INEUS: Iterative Neural Solver for High-Dimensional PIDEs

TL;DR

INEUS is a meshfree neural solver that efficiently addresses high-dimensional PIDEs by reformulating the problem as recursive regression, avoiding costly derivatives and enabling scalable solutions.

Contribution

The paper introduces INEUS, a novel neural method that improves the efficiency and scalability of solving high-dimensional PIDEs using a meshfree, iterative approach.

Findings

INEUS achieves accurate solutions for high-dimensional PIDEs.

The method is scalable to nonlinear and high-dimensional problems.

Numerical experiments confirm the efficiency and accuracy of INEUS.

Abstract

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.