Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting model is comprised of up to three neural networks, modelling terms representing conservation, dissipation and external forces, and discrete convolution operators that can either be learned or be given as input. We demonstrate numerically the superior performance of PHNN compared to a baseline model that models the full dynamics by a single neural network. Moreover, since the PHNN model consists of three parts with different physical interpretations, these can be studied separately to gain insight into the system, and the learned model is applicable also if external forces are removed or changed.

翻译：伪哈密顿神经网络（PHNN）最近被引入用于学习可由常微分方程建模的动力系统。本文将该方法扩展到偏微分方程。所得到的模型由最多三个神经网络组成，分别建模守恒、耗散和外力项，以及可学习或作为输入给定的离散卷积算子。我们通过数值实验证明，与使用单一神经网络建模完整动力学的基线模型相比，PHNN具有更优的性能。此外，由于PHNN模型包含三个具有不同物理意义的组成部分，这些部分可以单独研究以深入了解系统，且当外力被移除或改变时，所学习的模型仍然适用。