arXiv:2609.36942v1 Announce Type: cross
Abstract: Learning neural-network models of dynamical systems with safety guarantees is a fundamental requirement for their deployment in safety-critical setti...
By Simone Betteti, Morteza Lahijanian, Luca Laurenti
arXiv:2609. 16298v1 Announce Type: new Abstract: Despite recent advances in the verification of nonlinear neural feedback systems, scalability remains the central obstacle, as state-of-the-art solvers do not yet handle the network sizes and nonlinear dynamics of autonomy applications.
By I. Samuel Akinwande, Mykel J. Kochenderfer, Clark Barrett
The paper presents a theoretical framework for certifying the accuracy of physics‑informed neural networks (PINNs) used to solve partial differential equations. It derives generalization bounds that link the residual loss minimized during training to the actual error in the solution space, showing that if the neural approximation stays within a compact subset, a vanishing residual guarantees convergence to the true solution. Deterministic and probabilistic convergence results are provided, offering explicit error guarantees based on residual, boundary, and initial condition errors.
By Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fern\'andez, Jun Liu
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
By Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
By JR Huml, Jonathan Wenger, John P. Cunningham
arXiv:2606. 09746v1 Announce Type: cross Abstract: With AI increasingly deployed in safety-critical systems, providing formal robustness guarantees for the underlying models is essential.
By Sherwin Varghese, Matthew Wicker, Alessio Lomuscio