mlsanityData to 7 Oct 2026

SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems

arXiv 2201.05475 ↗First posted 14 Jan 2022math.OC cs.LGcited by 9

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Abstract (arXiv)

Solving high-dimensional optimal control problems in real-time is an important but challenging problem, with applications to multi-agent path planning problems, which have drawn increased attention given the growing popularity of drones in recent years. In this paper, we propose a novel neural network method called SympOCnet that applies the Symplectic network to solve high-dimensional optimal control problems with state constraints. We present several numerical results on path planning problems in two-dimensional and three-dimensional spaces. Specifically, we demonstrate that our SympOCnet can solve a problem with more than 500 dimensions in 1.5 hours on a single GPU, which shows the effectiveness and efficiency of SympOCnet. The proposed method is scalable and has the potential to solve truly high-dimensional path planning problems in real-time.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 38 of its 94 references that are in the map. First posted on arXiv 14 Jan 2022.

Builds on

38 of 94 references.

References · 38

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26 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 1; 2024: 1; 2025: 2; 2026: 2.

9 papers.

  1. 2025Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEscited by 11
  2. 2024Symplectic Neural Networks Based on Dynamical Systemscited by 4
  3. 2022Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEscited by 3
  4. 2022Offline Supervised Learning V.S. Online Direct Policy Optimization: A Comparative Study and A Unified Training Paradigm for Neural Network-Based Optimal Feedback Controlcited by 3
  5. 2023Solving Elliptic Optimal Control Problems via Neural Networks and Optimality Systemcited by 3
  6. 2026PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methodscited by 3
  7. 2022Neural Network Optimal Feedback Control with Guaranteed Local Stabilitycited by 2
  8. 2025Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equationscited by 0
  9. 2026Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEscited by 0