# Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise

arXiv: https://arxiv.org/abs/2512.14967 · HTML: https://mlsanity.com/paper/2512.14967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 7 of 7)

- [Learning in Mean Field Games: the Fictitious Play](https://mlsanity.com/paper/1507.06280/) (2015)
- [Numerical Methods for Mean Field Games and Mean Field Type Control](https://mlsanity.com/paper/2106.06231/) (2021)
- [Numerical resolution of McKean-Vlasov FBSDEs using neural networks](https://mlsanity.com/paper/1909.12678/) (2019)
- [Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence](https://mlsanity.com/paper/2204.11924/) (2022)
- [A deep learning algorithm for computing mean field control problems via forward-backward score dynamics](https://mlsanity.com/paper/2401.09547/) (2024)
- [Deep Signature Approach for McKean-Vlasov FBSDEs in a Random Environment](https://mlsanity.com/paper/2511.09112/) (2025)
- [A Class of Finite-Dimensional Numerically Solvable McKean-Vlasov Control Problems](https://mlsanity.com/paper/1803.00445/) (2018)

## Abstract (arXiv)

We present a novel numerical method for solving McKean-Vlasov forward-backward stochastic differential equations (MV--FBSDEs) with common noise, combining Picard iterations, elicitability and deep learning. The key innovation involves elicitability to derive a path-wise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise -- without requiring computationally expensive nested Monte Carlo simulations. The mean-field interaction term is parameterized via a recurrent neural network trained to minimize an elicitable score, while the backward process is approximated through a hybrid feedforward and recurrent network representing the decoupling field. We validate the algorithm on a systemic risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution. We further extend the model to quantile--mediated interactions, showcasing the flexibility of the elicitability framework beyond conditional means or moments. Finally, we apply the method to a non-stationary Aiyagari-Bewley-Huggett economic growth model with endogenous interest rates, illustrating its applicability to complex mean-field games without closed-form solutions.