mlsanityData to 7 Oct 2026

Hamilton-Jacobi Based Policy-Iteration via Deep Operator Learning

arXiv 2406.10920 ↗First posted 16 Jun 2024math.OC cs.AI cs.LGcited by 5

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Abstract (arXiv)

The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy iteration scheme to numerically solve optimal control problems and the corresponding Hamilton--Jacobi--Bellman (HJB) equations. A notable feature of our approach is that once the neural network is trained, the solution to the optimal control problem and HJB equations with different terminal functions can be inferred quickly thanks to the unique feature of operator learning. Furthermore, a quantitative analysis of the accuracy of the algorithm is carried out via comparison principles of viscosity solutions. The effectiveness of the method is verified with various examples, including 10-dimensional linear quadratic regulator problems (LQRs).

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 20 of its 48 references that are in the map. First posted on arXiv 16 Jun 2024.

Builds on

20 of 48 references.

References · 20

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
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8 more
  1. 2019Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architecturescited by 21
  2. 2019On Decomposition Models in Imaging Sciences and Multi-time Hamilton-Jacobi Partial Differential Equationscited by 8
  3. 2017Perspectives on characteristics based curse-of-dimensionality-free numerical approaches for solving Hamilton-Jacobi equationscited by 7
  4. 2023Policy iteration for the deterministic control problems -- a viscosity approachcited by 7
  5. 2017Algorithm for Overcoming the Curse of Dimensionality for State-dependent Hamilton-Jacobi equationscited by 6
  6. 2021Lax-Oleinik-type formulas and efficient algorithms for certain high-dimensional optimal control problemscited by 3
  7. 2021A Computationally Efficient Hamilton-Jacobi-based Formula for State-Constrained Optimal Control Problemscited by 2
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 2.

5 papers.

  1. 2025Physics-Informed Neural Networks for Optimal Vaccination Plan in SIR Epidemic Modelscited by 1
  2. 2025Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iterationcited by 1
  3. 2025Physics-Informed Policy Iteration for High-Dimensional Hamilton--Jacobi--Bellman Equations: Interior Error Bounds without Boundary Datacited by 1
  4. 2026Towards General Language-Conditioned Latent Safety Filterscited by 1
  5. 2026Monotone Neural Policy Iteration for High-Dimensional First-Order Hamilton--Jacobi--Bellman Equationscited by 0