Abstracts

Solving elliptic optimal control problems via neural networks and optimality system

Ramesh Ch Sau, IISER Tirupati

In this talk, we discuss a neural network-based solver for optimal control problems for the Poisson problem. It utilizes a coupled system derived from the first-order optimality system of the optimal control problem and employs neural networks to represent the solutions to the reduced system. We present an error analysis of the scheme and provide L^2-error bounds on the state, control, and adjoint state variables in terms of neural network parameters (e.g., depth, width, and parameter bounds) and the number of sampling points. We present some numerical examples to illustrate the method.