Physical information neural networks for 2D and 3D nonlinear Biot model and simulation on the pressure of brain

In this paper, we propose a self-adaptive algorithm of physics-informed neural networks (PINNs) for 2D and 3D linear and nonlinear Biot models, including solving the forward and inverse problems. Firstly, we apply the original PINNs algorithm to 2D and 3D linear and nonlinear Biot models. Secondly, we explore the performance of PINNs in solving Biot model when λ→∞ to show the potential of PINNs in avoiding locking phenomenon for displacement and pressure oscillation compared to the traditional numerical algorithms. Then, we propose a self-adaptive PINNs algorithm to solve the Biot model with high spatial-temporal complexity and apply the proposed algorithm to simulate the brain pressure distribution problem with irregular boundary. And the numerical results show that the physics-informed neural network has good precision in solving nonlinear problems, inverse problems and high-dimensional problems. Finally, we draw conclusions to summarize the main results of this work.