[Submitted on 7 May 2026 (v1), last revised 9 Nov 2026 (this version, v2)]
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.
Submission history
From: Jean-Loup Dupret [view email]
[v1] Thu, 7 May 2026 13:53:45 UTC (4,718 KB)
[v2] Mon, 9 Nov 2026 08:46:38 UTC (4,725 KB)
