Simulation of parametrized cardiac electrophysiology in three dimensions using physics-informed neural networks

Physics-informed neural networks (PINNs) are extensively used to represent various physical systems across multiple scientific domains. The same can be said for cardiac electrophysiology, wherein fully-connected neural networks (FCNNs) have been employed to predict the evolution of an action potential in a 2D space following the two-parameter phenomenological Aliev-Panfilov (AP) model. In this paper, the training behaviour of PINNs is investigated to determine optimal hyperparameters to predict the electrophysiological activity of the myocardium in 3D according to the AP model, with the inclusion of boundary and material parameters. An FCNN architecture is employed with the governing partial differential equations in their strong form, which are scaled consistently with normalization of network inputs. The finite element (FE) method is used to generate training data for the network. Numerical examples with varying spatial dimensions and parameterizations are generated using the trained models. The network predicted fields for both the action potential and the recovery variable are compared with the respective FE simulations. Network losses are weighed with individual scalar values. Their effect on training and prediction is studied to arrive at a method of controlling losses during training.