Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

TL;DR

This paper introduces a data-driven reachability analysis method for nonlinear systems using diffusion models, providing PAC guarantees and scaling beyond traditional approaches.

Contribution

It develops a novel diffusion model-based framework for reachability analysis that requires no explicit system model and offers probabilistic guarantees.

Findings

Empirically maintains miss rate below PAC bounds.

Scales to high-dimensional systems beyond classical methods.

Validated on diverse nonlinear systems.

Abstract

We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the form of a sublevel set of a nonconformity score derived from the reconstruction error, with the threshold calibrated via the Learn Then Test procedure so that the probability of excluding a reachable state is bounded with high probability. Experiments on three nonlinear systems, a forced Duffing oscillator, a planar quadrotor, and a high-dimensional reaction-diffusion system, confirm that the empirical miss rate remains below the Probably Approximately Correct (PAC) bound while scaling to state dimensions beyond the reach of classical grid-based and polynomial methods.