An adaptive adjoint-oriented neural network for solving parametric optimal control problems with singularities

TL;DR

This paper introduces an adaptive neural network approach that improves solving parametric optimal control problems with singularities by combining deep adaptive sampling and adjoint-oriented neural networks, enhancing accuracy and generalizability.

Contribution

It presents a novel adaptive AONN framework that effectively handles low-regularity solutions and improves surrogate modeling for complex PDE-governed control problems.

Findings

Enhanced handling of singularities in PDE-based control problems

Improved generalizability of surrogate models without labeled data

Numerical examples demonstrate superior performance

Abstract

In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The proposed method integrates deep adaptive sampling techniques with the adjoint-oriented neural network (AONN) framework. It alleviates the limitations of AONN in handling low-regularity solutions and enhances the generalizability of deep adaptive sampling for surrogate modeling without labeled data ($\text{DAS}^2$). The effectiveness of the adaptive AONN is demonstrated through numerical examples involving singularities.