The Deep Truncated FBSDE Method: A Robust Solver for High-dimensional PDEs

par Yunzhang LI (Fudan Université)

lundi 7 déc. 2026, 14:00 → 16:00 Europe/Paris

Salle 27 (Site des Carmes)

In this talk, we introduce a deep truncated FBSDE method for high-dimensional quasilinear PDEs. Compared to existing deep-learning BSDE solvers, which often suffer from instability when applied to strongly coupled problems, our approach demonstrates significantly enhanced stability. The proposed method applies gradient-truncated iterative decoupling alongside fictitious-play averaging to separate the forward and backward processes in coupled framework. This ensures the coupled dynamics are preserved while reducing the unstable feedback induced by parameter-dependent forward paths. Furthermore, we incorporate a pathwise consistency optimization strategy to generate explicit local gradient contributions and mitigate the vanishing gradient problem. Our approach is particularly effective for degenerate convection-dominated equations, where the coupled formulation provides a stable representation of nonlinear transport without introducing singular generator terms into the BSDE. Both theoretical analysis and numerical experiments confirm that this method improves stability, convergence, and accuracy, establishing a scalable and reliable framework for both low- and high-dimensional problems.