mlsanityData to 7 Oct 2026

Temporal Difference Learning for High-Dimensional PIDEs with Jumps

arXiv 2307.02766 ↗First posted 6 Jul 2023math.NA cs.LG cs.NAcited by 5

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Abstract (arXiv)

In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. Subsequently, we train the networks using the temporal difference error, termination condition, and properties of the non-local terms as the loss function. The relative error of the method reaches O(10^{-3}) in 100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump problems. Additionally, our method demonstrates the advantages of low computational cost and robustness, making it well-suited for addressing problems with different forms and intensities of jumps.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 19 of its 39 references that are in the map. First posted on arXiv 6 Jul 2023.

Builds on

19 of 39 references.

References · 19

  1. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
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  12. 2020Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networkscited by 122
7 more
  1. 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
  2. 2018Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equationscited by 54
  3. 2022Finite Expression Method for Solving High-Dimensional Partial Differential Equationscited by 21
  4. 2022Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Methodcited by 10
  5. 2022A deep solver for BSDEs with jumpscited by 9
  6. 2023Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumpscited by 6
  7. 2021Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematicscited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 1.

5 papers.

  1. 2023An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensionscited by 21
  2. 2024FBSJNN: A Theoretically Interpretable and Efficiently Deep Learning method for Solving Partial Integro-Differential Equationscited by 4
  3. 2024Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Methodcited by 3
  4. 2025Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domainscited by 0
  5. 2026INEUS: Iterative Neural Solver for High-Dimensional PIDEscited by 0