INEUS: Iterative Neural Solver for High-Dimensional PIDEs
For researchers solving high-dimensional PIDEs, INEUS offers a more efficient alternative to PINNs by avoiding costly differentiation of full residuals, with convergence guarantees for linear cases.
INEUS introduces a meshfree iterative neural solver for high-dimensional partial integro-differential equations (PIDEs) that replaces explicit nonlocal integral evaluation with single-jump sampling and recursive regression, achieving accurate and scalable solutions for linear and nonlinear examples up to 100 dimensions.
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.