A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch

2026-06-28 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new a posteriori error analysis framework has been developed for decoupled neural approximations of fully coupled forward--backward stochastic differential equations (FBSDEs). This framework specifically addresses the control mismatch arising when an auxiliary control process in the forward coefficients differs from the neural network's backward component approximation. The methodology first establishes a continuous-time stability estimate for FBSDEs under perturbations of drift, diffusion, generator, terminal condition, and auxiliary control input. This estimate is then transferred to a discrete-time setting, yielding computable error bounds dependent on the terminal defect, pathwise residual, and the critical control mismatch. Numerical experiments on a linear-quadratic FBSDE and a multidimensional Burgers-type FBSDE demonstrate the diagnostic utility of these indicators and the mismatch penalty's role in ensuring numerical approximation consistency and reproducibility.

Key takeaway

For AI Scientists developing or deploying neural network-based solvers for fully coupled FBSDEs, understanding the implications of control mismatch is crucial. This framework provides a robust method to quantify approximation errors, especially when using decoupled architectures. You should integrate a posteriori error analysis, including the control mismatch penalty, into your validation processes to ensure the consistency and reproducibility of your numerical solutions.

Key insights

A framework quantifies error in decoupled neural FBSDE approximations, accounting for control mismatch.

Principles

• Decoupling neural FBSDEs introduces control mismatch.
• Error bounds require terminal defect, residual, and mismatch.
• Mismatch penalty improves approximation consistency.

Method

The framework establishes continuous-time stability estimates under perturbations, then transfers them to discrete-time to derive computable a posteriori error bounds based on terminal defect, pathwise residual, and control mismatch.

In practice

• Diagnose approximation errors in decoupled FBSDEs.
• Improve consistency of neural FBSDE solvers.

Topics

• Forward-Backward SDEs
• Neural Approximations
• Error Analysis
• Control Mismatch
• Stochastic Differential Equations
• Numerical Methods

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.