INEUS：用于高维偏积分微分方程的迭代神经求解器
INEUS: Iterative Neural Solver for High-Dimensional PIDEs
- Department of Mathematics and RiskLab, ETH Zurich（数学系和风险实验室，苏黎世联邦理工学院）
- Applied Mathematics: Institute for Analysis and Numerics, University of Münster（应用数学：分析与数值计算研究所，蒙斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
INEUS通过单跳采样替代非局部跳跃积分的显式计算，将PIDE求解转化为递归回归问题，高效处理非局部项并避免复杂残差微分，适用于高维PDE和PIDE的准确可扩展求解。
AI中文摘要：
本文介绍了INEUS，一种用于偏积分微分方程（PIDEs）的无网格迭代神经求解器。该方法用单跳采样替代非局部跳跃积分的显式计算，将PIDE求解转化为一系列递归回归问题。与物理信息神经网络（PINNs）类似，INEUS在全域空间-时间域上学习解，但更高效地处理非局部项并避免了全PIDE残差的计算开销。这些特性使INEUS特别适合高维PDE和PIDE。通过基于收缩的收敛证明，我们的数值实验表明INEUS能为各种高维线性和非线性例子提供准确且可扩展的解。
英文摘要：
In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal jump integrals with single-jump sampling and reformulates PIDE solving as a sequence of recursive regression problems. Like Physics-Informed Neural Networks (PINNs), INEUS learns global solutions over the entire space-time domain, yet it offers a more efficient treatment of nonlocal terms and avoids the computationally expensive differentiation of full PIDE residuals. These features make INEUS particularly well suited for high-dimensional PDEs and PIDEs. Supported by a contraction-based convergence proof for linear PIDEs, our numerical experiments show that INEUS delivers accurate and scalable solutions for various high-dimensional linear and nonlinear examples.
