Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

• URL: http://arxiv.org/abs/2604.00283v1
• Date: Tue, 31 Mar 2026 22:14:36 GMT
• Title: Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees
• Abstract summary: We present a data-driven framework for reachability analysis of nonlinear dynamical systems.<n>A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone.
• Score: 3.651951296125688
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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