Pseudo-Hamiltonian neural networks for learning partial differential equations
This work addresses the challenge of modeling complex physical systems described by partial differential equations for researchers in computational physics and machine learning, representing an incremental extension of an existing method to a new domain.
The authors tackled the problem of learning partial differential equations by extending pseudo-Hamiltonian neural networks from ordinary to partial differential equations, resulting in a model with up to three neural networks and discrete convolution operators that demonstrated superior performance compared to a baseline single neural network in numerical tests.
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.