A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch
arXiv:2606.29474v1 Announce Type: cross Abstract: This paper develops an a posteriori error analysis framework for decoupled neural approximations of fully coupled forward--backward stochastic differential equations (FBSDEs). It provides an a posteriori error-analysis for the idealized discrete adapted trajectory. The main feature of the proposed formulation is the use of an auxiliary control process in the forward coefficients, which may differ from the backward component approximated by the neural network. This decoupling is useful in practical deep learning implementations, but it creates a
This research addresses a fundamental challenge in applying deep learning to complex stochastic differential equations, suggesting a maturation in the theoretical understanding of neural network approximations.
Improved error analysis for neural approximations in stochastic differential equations could enhance the reliability and application of AI in fields like quantitative finance, control systems, and scientific computing.
The development of robust a posteriori error analysis could accelerate the deployment of deep learning models in safety-critical or high-stakes applications where quantifiable error bounds are essential.
- · AI researchers in stochastic processes
- · Quantitative finance
- · Control systems engineering
- · Developers of less rigorous approximation methods
- · Traditional numerical analysis techniques in specific domains
More accurate and reliable AI models for forecasting and control based on complex stochastic dynamics.
Increased trust and adoption of deep learning solutions in highly regulated or sensitive industries due to better interpretability of error bounds.
Potential for new AI-driven financial products or autonomous systems that can operate with guaranteed levels of precision and risk assessment.
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Read at arXiv cs.AI