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<p>Partial differential equations (PDEs) are fundamental for modeling complex physical processes, often exhibiting structural features such as symmetries and conservation laws. While physics-informed neural networks (PINNs) can simulate and invert PDEs, they mainly rely on external loss functions for physical constraints, making it difficult to automatically discover and embed physically consistent network structures. We propose a physics structure-informed neural network discovery method based on physics-informed distillation, which decouples physical and parameter regularization via staged optimization in teacher and student networks. After distillation, clustering and parameter reconstruction are used to extract and embed physically meaningful structures. Numerical experiments on Laplace, Burgers, and Poisson equations, as well as fluid mechanics, show that the method can automatically extract relevant structures, improve accuracy and training efficiency, and enhance structural adaptability and transferability. This approach offers a new perspective for efficient modeling and automatic discovery of structured neural networks.</p>

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Automatic network structure discovery of physics informed neural networks via knowledge distillation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月29日

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  • Ziti Liu,
  • Yang Liu,
  • Xunshi Yan,
  • Wen Liu,
  • Han Nie,
  • Shuaiqi Guo,
  • Chen-an Zhang

摘要

Partial differential equations (PDEs) are fundamental for modeling complex physical processes, often exhibiting structural features such as symmetries and conservation laws. While physics-informed neural networks (PINNs) can simulate and invert PDEs, they mainly rely on external loss functions for physical constraints, making it difficult to automatically discover and embed physically consistent network structures. We propose a physics structure-informed neural network discovery method based on physics-informed distillation, which decouples physical and parameter regularization via staged optimization in teacher and student networks. After distillation, clustering and parameter reconstruction are used to extract and embed physically meaningful structures. Numerical experiments on Laplace, Burgers, and Poisson equations, as well as fluid mechanics, show that the method can automatically extract relevant structures, improve accuracy and training efficiency, and enhance structural adaptability and transferability. This approach offers a new perspective for efficient modeling and automatic discovery of structured neural networks.