Deep neural network (DNN) architectures are constructed that are the exact equivalent of explicit Runge-Kutta schemes for numerical time integration. The network weights and biases are given, i.e., no training is needed. In this way, the only task left for physics-based integrators is the DNN approximation of the right-hand side. This allows to clearly delineate the approximation estimates for right-hand side errors and time integration errors. The architecture required for the integration of a simple mass-damper-stiffness case is included as an example.
@article{arxiv.2211.17039,
title = {Neural Network Representation of Time Integrators},
author = {Rainald Löhner and Harbir Antil},
journal= {arXiv preprint arXiv:2211.17039},
year = {2022}
}