  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.
