Stiffness-Aware Neural Network for Learning Hamiltonian Systems
Abstract
We propose stiffness-aware neural network (SANN), a new method for learning Hamiltonian dynamical systems from data. SANN identifies and splits the training data into stiff and nonstiff portions based on a stiffness-aware index, a simple, yet effective metric we introduce to quantify the stiffness of the dynamical system. This classification along with a resampling technique allows us to apply different time integration strategies such as step size adaptation to better capture the dynamical characteristics of the Hamiltonian vector fields. We evaluate SANN on complex physical systems including a three-body problem and billiard model. We show that SANN is more stable and can better preserve energy when compared with the state-of-the-art methods, leading to significant improvement in accuracy.
Cite
Text
Liang et al. "Stiffness-Aware Neural Network for Learning Hamiltonian Systems." International Conference on Learning Representations, 2022.Markdown
[Liang et al. "Stiffness-Aware Neural Network for Learning Hamiltonian Systems." International Conference on Learning Representations, 2022.](https://mlanthology.org/iclr/2022/liang2022iclr-stiffnessaware/)BibTeX
@inproceedings{liang2022iclr-stiffnessaware,
title = {{Stiffness-Aware Neural Network for Learning Hamiltonian Systems}},
author = {Liang, Senwei and Huang, Zhongzhan and Zhang, Hong},
booktitle = {International Conference on Learning Representations},
year = {2022},
url = {https://mlanthology.org/iclr/2022/liang2022iclr-stiffnessaware/}
}