mlsanityData to 14 Oct 2026

Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System

arXiv 2308.11925 ↗First posted 23 Aug 2023math.OC cs.LG cs.NAcited by 3

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Abstract (arXiv)

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 L2(Omega) error bounds on the state, control and adjoint in terms of neural network parameters (e.g., depth, width, and parameter bounds) and the numbers of sampling points. The main tools in the analysis include offset Rademacher complexity and boundedness and Lipschitz continuity of neural network functions. We present several numerical examples to illustrate the method and compare it with two existing ones.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 24 of its 61 references that are in the map. First posted on arXiv 23 Aug 2023.

Builds on

24 of 61 references.

References · 24

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12 more
  1. 2021Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimalitycited by 40
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Citing papers per year: 2024: 3.

3 papers.

  1. 2024PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problemscited by 3
  2. 2024KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problemscited by 3
  3. 2024Point Source Identification Using Singularity Enriched Neural Networkscited by 1