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. A simple and interpretable way to learn a dynamical system from data is to interpolate its vector-field with a data-adapted kernel which can be learned by using Kernel Flows. The method of Kernel Flows is a trainable machine learning method that learns the optimal parameters of a kernel based on the premise that a kernel is good if there is no significant loss in accuracy if half of the data is used. The objective function could be a short-term prediction or some other objective for other variants of Kernel Flows). However, this method is limited by the choice of the base kernel. In this paper, we introduce the method of \emph{Sparse Kernel Flows } in order to learn the ``best'' kernel by starting from a large dictionary of kernels. It is based on sparsifying a kernel that is a linear combination of elemental kernels. We apply this approach to a library of 132 chaotic systems.
翻译:从有限数量观测到的状态中倒退动态系统的矢量场是学习这些系统替代模型的一种自然方式。从数据中学习动态系统的简单和可解释的方法是用数据调适的内核对矢量场进行内插,可以通过使用内核流来学习。内核流的方法是一种可训练的机器学习方法,其前提是:如果使用一半的数据,内核的精确度不会显著下降,内核是好的。客观功能可以是短期预测,或者对内核流的其他变体的其他目标。然而,这种方法受基内核选择的限制。在本文件中,我们引入了 emph{Sparse内核流的方法 } 以便从大型内核词典开始学习“最佳内核” 的最佳参数。我们采用这一方法是为了从大型内核词典开始学习“最佳内核”内核的内核。它基于对内核的内核流进行透析,而内核是元素内核的线性组合。我们将这一方法应用到一个132个系统图书馆。