Variationally Mimetic Operator Networks

Understand

In recent years operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs).

• These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE.
• This work describes a new architecture for operator networks that mimics the form of the numerical solution obtained from an approximate variational or weak formulation of the problem.
• The application of these ideas to a generic elliptic PDE leads to a variationally mimetic operator network (VarMiON).