We detail how incorporating physics into neural network design can significantly improve the learning and forecasting of dynamical systems, even nonlinear systems of many dimensions. A map building perspective elucidates the superiority of Hamiltonian neural networks over conventional neural networks. The results clarify the critical relation between data, dimension, and neural network learning performance.
@article{arxiv.2008.04214,
title = {Mastering high-dimensional dynamics with Hamiltonian neural networks},
author = {Scott T. Miller and John F. Lindner and Anshul Choudhary and Sudeshna Sinha and William L. Ditto},
journal= {arXiv preprint arXiv:2008.04214},
year = {2020}
}