Abstract
In this study, we aim to solve Biot’s consolidation models by employing physics-informed neural networks. Based on the fixed-stress splitting method, loss functions are designed for the displacement variable and the pressure variables separately. Such a strategy enables us to train two independent and smaller neural networks. The coupling of different variables is realized via the fixed-stress iterative algorithm. Numerical experiments are provided to show that the fixed-stress iterative algorithm can improve the performance of neural network approximations of the solution of Biot’s model. Error analysis is provided to justify the capability of the fixed-stress PINNs for approximating the solution of Biot’s model.
Brief Biography
Mingchao Cai is an associate professor in Department of Mathematics, Morgan State University. He earned his Ph.D. degree from The Hong Kong University of Science and Technology in 2008. His research interests include: (i) Modeling and numerical simulations of biomechanic problems, (ii) Fast numerical methods for PDEs (Multigrid methods, Domain Decomposition Methods, and Preconditioning), (iii) Numerical linear algebra with applications in data science, and (iv) Parallel computing.