PING: A Physics-Informed Neuro-Symbolic Generator for Continuous-Time Planning

We present PING (Physics-Informed Neuro-Symbolic Gener-ator), a novel, continuous planning framework that leverages untrained neural networks as generative function approxima-tors to synthesize high-fidelity trajectory candidates without data or training. Departing from conventional hybrid planners that oscillate between discrete search and numerical optimization, PING operates natively in continuous function-valued action spaces, embedding symbolic constraints directly into the generation process. We introduce a generative mechanism where neural networks produce function-space candidates that are structurally guaranteed to satisfy boundary conditions using symbolic rules, thereby circumventing discretization artifacts and the local minima traps inherent to gradient-based trajectory optimization. To ensure feasibility, a rigorous verification engine exploits automatic differentiation to validate candidates against domain-specific differential equations and manifold constraints. This architecture enables a dual-mode strategy: a primary generation phase for rapid solution synthesis, backed by an iterative refinement mechanism when validation fails. By decoupling generation from optimization, PING provides a training-free framework that can be instantiated for different domains via domain-specific dynamics and constraints. Empirical evaluation across navigation, reservoir control, and HVAC domains demonstrates highly efficient runtime performance and broader coverage, with planning latencies reduced to seconds through massive parallel verification of thousands of symbolic candidates.