STEER2REACH: New PINN solver accelerates Hamilton-Jacobi safety verification

Hamilton-Jacobi (HJ) reachability analysis provides mathematically rigorous safety guarantees for dynamical systems, but solving the underlying Hamilton-Jacobi-Isaacs PDEs becomes computationally intractable in high dimensions. Physics-informed neural networks (PINNs) have emerged as a scalable alternative to classical mesh-based solvers, yet they are notoriously sensitive to how collocation points are sampled during training. Existing PINN-based HJ solvers often require complex training pipelines and auxiliary supervision to achieve accurate safety value functions, limiting their practical adoption.

In a new paper accepted to IEEE CDC 2026, Sungje Park and Stephen Tu propose STEER2REACH (S2R), a PINN-based HJ reachability solver that needs only a lightweight addition to standard PINN training. S2R's core innovation is an adaptive collocation sampling distribution built by steering forward trajectories using the optimal control and disturbance signals derived from the current value function, augmented with stochastic exploration noise. Despite its simplicity, S2R achieves competitive and sometimes better safety metrics than state-of-the-art MPC-guided solvers, while reducing relative L2 error on multiple reachability benchmarks—and it does so without multi-stage training or MPC-based supervision. The results suggest that intelligently focusing samples along dynamically relevant trajectories can replace expensive supervisory pipelines, making high-dimensional safety verification more practical.