Title: Certified Neural Approximations of Nonlinear Dynamics

Abstract:

Neural networks offer significant promise as surrogate models for nonlinear dynamical systems, facilitating their verification and control through neural approximations. However, deploying these approximations in safety-critical applications necessitates formal guarantees regarding their fidelity to the true underlying system. To resolve this core issue, we introduce a new verification framework that is adaptive, parallelizable, and grounded in certified first-order models. This methodology delivers rigorous error bounds for neural approximations of dynamical systems, thereby permitting their safe utilization as surrogates by treating the error bound as a bounded disturbance within the approximated dynamics. Our experimental evaluation on various standard benchmarks from existing literature demonstrates that our approach not only scales effectively but also substantially surpasses current state-of-the-art techniques. Additionally, we illustrate the framework’s capability to tackle previously unsolvable challenges, including neural network compression and the training of Koopman operators via an autoencoder-based deep learning architecture for trajectory prediction.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC