A Spatial-Temporally Adaptive PINN Framework for 3D Bi-Ventricular Electrophysiological Simulations and Parameter Inference

Physics-informed neural networks (PINNs) is a new paradigm for solving the forward and inverse problems of partial differential equations (PDEs). Its penetration into 3D bi-ventricular electrophysiology (EP) however has been slow, owing to its fundamental limitations to solve PDEs over large or complex solution domains with sharp transitions. In this paper, we propose a new PINN framework to overcome these challenges via three key innovations: 1) a weak-form PDE residual to bypass the challenges of high-order spatial derivatives over irregular spatial domains, 2) a spatial-temporally adaptive training strategy to mitigate the failure of PINN to propagate correct solutions and accelerate convergence, and 3) a sequential learning strategy to enable solutions over longer time domains. We experimentally demonstrated the effectiveness of the presented PINN framework to obtain the complete forward and inverse EP solutions over the 3D bi-ventricular geometry, which is otherwise not possible with vanilla PINN frameworks.