mlsanityData to 7 Oct 2026

Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learning

arXiv 1907.05327 ↗First posted 11 Jul 2019math.NA cs.LG cs.NAcited by 15

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Abstract (arXiv)

Recently, the deep learning method has been used for solving forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). It has good accuracy and performance for high-dimensional problems. In this paper, we mainly solve fully coupled FBSDEs through deep learning and provide three algorithms. Several numerical results show remarkable performance especially for high-dimensional cases.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jul 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 4; 2024: 3; 2025: 3; 2026: 2.

15 papers.

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  1. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 78
  2. 2023Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networkscited by 23
  3. 2023Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEscited by 19
  4. 2022Convergence of a robust deep FBSDE method for stochastic controlcited by 11
  5. 2025A brief review of the Deep BSDE method for solving high-dimensional partial differential equationscited by 5
  6. 2024A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equationscited by 4
  7. 2022A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEscited by 2
  8. 2021A novel control method for solving high-dimensional Hamiltonian systems through deep neural networkscited by 1
  9. 2024An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Controlcited by 1
  10. 2025A deep solver for backward stochastic Volterra integral equationscited by 1
  11. 2023Deep Generative Modeling with Backward Stochastic Differential Equationscited by 0
  12. 2024A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agentscited by 0
3 more
  1. 2025A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applicationscited by 0
  2. 2026Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solverscited by 0
  3. 2026A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatchcited by 0