mlsanityData to 13 Oct 2026

ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks

arXiv 2502.00803 ↗First posted 2 Feb 2025cs.LGcited by 6

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Abstract (arXiv)

Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs), but their optimization usually faces thorny challenges due to the unique derivative-dependent loss function. By analyzing the loss distribution, previous research observed the propagation failure phenomenon of PINNs, intuitively described as the correct supervision for model outputs cannot ''propagate'' from initial states or boundaries to the interior domain. Going beyond intuitive understanding, this paper provides a formal and in-depth study of propagation failure and its root cause. Based on a detailed comparison with classical finite element methods, we ascribe the failure to the conventional single-point-processing architecture of PINNs and further prove that propagation failure is essentially caused by the lower gradient correlation of PINN models on nearby collocation points. Compared to superficial loss maps, this new perspective provides a more precise quantitative criterion to identify where and why PINN fails. The theoretical finding also inspires us to present a new PINN architecture, named ProPINN, which can effectively unite the gradients of region points for better propagation. ProPINN can reliably resolve PINN failure modes and significantly surpass advanced Transformer-based models with 46% relative promotion.

Key facts. Cited by 6 papers in the map (data through 13 Oct 2026). Builds on 23 of its 50 references that are in the map. First posted on arXiv 2 Feb 2025.

Builds on

23 of 50 references.

References · 23

  1. 2017Attention Is All You Needcited by 60,106
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,223
  3. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,610
  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,183
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,336
  6. 2024KAN: Kolmogorov-Arnold Networkscited by 641
  7. 2021Characterizing possible failure modes in physics-informed neural networkscited by 637
  8. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 633
  9. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 234
  10. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  11. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 123
  12. 2024Challenges in Training PINNs: A Loss Landscape Perspectivecited by 111
11 more
  1. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 90
  2. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 78
  3. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 72
  4. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 72
  5. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 62
  6. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
  7. 2021Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEscited by 42
  8. 2024RoPINN: Region Optimized Physics-Informed Neural Networkscited by 26
  9. 2024Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operatorscited by 20
  10. 2023Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEscited by 19
  11. 2024SetPINNs: Set-based Physics-informed Neural Networkscited by 2

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 4; 2026: 2.

6 papers.

  1. 2025FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networkscited by 11
  2. 2025A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learningcited by 6
  3. 2025Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networkscited by 2
  4. 2025Revisiting Heat Flux Analysis of Tungsten Monoblock Divertor on EAST using Physics-Informed Neural Networkcited by 2
  5. 2026PINNs Failure Modes are Overfittingcited by 0
  6. 2026PhysFieldBench: Can Multimodal Models Understand Physical Fields?cited by 0