Safe-by-Design Learning via Energy-based Neural Networks

Abstract:Learning neural-network models of dynamical systems with safety guarantees is a fundamental requirement for their deployment in safety-critical settings. Safety is commonly established by proving the invariance of a desired subset in state-space, ensuring that every trajectory initialized in this subset remains confined to it for all time under admissible inputs. Existing frameworks, however, either rely on computationally expensive post-hoc verification or employ safety-enforcing mechanisms without formal correctness guarantees. In this paper, we introduce a novel neural architecture grounded in energy-based modern Hopfield networks to guarantee safety-by-design while retaining sufficient expressiveness to model complex nonlinear dynamics. Specifically, we integrate modern Hopfield networks with a port-Hamiltonian neural ODE, enabling by design the construction of barrier functions yielding explicit admissible-input sets and quantitative robustness radii. Across several benchmarks, including an 12-dimensional nanodrone model, our framework achieves state-of-the-art performance while producing certified invariant sets that are more robust to external solicitations than comparable existing approaches.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Systems and Control (eess.SY)

arXiv:2609.36942 [cs.LG]

(or arXiv:2609.36942v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.36942 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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