A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivatives
发布时间：2022-10-17
点击次数：
所属单位：数学与统计学院
发表刊物：to appear in SIAM J. Optimization
关键字：deep learning-based inverse problems and optimal control of PDEs
摘要：We propose and analyze a numerical algorithm for solving a class of optimal control problems for learning-informed semilinear partial differential equations. The latter is a class of PDEs with constituents that are in principle unknown and are approximated by nonsmooth ReLU neural networks. We first show that a direct smoothing of the ReLU network with the aim to make use of classical numerical solvers can have certain disadvantages, namely potentially introducing multiple solutions for the corresponding state equation. This motivates us to devise a numerical algorithm that treats directly the nonsmooth optimal control problem, by employing a descent algorithm inspired by a bundle-free method. Several numerical examples are provided and the efficiency of the algorithm is shown.
论文类型：文章
学科门类：理学
一级学科：数学
文献类型：J
页面范围：1-29
是否译文：否
发表时间：2024-03-27
收录刊物：SCI