R.B. Sills, P. Sunil, M. Vasoya
Rutgers University,
United States
Keywords: physics-informed neural network, finite element method, surrogate model
Summary:
The physics-informed neural network (PINN) methodology enables training of NNs for solving physical problems without requiring labeled data. However traditional PINNs cannot serve as surrogate models which can be queried arbitrarily because the PINN must be retrained if any conditions (e.g., geometry, boundary conditions) change after training. Furthermore, the governing equations must be coded from scratch for each class of physical problem of interest. Here we introduce the finite-element-based PINN (FE-PINN) methodology, which utilizes a custom convolution called stencil convolution to enable training of PINN surrogate models using the FE method. The FE-PINN method is designed so that a pre-existing FE code can be utilized to evaluate the loss function and initiate backpropagation, making it possible to train a FE-PINN surrogate model for any physical problem currently solvable using an FE code. Such FE-PINNs could be trained to provide a high-throughput methodology to aid in material and microstructure design. We demonstrate the performance of the FE-PINN method on a few classes of solid mechanics problems with variable conditions and nonlinear response.