mlsanityData to 7 Oct 2026

Densely Multiplied Physics Informed Neural Networks

arXiv 2402.04390 ↗First posted 6 Feb 2024cs.LG cs.AIcited by 3

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Abstract (arXiv)

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining incorrect outcomes. Unlike most of the existing solutions trying to enhance the ability of PINN by optimizing the training process, this paper improved the neural network architecture to improve the performance of PINN. We propose a densely multiply PINN (DM-PINN) architecture, which multiplies the output of a hidden layer with the outputs of all the behind hidden layers. Without introducing more trainable parameters, this effective mechanism can significantly improve the accuracy of PINNs. The proposed architecture is evaluated on four benchmark examples (Allan-Cahn equation, Helmholtz equation, Burgers equation and 1D convection equation). Comparisons between the proposed architecture and different PINN structures demonstrate the superior performance of the DM-PINN in both accuracy and efficiency.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 18 of its 40 references that are in the map. First posted on arXiv 6 Feb 2024.

Builds on

18 of 40 references.

References · 18

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6 more
  1. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  2. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  3. 2021Exact imposition of boundary conditions with distance functions in physics-informed deep neural networkscited by 135
  4. 2018Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profilescited by 55
  5. 2020A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applicationscited by 53
  6. 2020Deep learning of free boundary and Stefan problemscited by 33

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Cited by year

Citing papers per year: 2024: 3.

3 papers.

  1. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  2. 2024Learning in PINNs: Phase transition, diffusion equilibrium, and generalizationcited by 13
  3. 2024Element-wise Multiplication Based Deeper Physics-Informed Neural Networkscited by 3