Variationally mimetic operator neural networks for the time-dependent heat equation

Operator networks are used as deep learning tools for approximating solutions of partial differential equations (PDEs). Robust methods for solving PDEs have already been developed, such as the finite element method (FEM), but they have a high computational cost. The architecture of a variationally mimetic operator network (VarMiON) mimics the form of the numerical solution obtained from an approximate variational or weak formulation of a PDE making it possible to obtain an efficient method that can solve multiple instances of a problem with different input functions. The literature on operator networks has already considered the steady-state heat equation. This thesis explores the problem of solving the time-dependent heat equation with a VarMiON.