# The deep multi-FBSDE method: a robust deep learning method for coupled FBSDEs

arXiv: https://arxiv.org/abs/2503.13193 · HTML: https://mlsanity.com/paper/2503.13193/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Mar 2025.

## Built on by (most cited first, 4 of 4)

- [A deep solver for backward stochastic Volterra integral equations](https://mlsanity.com/paper/2505.18297/) (2025)
- [Nonlinear filtering based on density approximation and deep BSDE prediction](https://mlsanity.com/paper/2508.10630/) (2025)
- [High-dimensional Bayesian filtering through deep density approximation](https://mlsanity.com/paper/2511.07261/) (2025)
- [A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch](https://mlsanity.com/paper/2606.29474/) (2026)

## Abstract (arXiv)

We introduce the deep multi-FBSDE method for robust approximation of coupled forward-backward stochastic differential equations (FBSDEs), focusing on cases where the deep BSDE method of Han, Jentzen, and E (2018) fails to converge. To overcome the convergence issues, we consider a family of FBSDEs that are equivalent to the original problem in the sense that they satisfy the same associated partial differential equation (PDE). Our algorithm proceeds in two phases: first, we approximate the initial condition for the FBSDE family, and second, we approximate the original FBSDE using the initial condition approximated in the first phase. Numerical experiments show that our method converges even when the standard deep BSDE method does not.