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

TL;DR

The paper presents a neural network architecture that ensures safety by design for dynamical systems using energy-based modern Hopfield networks integrated with port-Hamiltonian neural ODEs. This approach enables the automatic construction of barrier functions that define invariant sets and quantify robustness to disturbances. It outperforms existing methods in safety certification and robustness across multiple benchmarks, including a high-dimensional nanodrone model.

Why It Matters

Safety-critical applications like autonomous drones and robotics require guaranteed system behavior under all conditions. This method provides formal safety guarantees during training, eliminating the need for post-hoc verification and enabling reliable deployment in real-world environments.

Key Findings

• The proposed architecture integrates modern Hopfield networks with port-Hamiltonian neural ODEs to enforce safety by design.
• It generates explicit barrier functions that define invariant sets and compute robustness radii for admissible inputs.
• The framework achieves superior safety robustness and performance compared to state-of-the-art methods on complex dynamical systems.