Learning phase-space flows using time-discrete implicit Runge-Kutta PINNs
Abstract
We present a computational framework for obtaining multidimensional phase-space solutions of systems of non-linear coupled differential equations, using high-order implicit Runge-Kutta Physics- Informed Neural Networks (IRK-PINNs) schemes. Building upon foundational work originally solving differential equations for fields depending on coordinates [J. Comput. Phys. 378, 686 (2019)], we adapt the scheme to a context where the coordinates are treated as functions. This modification enables us to efficiently solve equations of motion for a particle in an external field. Our scheme is particularly useful for explicitly time-independent and periodic fields. We apply this approach to successfully solve the equations of motion for a mass particle placed in a central force field and a charged particle in a periodic electric field.
Cite
@article{arxiv.2409.16826,
title = {Learning phase-space flows using time-discrete implicit Runge-Kutta PINNs},
author = {Álvaro Fernández Corral and Nicolás Mendoza and Armin Iske and Andrey Yachmenev and Jochen Küpper},
journal= {arXiv preprint arXiv:2409.16826},
year = {2024}
}
Comments
10 pages, 4 figures, published in the International Conference on Scientific Computing and Machine Learning, see http://scml.jp