Optimization with learning-informed differential equation constraints and its applications

2020/08/25 by Guozhi Dong, Dong, Guozhi, Michael Hintermueller +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #35J61 #49M15 #65J15 #65J20 #65K10 #68T07 #90C30 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2008.10893

openalex publication_date 2020/08/25 · openalex created_date 2020/09/01 · openalex updated_date 2026/08/01

Abstract

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided.

Citations

• Designing Neural Network Architectures using Reinforcement Learning

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• Mission-Aligned Learning-Informed Control of Autonomous Systems: Formulation and Foundations

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