Optimizing Variational Physics-Informed Neural Networks Using Least Squares

Pieces of code for the experiments described in the manuscript "Optimizing Variational Physics-Informed Neural Networks Using Least Squares", whose preprint is available at https://arxiv.org/pdf/2407.20417.

The code is organized into independent and self-contained sections as follows:

Section S3_automatic_differentiation

Relates to Section 3 in the manuscript. To reproduce the manuscript results, execute outerAD.py.*

Section S4_GD_and_LSGD_optimizers

Relates to Section 4 in the manuscript. To reproduce the manuscript results, execute outerGDandLSGD.py.*

Section S5_numerical_results

Relates to Section 5 in the manuscript. To reproduce the manuscript results, execute S5_all_experiments.py.

We carried out the experiments in an Ubuntu 22.04.4 LTS system running Linux kernel version 5.15.0-102-generic on an x86_64 architecture, equipped with an AMD EPYC 9474F 48-Core Processor (2 threads per core) operating at a frequency of 4.11 GHz with 377 GB of RAM.

*For measuring floating-point operations (FLOPs), we utilized the 'perf' profiler tool for Linux (https://perf.wiki.kernel.org) via the CPU-dependent command perf stat -e fp_ret_sse_avx_ops.all [python-path] [python-script]. We highlight that such a command depends on the machine's specifications.