A Neural Finite Element Control Problem

Artificial neural networks are increasing being employed in the solutions of partial differential equations, but issues of control of these equations using such methods are unresolved. This work seeks to blend a neural finite element approach with a partial differential equation control technique. A one-dimensional heat equation is considered. Linear quadratic control is employed on the neural element model. Results successfully achieve the control objective, indicating the neural element method shows promise with future partial differential equation control techniques.