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optimizing-vpinns-using-ls

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

https://github.com/mathmode/optimizing-vpinns-using-ls

Science Score: 36.0%

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Keywords

gradient-descent gradient-descent-optimizer least-squares neural-network neural-networks variational-problems
Last synced: 9 months ago · JSON representation

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

Basic Info
  • Host: GitHub
  • Owner: Mathmode
  • Language: Python
  • Default Branch: main
  • Homepage:
  • Size: 173 MB
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  • Stars: 3
  • Watchers: 3
  • Forks: 0
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Topics
gradient-descent gradient-descent-optimizer least-squares neural-network neural-networks variational-problems
Created about 2 years ago · Last pushed over 1 year ago
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Readme Citation

README.md

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.

Owner

  • Name: Mathmode
  • Login: Mathmode
  • Kind: organization
  • Location: Spain

Group on Applied Mathematical Modeling, Statistics, and Optimization

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