On 22.5.2024 in the meeting room in the DMS from 2pm will take place this lecture:

Dr. Sebastien Court (Institut für Mathematik, Universität Innsbruck)

Designing the monodomain model with artificial neural networks

Abstract:
We propose a data-driven method in order to identify the nonlinearity in the monodomain model. The monodomain model is a system coupling a semilinear parabolic PDE with an ODE, describing the time evolution of an electric potential. Our approach provides a general answer to the problem of selecting the model when studying phenomena related to cardiac electrophysiology: From measurements, instead of determining coefficients of a prescribed nonlinearity (like the FitzHugh-Nagumo model for instance), we design the nonlinearity itself, in the form of an artificial neural network (ANN), more specifically a feedforward residual network. The relevance of this approach relies on the approximation capacities of neural networks. Training the ANN corresponds to solving an identification problem constrained by the monodomain model so parameterized. We formulate this inverse problem as an optimal control problem, and provide mathematical analysis and derivation of optimality conditions for identifying the weights of the ANN. One of the difficulties comes from the lack of smoothness of activation functions which are classically used for training deep neural networks. We will also present numerical results that demonstrate the feasibility of the strategy proposed in this work. This is joint work with Prof. Karl Kunisch (RICAM & University of Graz).

Organizers:
doc. RNDr. Lenka Přibylová, Ph.D.
Department of Mathematics and Statistics, SCI MUNI
the Nonlinear Dynamics Team
https://science.math.muni.cz/ndteam/
Funding: European Horizon MSCA grant 101063853