Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations
arXiv:2603.19545v2 Announce Type: replace-cross Abstract: Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equations. Physics-informed neural networks (PINNs) have emerged as a promising mesh-free approach for approximating their solutions, but in most existing works there is no rigorous guarantee that a small PDE residual implies a small solution error. This paper develops verifiable error bounds for approximate solutions of Lyapunov and HJB equations, with particular
The increasing complexity of AI systems necessitates robust methods for verifying their outputs, especially in critical applications like control systems.
This development addresses a fundamental limitation of physics-informed neural networks (PINNs), enhancing their trustworthiness and expanding their applicability in high-stakes fields.
The ability to rigorously quantify error bounds for PINN solutions reduces the barrier to adoption for these powerful AI tools in areas requiring verifiable correctness.
- · AI developers
- · Automation engineers
- · Aerospace & Defence
- · Energy sector
Increased real-world deployment of PINN-based control systems and optimization algorithms.
Faster design and validation cycles for complex engineering solutions across various industries.
New safety standards and regulatory frameworks emerging to incorporate verified AI systems in critical infrastructure.
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Read at arXiv cs.LG