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Fourier Neural Operators applied to Stochastic Volterra Equations

By PulseAugur Editorial · [1 sources] ·

This paper explores the application of Fourier Neural Operators (FNOs) to learn solutions for stochastic Volterra integral equations (SVIEs), which model random systems with memory. The authors establish a Wong--Zakai convergence theorem, demonstrating that pathwise solutions driven by piecewise linear approximations of Brownian motion converge to the true SVIE solution. This theoretical foundation supports the use of FNOs to map initial conditions and noise to solution trajectories, with numerical experiments showing accurate predictions and generalization to finer temporal grids than those used in training. AI

IMPACT Extends operator-learning frameworks to stochastic systems with memory, potentially improving predictive accuracy for complex dynamic models.

RANK_REASON Academic paper detailing a theoretical concept and its application to a specific class of equations. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Fourier Neural Operators applied to Stochastic Volterra Equations

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Academic paper detailing a theoretical concept and its application to a specific class of equations. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Wonjae Lee, Jiuk Jang, Hyungbin Park ·

    Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations

    arXiv:2610.18939v1 Announce Type: cross Abstract: This paper studies Wong--Zakai convergence and Fourier neural operator learning for stochastic Volterra integral equations (SVIEs) describing random systems with memory. A Wong--Zakai theorem establishes convergence of pathwise so…

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