mlsanityData to 7 Oct 2026

Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs

arXiv 2105.03336 ↗First posted 7 May 2021math.OC cs.LGcited by 5

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Abstract (arXiv)

Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are respectively used to compute the value function and the optimal control for certain class of high dimensional optimal control problems. We provide the mathematical analysis for the two abstract architectures. We also show several numerical results computed using the deep neural network implementations of these abstract architectures. A preliminary implementation of our proposed neural network architecture on FPGAs shows promising speed up compared to CPUs. This work paves the way to leverage efficient dedicated hardware designed for neural networks to solve high dimensional optimal control problems and Hamilton-Jacobi PDEs.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 59 of its 166 references that are in the map. First posted on arXiv 7 May 2021.

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59 of 166 references.

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Cited by year

Citing papers per year: 2022: 1; 2023: 2; 2024: 0; 2025: 2.

5 papers.

  1. 2022SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problemscited by 9
  2. 2023Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problemscited by 5
  3. 2023Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learningcited by 4
  4. 2025Neural Implicit Solution Formula for Efficiently Solving Hamilton-Jacobi Equationscited by 4
  5. 2025Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equationscited by 0