Problem
Research questions and friction points this paper is trying to address.
Safety guarantees
Dynamical systems
Invariant sets
Neural network learning
Safety-critical settings
Safe-by-Design Learning via Energy-based Neural Networks
🤖 AI Summary
This study addresses the lack of formal guarantees and high verification costs associated with neural networks for dynamical systems in safety-critical scenarios by proposing an energy-based "safe-by-design" architecture. The proposed method integrates modern Hopfield networks with port-Hamiltonian neural ordinary differential equations to directly synthesize explicit barrier functions and robustness radii, thereby eliminating the need for post-hoc verification. Experimental evaluations demonstrate that this model achieves state-of-the-art performance on benchmark tasks, including a 12-dimensional nano-drone system. Furthermore, the certified invariant sets produced by the framework exhibit significantly enhanced robustness against external disturbances compared to existing approaches.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Energy-based Neural Networks
Modern Hopfield Networks
Port-Hamiltonian Neural ODE
Safety-by-Design
Barrier Functions
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