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arXiv · 2605.06281

INEUS: Iterative Neural Solver for High-Dimensional PIDEs

Jean-Loup Dupret·Davide Gallon·Patrick Cheridito
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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.

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BibTeXRIS

Jean-Loup Dupret, Davide Gallon, Patrick Cheridito. 2026-05-07. INEUS: Iterative Neural Solver for High-Dimensional PIDEs. https://arxiv.org/abs/2605.06281

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