mlsanityData to 7 Oct 2026

FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries

arXiv 2404.12063 ↗First posted 18 Apr 2024cs.LG cs.CE cs.NAcited by 5

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Abstract (arXiv)

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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 11 of its 29 references that are in the map. First posted on arXiv 18 Apr 2024.

Builds on

11 of 29 references.

References · 11

  1. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  2. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  3. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  4. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  5. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  6. 2019Towards Understanding the Spectral Bias of Deep Learningcited by 173
  7. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 169
  8. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 144
  9. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  10. 2019VarNet: Variational Neural Networks for the Solution of Partial Differential Equationscited by 35
  11. 2020Meshless physics-informed deep learning method for three-dimensional solid mechanicscited by 27

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 1; 2026: 1.

5 papers.

  1. 2024Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problemscited by 1
  2. 2026FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solverscited by 1
  3. 2024An efficient hp-Variational PINNs framework for incompressible Navier-Stokes equationscited by 0
  4. 2024Variational autoencoders with latent high-dimensional steady geometric flows for dynamicscited by 0
  5. 2025The Finite Element Neural Network Method: One Dimensional Studycited by 0