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

arXiv: https://arxiv.org/abs/1907.05327 · HTML: https://mlsanity.com/paper/1907.05327/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2019.

## Built on by (most cited first, 15 of 15)

- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks](https://mlsanity.com/paper/2312.14499/) (2023)
- [Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs](https://mlsanity.com/paper/2311.15283/) (2023)
- [Convergence of a robust deep FBSDE method for stochastic control](https://mlsanity.com/paper/2201.06854/) (2022)
- [A brief review of the Deep BSDE method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2505.17032/) (2025)
- [A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations](https://mlsanity.com/paper/2404.08456/) (2024)
- [An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Control](https://mlsanity.com/paper/2410.05163/) (2024)
- [A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs](https://mlsanity.com/paper/2204.05796/) (2022)
- [A novel control method for solving high-dimensional Hamiltonian systems through deep neural networks](https://mlsanity.com/paper/2111.02636/) (2021)
- [A deep solver for backward stochastic Volterra integral equations](https://mlsanity.com/paper/2505.18297/) (2025)
- [Deep Generative Modeling with Backward Stochastic Differential Equations](https://mlsanity.com/paper/2304.04049/) (2023)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)
- [A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications](https://mlsanity.com/paper/2511.08735/) (2025)
- [Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers](https://mlsanity.com/paper/2606.22150/) (2026)
- [A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch](https://mlsanity.com/paper/2606.29474/) (2026)

## 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.