Soufiane Abid, Khalid Atifi, El-Hassan Essoufi

An Inverse Backward Problem for a Heat Equation with a Memory Term, Solved by a Deep Learning Method

Our goal of this paper is the identification of an initial condition in a heat equation that contains a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. Then we prove the continuity and the G-derivability of the cost function. Finally, we validate the results numerically by using a deep neural network. Our algorithm is meshfree.

Mathematics Subject Classification: 35R30, 35Q93, 35R09, 68T07

Key words and phrases: Inverse problem, memory term, optimization, deep learning