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This paper introduces a novel approach that combines two methodologies, normalization and boundary condition enforcement, seamlessly integrated into a physics-informed neural networks (PINN) for addressing inverse problems. The model aims to leverage normalization to alleviate gradient failures induced by intensity variations in partial differential equations (PDEs). Subsequently, a reduced-order method is applied to transform high-order PDEs into lower-order PDEs, facilitating the complete transfer of boundary conditions to Essential Boundary Conditions (EBCs). The entirety of EBC is then processed by multiplying the NN’s output with a trial function generated by another independent DNN. The effectiveness of the proposed model is demonstrated through various examples involving inverse problems in solid mechanics.

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Physics-Informed Neural Network with Normalization and Full-Imposed Boundary Conditions for Solving Inverse Problems

  • 会议论文

  • 发表日期：

    2025年

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  • Khang A. Luong,
  • Ermal Elbasani,
  • Duy-Trung Vo,
  • Thanh-Nhat Huynh,
  • Zing T. L. Tran,
  • Jaeho Jang,
  • Seunghye Lee,
  • Jaehong Lee

摘要

This paper introduces a novel approach that combines two methodologies, normalization and boundary condition enforcement, seamlessly integrated into a physics-informed neural networks (PINN) for addressing inverse problems. The model aims to leverage normalization to alleviate gradient failures induced by intensity variations in partial differential equations (PDEs). Subsequently, a reduced-order method is applied to transform high-order PDEs into lower-order PDEs, facilitating the complete transfer of boundary conditions to Essential Boundary Conditions (EBCs). The entirety of EBC is then processed by multiplying the NN’s output with a trial function generated by another independent DNN. The effectiveness of the proposed model is demonstrated through various examples involving inverse problems in solid mechanics.