On the Metastability of Learning Algorithms in Physics-Informed Neural Networks: A Case Study on Schr\"odinger Operators
Abstract
In this manuscript, we discuss an interesting phenomenon that happens in the training of physics-informed neural networks: PINNs seem to go through metastable states during the optimization process. This behaviour is present in several dynamical systems of interest to physics and was first noticed in the Fermi-Pasta-Ulam-Tsingou model, in which the system spends a lot of time in an intermediate state, before, eventually, reaching thermalization. We concentrate on some examples of Schr\"odinger equations in spatial dimension $n=1$, including the nonlinear Schr\"odinger equation with quintic polynomial nonlinearity, the linear Schr\"odinger equation with trapping potential, and and the linear Schr\"odinger equation with asymptotically constant potential.
Cite
Text
Selvitella. "On the Metastability of Learning Algorithms in Physics-Informed Neural Networks: A Case Study on Schr\"odinger Operators." ICML 2024 Workshops: HiLD, 2024.Markdown
[Selvitella. "On the Metastability of Learning Algorithms in Physics-Informed Neural Networks: A Case Study on Schr\"odinger Operators." ICML 2024 Workshops: HiLD, 2024.](https://mlanthology.org/icmlw/2024/selvitella2024icmlw-metastability/)BibTeX
@inproceedings{selvitella2024icmlw-metastability,
title = {{On the Metastability of Learning Algorithms in Physics-Informed Neural Networks: A Case Study on Schr\"odinger Operators}},
author = {Selvitella, Alessandro Maria},
booktitle = {ICML 2024 Workshops: HiLD},
year = {2024},
url = {https://mlanthology.org/icmlw/2024/selvitella2024icmlw-metastability/}
}