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INEUS: Iterative Neural Solver for High-Dimensional PIDEs

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  • Jean-Loup Dupret
  • Davide Gallon
  • Patrick Cheridito

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.

Suggested Citation

  • Jean-Loup Dupret & Davide Gallon & Patrick Cheridito, 2026. "INEUS: Iterative Neural Solver for High-Dimensional PIDEs," Papers 2605.06281, arXiv.org.
    • Handle: RePEc:arx:papers:2605.06281
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    References listed on IDEAS

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    1. Rüdiger Frey & Verena Köck, 2022. "Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics," Springer Books, in: Marco Corazza & Cira Perna & Claudio Pizzi & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 272-277, Springer.
    2. Victor Duarte & Diogo Duarte & Dejanir H Silva, 2024. "Machine Learning for Continuous-Time Finance," The Review of Financial Studies, Society for Financial Studies, vol. 37(11), pages 3217-3271.
    3. Anindya Goswami & Jeeten Patel & Poorva Shevgaonkar, 2015. "A system of non-local parabolic PDE and application to option pricing," Papers 1506.01467, arXiv.org, revised May 2016.
    4. Kristoffer Andersson & Alessandro Gnoatto & Marco Patacca & Athena Picarelli, 2022. "A deep solver for BSDEs with jumps," Papers 2211.04349, arXiv.org, revised May 2025.
    5. Victor Duarte & Diogo Duarte & Dejanir H. Silva, 2024. "Machine Learning for Continuous-Time Finance," CESifo Working Paper Series 10909, CESifo.
    6. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
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