We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a dataset of $K$-step trajectories. The reachability problem is to construct a probabilistic flowpipe such that the probability that a $K$-step trajectory can violate the bounds of the flowpipe does not exceed a user-specified failure probability threshold. The key ideas in this paper are: (1) to learn a surrogate predictor model from data, (2) to perform reachability analysis using the surrogate model, and (3) to quantify the surrogate model's incurred error using conformal inference in order to give probabilistic reachability guarantees. We focus on learning-enabled control systems with complex closed-loop dynamics that are difficult to model symbolically, but where state transition pairs can be queried, e.g., using a simulator. We demonstrate the applicability of our method on examples from the domain of learning-enabled cyber-physical systems.

翻译：我们考虑使用一致推断对离散时间随机动力学系统进行基于数据驱动的可达性分析。假设我们未获得随机系统的符号表示，但可以访问一个包含$K$步轨迹的数据集。可达性问题的目标是构造一个概率流管，使得$K$步轨迹违反流管边界的概率不超过用户指定的失效概率阈值。本文的核心思路包括：(1) 从数据中学习代理预测模型；(2) 利用代理模型进行可达性分析；(3) 通过一致推断量化代理模型的误差，从而提供概率性的可达性保证。我们重点关注具有复杂闭环动态特性的学习型控制系统，这类系统难以用符号方法建模，但可以查询状态转移对（例如通过仿真器）。我们通过来自学习型信息物理系统领域的示例验证了所提方法的适用性。