arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
By Frederik Baymler Mathiesen, Nikolaus Vertovec, Francesco Fabiano, Luca Laurenti, Alessandro Abate
arXiv:2607. 17614v1 Announce Type: cross Abstract: Recent advances in deep-learning-based nonlinear system identification have led to encoder-based estimation of neural state-space (ANN-SS) models that achieve state-of-the-art performance in offline settings by estimating initial model states from past input-output data.
By Bendeg\'uz Gy\"or\"ok, Tam\'as P\'eni, Maarten Schoukens, Roland T\'oth
arXiv:2610.27970v1 Announce Type: cross
Abstract: Neural networks are expressive models of nonlinear dynamics, but identifying such systems from closed-loop data raises two difficulties: the feedback...
By Laura Meroi, Mahrokh G. Boroujeni, Leonardo Massai, Giancarlo Ferrari-Trecate
The paper introduces a finite‑dimensional sensitivity framework called the Learning Stability Profile, which captures how perturbations in inputs, parameter initialization, and update mechanisms propagate along a learning trajectory. It presents a Lyapunov criterion that, under regularity, coercivity, and dissipation assumptions, yields uniform or exponentially decaying bounds on linearized transition operators, distinguishing between terminal decay, boundedness, and subexponential growth. The framework is applied to various learning mechanisms—including feedforward networks, residual architectures, stochastic gradient methods, and locally Lipschitz systems—providing spectral, dissipativity, and contraction‑based stability bounds.
By Ronald Katende
The article introduces deep Bayesian filtering techniques for nonlinear structural system identification, emphasizing how learnable dynamics can be integrated with physical inductive biases to achieve uncertainty-aware inference. It reviews key models such as the Deep Markov Model, Physics-guided Deep Markov Model, and Neural Extended Kalman Filter, and evaluates them on a three‑dimensional shear‑frame benchmark with hysteretic Bouc‑Wen connections. The study compares measurement‑conditioned reconstruction versus open‑loop forecasting, explores the impact of physical structure on latent‑state interpretability, and discusses robustness in response and parameter estimation, offering practical guidelines for model construction and deployment.
By Wei Liu, Konstantinos Vlachas, Eleni Chatzi
arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.
By Jiale Gong (School of Mathematics), Pengzhan Jin (National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China), Dongyang Kuang (School of Mathematics), Lu Li (School of Mathematics), Yifa Tang (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)