Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System

arXiv:2308.11925v2 Announce Type: replace-cross
Abstract: In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order optimality system of the optimal control problem, and employs deep neural networks to represent the solutions to the reduced system. We present an error analysis of the scheme, and provide $L^2(\Omega)$ error bounds on the state, control and adjoint in …

abstract arxiv box control cs.lg cs.na linear math.na math.oc network networks neural network neural networks solver type via work