所属:Kyoto University, Dept. of Civil and Earth Resources Engineering
概要:Physics-informed neural networks (PINNs) have been rapidly developed for solving partial differential equations. The Exact Dirichlet boundary condition Physics-informed Neural Network (EPINN) is proposed to achieve efficient simulation of solid mechanics problems based on the principle of least work with notably reduced training time. There are five major building features in the EPINN framework. First, for the 1D solid mechanics problem, the neural networks are formulated to exactly replicate the shape function of linear or quadratic truss elements. Second, for 2D and 3D problems, the tensor decomposition was adopted to build the solution field without the need to generate the finite element mesh of complicated structures to reduce the number of trainable weights in the PINN framework. Third, the principle of least work was adopted to formulate the loss function. Fourth, the exact Dirichlet boundary condition (i.e., displacement boundary condition) was implemented. Finally, the meshless finite difference (MFD) was adopted to calculate gradient information efficiently. By minimizing the total energy of the system, the loss function is selected to be the same as the total work of the system, which is the total strain energy minus the external work done on the Neumann boundary conditions (i.e., force boundary conditions). The exact Dirichlet boundary condition was implemented as a hard constraint compared to the soft constraint (i.e., added as additional terms in the loss function), which exactly meets the requirement of the principle of least work. The EPINN framework is implemented in the Nvidia Modulus platform and achieved notably reduced training time compared to the conventional PINN for solid mechanics. Compared to conventional PINN architecture, EPINN achieved a speedup of more than 13 times for 1D problems and more than 126 times for 3D problems.
論文掲載,発表実績:
(学術雑誌掲載論文)
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Jiaji Wang, Y.L. Mo, Bassam Izzuddin, Chul-Woo Kim. Exact Dirichlet Boundary Physics-informed Neural Network EPINN for Solid Mechanics, Computer Methods in Applied Mechanics and Engineering, September 2023, 116184.
https://doi.org/10.1016/j.cma.2023.116184 -
Chawit Kaewnuratchadasorn, Jiaji Wang, Chul-Woo Kim. Vehicle-bridge Interaction Neural Operator for Data-driven Structural Health Monitoring and Structural Simulation. Computer-aided Civil and Infrastructure Engineering, October 2023,
https://doi.org/10.1111/mice.13105 - Chawit K, Jiaji Wang*, Chul-Woo Kim. Physics-informed Neural Operator Solver and Super Resolution for Solid Mechanics, currently under review by Computer-aided Civil and Infrastructure Engineering, 2024.
Posted : 2024年03月31日