FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries

Thivin Anandh, Divij Ghose, Himanshu Jain, Sashikumaar Ganesan
4/18/2024
cs.LGcs.CEcs.NE

No official code found. Best implementation: airexlab/fastvpinns (47 stars, MIT, last commit 2025-02-02). 1 more below.

Abstract

Variational Physics-Informed Neural Networks (VPINNs) utilize a variational loss function to solve partial differential equations, mirroring Finite Element Analysis techniques. Traditional hp-VPINNs, while effective for high-frequency problems, are computationally intensive and scale poorly with increasing element counts, limiting their use in complex geometries. This work introduces FastVPINNs, a tensor-based advancement that significantly reduces computational overhead and improves scalability. Using optimized tensor operations, FastVPINNs achieve a 100-fold reduction in the median training time per epoch compared to traditional hp-VPINNs. With proper choice of hyperparameters, FastVPINNs surpass conventional PINNs in both speed and accuracy, especially in problems with high-frequency solutions. Demonstrated effectiveness in solving inverse problems on complex domains underscores FastVPINNs' potential for widespread application in scientific and engineering challenges, opening new avenues for practical implementations in scientific machine learning.

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Code Implementations(2)

airexlab/fastvpinnsCommunity100%
MIT

FastVPINNs - A tensor-driven acceleration of VPINNs for complex geometries

4765TeX, PythonApr 22, 20241 years agoMIT
deep-learninginverse-problemsneural-networkpartial-differential-equationsphysics-informed-neural-networks+3 more
divijghose/fastvpinns-devCommunity72%
MIT

FastVPINNs - A tensor-driven acceleration of VPINNs for complex geometries

10TeX, PythonJul 23, 20241 years agoMIT

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Cite this paper

@article{anandh2024fastvpinns,
  title  = {FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries},
  author = {Thivin Anandh and Divij Ghose and Himanshu Jain and Sashikumaar Ganesan},
  year   = {2024},
  eprint = {2404.12063},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2404.12063v1}
}

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