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INEUS: Iterative Neural Solver for High-Dimensional PIDEs

arXiv 2605.06281 ↗First posted 7 May 2026cs.LG cs.NA math.NAcited by 0

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Abstract (arXiv)

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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References · 25

  1. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 784
  2. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  4. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  5. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 572
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  7. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
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  10. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
  11. 2017A unified deep artificial neural network approach to partial differential equations in complex geometriescited by 122
  12. 2018Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equationscited by 54
13 more
  1. 2019Deep splitting method for parabolic PDEscited by 53
  2. 2021Optimal control of PDEs using physics-informed neural networkscited by 51
  3. 2018Solving the Kolmogorov PDE by means of deep learningcited by 41
  4. 2020Physics Informed Neural Networks for Simulating Radiative Transfercited by 35
  5. 2018Machine Learning for semi linear PDEscited by 28
  6. 2024Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEscited by 12
  7. 2022A deep solver for BSDEs with jumpscited by 9
  8. 2023Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumpscited by 6
  9. 2025Deep Learning for Continuous-Time Stochastic Control with Jumpscited by 6
  10. 2023Temporal Difference Learning for High-Dimensional PIDEs with Jumpscited by 5
  11. 2023Learning from Integral Losses in Physics Informed Neural Networkscited by 4
  12. 2024FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equationscited by 4
  13. 2025Convergence of a Deep BSDE solver with jumpscited by 4

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