Neural Continuous-Time Supermartingale Certificates

• URL: http://arxiv.org/abs/2412.17432v1
• Date: Mon, 23 Dec 2024 09:51:54 GMT
• Title: Neural Continuous-Time Supermartingale Certificates
• Authors: Grigory Neustroev, Mirco Giacobbe, Anna Lukina,
• Abstract summary: We introduce for the first time a neural-certificate framework for continuous-time dynamical systems.<n>Inspired by the success of training neural Lyapunov certificates for deterministic continuous-time systems, we propose a framework that bridges the gap between continuous-time and probabilistic neural certification.
• Score: 7.527234046228324
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce for the first time a neural-certificate framework for continuous-time stochastic dynamical systems. Autonomous learning systems in the physical world demand continuous-time reasoning, yet existing learnable certificates for probabilistic verification assume discretization of the time continuum. Inspired by the success of training neural Lyapunov certificates for deterministic continuous-time systems and neural supermartingale certificates for stochastic discrete-time systems, we propose a framework that bridges the gap between continuous-time and probabilistic neural certification for dynamical systems under complex requirements. Our method combines machine learning and symbolic reasoning to produce formally certified bounds on the probabilities that a nonlinear system satisfies specifications of reachability, avoidance, and persistence. We present both the theoretical justification and the algorithmic implementation of our framework and showcase its efficacy on popular benchmarks.

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