Design of the monodomain model by artificial neural networks

TL;DR

This paper introduces a novel data-driven method using neural networks to identify the nonlinearities in the monodomain model for cardiac electrophysiology, replacing traditional coefficient estimation with model design.

Contribution

It formulates the inverse problem as an optimal control problem and provides mathematical analysis, addressing the challenge of non-smooth activation functions.

Findings

Numerical simulations confirm the feasibility of the neural network-based approach.

The method effectively identifies nonlinearities in the monodomain model.

The approach offers a new way to model cardiac electrophysiology phenomena.

Abstract

We propose an optimal control approach in order to identify the nonlinearity in the monodomain model, from given data. This data-driven approach gives an answer to the problem of selecting the model when studying phenomena related to cardiac electrophysiology. Instead of determining coefficients of a prescribed model (like the FitzHugh-Nagumo model for instance) from empirical observations, we design the model itself, in the form of an artificial neural network. The relevance of this approach relies on the approximation capacities of neural networks. We formulate this inverse problem as an optimal control problem, and provide mathematical analysis and derivation of optimality conditions. One of the difficulties comes from the lack of smoothness of activation functions which are classically used for training neural networks. Numerical simulations demonstrate the feasibility of the strategy proposed in this work.