sPINNacle: Scale-Invariant Collocation Point Selection with NTK Learning Rate Adaptation

Author: Moritz Hauschulz (moritz.hauschulz@gmail.com)

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📖 Abstract

Physics-informed neural networks (PINNs) have demonstrated remarkable performance in modeling partial differential equations. PINNacle is a recently proposed algorithm that efficiently selects the most informative points in the domain during training. However, as we show, it is not robust to domain-rescaling. In this paper, we propose sPINNacle, which mitigates this short-coming by introducing NTK-based learning rate adaptation. We conduct experiments on the two-dimensional Poisson equation and find that sPINNacle improves on PINNacle across scales in this setting. It also outperforms an alternative based on the MultiAdam optimizer.

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🚀 Project Overview

The code is based on that from the paper "PINNACLE: PINN Adaptive ColLocation and Experimental points selection" (https://arxiv.org/abs/2404.07662).

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⚡ Quick Start

Follow these steps to quickly set up and run the project.

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1 Clone the Repository

Clone this repository to your local machine:

git clone https://github.com/moritzhauschulz/sPINNacle

cd sPINNacle/

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2 Install Packages (ideally in a .venv)

pip install -r requirements.txt

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3 Download Data

Some data is available in the repo, other data needs to be obtained from https://github.com/pdebench/PDEBench due to large file sizes.

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4 Run Code

e.g.

cd pinnacle_code/

bash al_pinn_meh.sh "0" "0" "0" "--pdebench_dir /path/to/pdebench"

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