INEUS: Iterative Neural Solver for High-Dimensional PIDEs
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| Format: | Preprint |
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2026
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| _version_ | 1866917468467888128 |
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| author | Dupret, Jean-Loup Gallon, Davide Cheridito, Patrick |
| author_facet | Dupret, Jean-Loup Gallon, Davide Cheridito, Patrick |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_06281 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | INEUS: Iterative Neural Solver for High-Dimensional PIDEs Dupret, Jean-Loup Gallon, Davide Cheridito, Patrick Machine Learning Numerical Analysis Computational Finance 35R09, 65M99 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. |
| title | INEUS: Iterative Neural Solver for High-Dimensional PIDEs |
| topic | Machine Learning Numerical Analysis Computational Finance 35R09, 65M99 |
| url | https://arxiv.org/abs/2605.06281 |