用扩散模型从数据学习非线性系统可达集，保证高概率不遗漏真实状态。
Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees
- 基于轨迹数据训练扩散模型，直接学习系统状态随时间演化的分布。
- 预测的可达集满足PAC边界，实测漏检率低于理论上限。
- 适用于高维系统，突破传统网格和多项式方法的维度限制。
我们提出一种无需显式模型的非线性动力系统可达性分析的数据驱动框架。通过去噪扩散概率模型仅从轨迹数据中学习系统状态随时间演化的分布。预测的可达集以重构误差导出的非一致性评分的子水平集形式呈现，阈值通过“学后检验”程序校准，确保排除可达状态的概率在高概率下受控。在三个非线性系统上的实验——受迫Duffing振子、平面四旋翼飞行器以及高维反应-扩散系统——验证了经验漏检率始终低于可能近似正确（PAC）边界，且可扩展至经典网格法与多项式方法无法处理的高维状态空间。
原文摘要 · Abstract (English)
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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