mlsanityData to 14 Oct 2026

A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problems

arXiv 2103.13878 ↗First posted 19 Mar 2021cs.LG cs.NA math.NAcited by 5

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Abstract (arXiv)

In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the surface differential operators so that PINN's loss value will be an indicator of the residue of the surface PDEs. Numerical experiments verify efficacy of our algorithm.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 7 of its 33 references that are in the map. First posted on arXiv 19 Mar 2021.

Builds on

7 of 33 references.

References · 7

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2015Automatic differentiation in machine learning: a surveycited by 855
  3. 2016XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networkscited by 849
  4. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  5. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
  6. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 148
  7. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 1; 2024: 0; 2025: 0; 2026: 2.

5 papers.

  1. 2026A Machine Learning Approach to the Nirenberg Problemcited by 5
  2. 2021Deep learning for solution and inversion of structural mechanics and vibrationscited by 3
  3. 2023Physics-informed neural networks for transformed geometries and manifoldscited by 3
  4. 2026Minimal surfaces, Knots, and Neural Networkscited by 2
  5. 2022A shallow physics-informed neural network for solving partial differential equations on surfacescited by 1