arXiv：cs.LG· Wonjae Lee, Jiuk Jang, Hyungbin Park·· 10 小时前
Wong–Zakai 收敛性与 FNO 学习在随机 Volterra 方程中的应用
Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations
AI 导读
该研究为描述带记忆随机系统的随机 Volterra 积分方程（SVIE）建立了 Wong–Zakai 收敛定理，证明由布朗运动分段线性逼近驱动的路径解收敛至对应 SVIE 解。基于此，作者用镜像填充的傅里叶神经算子（FNO）学习从初始条件与驱动噪声到完整解轨迹的算子映射，数值实验显示其预测精度具竞争力，且能泛化到比训练更细的时间网格，同时评估了填充与计算成本的影响。
正文
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 solutions driven by piecewise linear approximations of Brownian motion to the corresponding SVIE solution. This convergence provides a foundation for using mirror-padded Fourier neural operators to learn the solution operator mapping initial conditions and driving noise to entire solution trajectories. Numerical experiments demonstrate competitive prediction accuracy and generalization to temporal grids finer than those used for training, while assessing the influence of padding and computational cost. As a follow-up to \citet{LKP:26}, this study extends their operator-learning framework to SVIEs through separate convergence and approximation analyses tailored to convolutional memory.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR) |
| Cite as: | arXiv:2610.18939 [stat.ML] |
| (or arXiv:2610.18939v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.18939 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Wonjae Lee [view email]
[v1]
Tue, 13 Oct 2026 13:23:09 UTC (1,388 KB)
来源：arXiv：cs.LG · arxiv.org