HJRNO: Hamilton-Jacobi Reachability with Neural Operators

Abstract: Ensuring the safety of autonomous systems under uncertainty is a critical challenge. Hamilton-Jacobi reachability (HJR) analysis is a widely used method for guaranteeing safety under worst-case disturbances. In this work, we propose HJRNO, a neural operator-based framework for solving backward reachable tubes (BRTs) efficiently and accurately. By leveraging neural operators, HJRNO learns a mapping between value functions, enabling fast inference with strong generalization across different obstacle shapes and system configurations. We demonstrate that HJRNO achieves low error on random obstacle scenarios and generalizes effectively across varying system dynamics. These results suggest that HJRNO offers a promising foundation model approach for scalable, real-time safety analysis in autonomous systems.