用神经网络提升非线性系统可达性分析，保证安全概率且计算更快。
Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guarantees
- 通过神经网络将复杂系统转为线性空间，实现高效闭环控制
- 在11维跳步者和28维游泳者任务中，覆盖率达95%以上
- 支持跨参考轨迹复用误差边界，适合高维机器人安全验证
我们提出一种可扩展的基于可达性的概率化、数据驱动安全验证框架，用于未知非线性动态系统。采用带神经网络升维函数的Koopman理论，学习系统近似线性表示，并在此空间设计线性控制器以实现对参考轨迹分布的闭环跟踪。闭环可达集在升维空间中高效计算，并通过神经网络验证工具映射回原始状态空间。为捕捉Koopman模型与真实系统间的偏差，引入共形预测生成统计有效的误差界，对可达集进行膨胀，确保真实轨迹以用户指定概率被包含。该误差界可泛化至不同参考轨迹，无需重新计算。在高维MuJoCo任务（11维跳步者、28维游泳者）及12维四旋翼上测试，相较现有方法在可达集覆盖率、计算效率和保守性方面均有提升。
原文摘要 · Abstract (English)
We propose a scalable reachability-based framework for probabilistic, data-driven safety verification of unknown nonlinear dynamics. We use Koopman theory with a neural network (NN) lifting function to learn an approximate linear representation of the dynamics and design linear controllers in this space to enable closed-loop tracking of a reference trajectory distribution. Closed-loop reachable sets are efficiently computed in the lifted space and mapped back to the original state space via NN verification tools. To capture model mismatch between the Koopman dynamics and the true system, we apply conformal prediction to produce statistically-valid error bounds that inflate the reachable sets to ensure the true trajectories are contained with a user-specified probability. These bounds generalize across references, enabling reuse without recomputation. Results on high-dimensional MuJoCo tasks (11D Hopper, 28D Swimmer) and 12D quadcopters show improved reachable set coverage rate, computational efficiency, and conservativeness over existing methods.
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