Computer Vision News - September 2022

49 Cardiac Electrophysiological Imaging In the last few years, Deep Learning neural networks have been increasingly used in order to learn dynamical models from data. For instance, Long et al. and Chen et al. endowed neural layers with additional structure to learn PDEs. This is a proposed framework for learning models using a purely data-driven approach in partially observable settings and various ML for physics-based modelling. Despite their good progress in cardiac electrophysiology simulations, data-driven models could not reproduce the complex dynamics like the repolarization. For this reason, researchers are turning to coupled physio-statistical approaches to simulate the body's electrophysiology. This can be useful, but sometimes simulations cannot manage large discrepancies between the simulated data and the real thing. They include techniques like Court and Kunisch's neural network which approximates the FitzHugh-Nagumo model and Sahli Costabal et al.'s neural network that maps out the body's electrophysiology. They also include a nonlinear reduced order model in the form of a physics-informed neural network and a deep learning algorithm for action potential simulation. This research addresses the limitation of incomplete physical models by adding a deep learning component. The idea is to identify a low-fidelity physical model and then learn that model parameter together with the neural network parameters. The model is designed specifically for the complexity of cardiac electrophysiology dynamics and incorporates Yin et al. (2021) model. The proposed approach can be used for forecasting at multiple horizons and with minimal data. Approach and learning framework The idea of the framework is to solve an optimization problem via a physics-based data- driven framework, APHYN-EP. This is shown in the figure below, with the two-component framework learning the parameters and the data-driven components from the data. A combination of a physical model (Fp) representing an incomplete description of the underlying phenomenon and a neural network (Fa) which will complement the physical model by capturing the information that cannot be modelled by the physics component.