Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. We present variants of cross-validation (Kernel Flows (Owhadi and Yoo, 2019) and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) as simple approaches for learning the kernel used in these emulators.

中文翻译：

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从数据学习动力系统：简单的交叉验证观点，第一部分：参数化内核流

从有限数量的观察状态回归动力学系统的矢量场是学习此类系统的替代模型的自然方法。我们介绍了交叉验证的变体（内核流（Owhadi和Yoo，2019年）及其基于最大均值差异和Lyapunov指数的变体），作为学习这些仿真器中使用的内核的简单方法。