and transmission compliance. This paper proposes a differentiable learning framework that integrates high-fidelity dynamics modeling with robust neural control. We develop a GRU-based dynamics model featuring bidirectional multi-channel connectivity and residual prediction to effectively suppress compounding errors during long-horizon auto-regressive prediction. By treating this model as a gradient bridge, an end-to-end neural control policy is optimized through backpropagation, allowing it to implicitly internalize compensation for intricate nonlinearities. Experimental validation on a physical three-section TDCR demonstrates that our framework achieves accurate tracking and superior robustness against unseen payloads, outperforming Jacobian-based methods by eliminating self-excited oscillations. For implementation details and source code, please refer to https://github.com/ZiqingZou/ContinuumControl.

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.

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.

Digital twins of natural systems must remain aligned with physical systems that evolve over time, are only partially observed, and are typically modeled by mechanistic simulators whose parameters cannot be measured directly. In such settings, model adaptation is naturally posed as a simulation-based inference problem. However, sparse and indirect observations often fail to identify a unique and optimal calibration, leaving several simulator parameterizations compatible with the available evidence. This article presents a GFlowNet-based approach to model adaptation for digital twins of natural systems. We formulate adaptation as a generative modeling problem over complete simulator configurations, so that plausible parameterizations can be sampled with probability proportional to a reward derived from agreement between simulated and observed behavior. Using a controlled environment agriculture case study based on a mechanistic tomato model, we show that the learned policy recovers dominant regions of the adaptation landscape, retrieves strong calibration hypotheses, and preserves multiple plausible configurations under uncertainty.

Capturing both geometry and rigid motion for structured dynamic objects, like multi-part assemblies or jointed mechanisms, remains a key challenge. Existing dynamic methods, such as deformable meshes or 3DGS, rely on unstructured representations and fail to jointly model suitable geometry and articulated motion. Primitive-based methods excel at structured static scenes, but their dynamic potential is still unexplored. We propose D-Prism, the first framework to achieve high-fidelity structured dynamic modeling by extending differentiable primitives to the dynamic domain. Specifically, we bind 3DGS to primitive surfaces, leveraging their respective strengths in appearance and geometry. We introduce a deformation network to control primitive motion, ensuring it accurately matches the object's movement. Furthermore, we design a novel adaptive control strategy to dynamically adjust primitive counts, better matching objects' true spatial footprint. Experiments confirm that our method excels at structured dynamic modeling, providing both structured geometry and precise motion tracking.

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.

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to theoretical understanding, interpretability, and generalization. To address these issues, researchers are increasingly adopting a differential equations perspective to propose a unified theoretical framework and systematic design methodologies for neural networks. In this paper, we provide an extensive review of deep neural network architectures and dynamic modeling methods inspired by differential equations. We specifically examine deep neural network models and deterministic dynamical network constructs based on ordinary differential equations (ODEs), as well as regularization techniques and stochastic dynamical network models informed by stochastic differential equations (SDEs). We present numerical comparisons of these models to illustrate their characteristics and performance. Finally, we explore promising research directions in integrating differential equations with deep learning to offer new insights for developing intelligent computational methods that boast enhanced interpretability and generalization capabilities.

Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.

Background: Causal loop diagrams (CLDs) are widely used in health and environmental research to represent hypothesized causal structures underlying complex problems. However, as qualitative and static representations, CLDs are limited in their ability to support dynamic analysis and inform intervention strategies. We propose Diagrams-to-Dynamics (D2D), a method for converting CLDs into exploratory system dynamics models in the absence of empirical data. With minimal user input - following a protocol to label variables as stocks, flows or auxiliaries, and constants - D2D utilizes the structural information already encoded in CLDs, namely the existence and polarity of causal connections, to simulate hypothetical interventions and explore potentially influential places to intervene, known as 'leverage points,' under uncertainty. Results: D2D helps distinguish between high- and low-ranked leverage points. We compare D2D to a calibrated system dynamics model constructed from the same CLD and variable labels. D2D showed greater consistency with the calibrated model than did static network centrality analysis, while also providing uncertainty estimates and guidance for future data collection. Conclusions: The D2D method is implemented in an open-source Python package and a web-based application to support further testing and to lower the barrier to dynamic modeling for researchers working with CLDs. Future studies could help establish the approach's utility across a broad range of cases and domains.

Robot learning has produced remarkably effective ``black-box'' controllers for complex tasks such as dynamic locomotion on humanoids. Yet ensuring dynamic safety, i.e., constraint satisfaction, remains challenging for such policies. Reinforcement learning (RL) embeds constraints heuristically through reward engineering, and adding or modifying constraints requires retraining. Model-based approaches, like control barrier functions (CBFs), enable runtime constraint specification with formal guarantees but require accurate dynamics models. This paper presents SHIELD, a layered safety framework that bridges this gap by: (1) training a generative, stochastic dynamics residual model using real-world data from hardware rollouts of the nominal controller, capturing system behavior and uncertainties; and (2) adding a safety layer on top of the nominal (learned locomotion) controller that leverages this model via a stochastic discrete-time CBF formulation enforcing safety constraints in probability. The result is a minimally-invasive safety layer that can be added to the existing autonomy stack to give probabilistic guarantees of safety that balance risk and performance. In hardware experiments on an Unitree G1 humanoid, SHIELD enables safe navigation (obstacle avoidance) through varied indoor and outdoor environments using a nominal (unknown) RL controller and onboard perception.