Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees
This provides a scalable, data-driven solution for safety-critical applications in control and robotics, though it is incremental as it builds on existing diffusion and conformal prediction methods.
The authors tackled the problem of reachability analysis for nonlinear dynamical systems without requiring an explicit model, by using a denoising diffusion probabilistic model trained on trajectory data to predict reachable sets with Probably Approximately Correct (PAC) guarantees, achieving empirical miss rates below the bound across systems including a high-dimensional reaction-diffusion case.
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.