mlsanityData to 7 Oct 2026

Element-wise Multiplication Based Deeper Physics-Informed Neural Networks

arXiv 2406.04170 ↗First posted 6 Jun 2024cs.LG cs.AI cs.NEcited by 3

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Abstract (arXiv)

As a promising framework for resolving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have received widespread attention from industrial and scientific fields. However, lack of expressive ability and initialization pathology issues are found to prevent the application of PINNs in complex PDEs. In this work, we propose Deeper Physics-Informed Neural Network (Deeper-PINN) to resolve these issues. The element-wise multiplication operation is adopted to transform features into high-dimensional, non-linear spaces. Benefiting from element-wise multiplication operation, Deeper-PINNs can alleviate the initialization pathologies of PINNs and enhance the expressive capability of PINNs. The proposed structure is verified on various benchmarks. The results show that Deeper-PINNs can effectively resolve the initialization pathology and exhibit strong expressive ability.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 19 of its 29 references that are in the map. First posted on arXiv 6 Jun 2024.

Builds on

19 of 29 references.

References · 19

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  5. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  6. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  7. 2021Exact imposition of boundary conditions with distance functions in physics-informed deep neural networkscited by 135
  8. 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
  9. 2020A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networkscited by 86
  10. 2021Multi-Objective Loss Balancing for Physics-Informed Deep Learningcited by 86
  11. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  12. 2023Residual-based attention in physics-informed neural networkscited by 72
7 more
  1. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 71
  2. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 70
  3. 2023Separable Physics-Informed Neural Networkscited by 64
  4. 2020A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applicationscited by 53
  5. 2024Learning in PINNs: Phase transition, diffusion equilibrium, and generalizationcited by 13
  6. 2022Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Methodcited by 10
  7. 2024Densely Multiplied Physics Informed Neural Networkscited by 3

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Cited by year

Citing papers per year: 2024: 2; 2025: 1.

3 papers.

  1. 2024Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?cited by 3
  2. 2024About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networkscited by 0
  3. 2025Mask-PINNs: Mitigating Internal Covariate Shift in Physics-Informed Neural Networkscited by 0