Modelling dynamical systems is an integral component for understanding the natural world. To this end, neural networks are becoming an increasingly popular candidate owing to their ability to learn complex functions from large amounts of data. Despite this recent progress, there has not been an adequate discussion on the architectural regularization that neural networks offer when learning such systems, hindering their efficient usage. In this paper, we initiate a discussion in this direction using coordinate networks as a test bed. We interpret dynamical systems and coordinate networks from a signal processing lens, and show that simple coordinate networks with few layers can be used to solve multiple problems in modelling dynamical systems, without any explicit regularizers.

翻译：动力系统建模是理解自然世界的重要组成部分。近年来，神经网络因其能从大量数据中学习复杂函数的能力，正成为越来越受欢迎的建模工具。尽管取得了这些进展，但对于神经网络在动力系统学习过程中提供的架构正则化作用，目前尚缺乏充分的讨论，这阻碍了其有效应用。本文以坐标网络为测试平台，开启了这一方向的探讨。我们从信号处理的角度对动力系统和坐标网络进行解读，并证明无需显式正则化项，仅使用简单且层数较少的坐标网络即可解决动力系统建模中的多个问题。