mlsanityData to 14 Oct 2026

MC-Nonlocal-PINNs: handling nonlocal operators in PINNs via Monte Carlo sampling

arXiv 2212.12984 ↗First posted 26 Dec 2022math.NA cs.LG cs.NAcited by 1

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Abstract (arXiv)

We propose, Monte Carlo Nonlocal physics-informed neural networks (MC-Nonlocal-PINNs), which is a generalization of MC-fPINNs in citeguo2022monte, for solving general nonlocal models such as integral equations and nonlocal PDEs. Similar as in MC-fPINNs, our MC-Nonlocal-PINNs handle the nonlocal operators in a Monte Carlo way, resulting in a very stable approach for high dimensional problems. We present a variety of test problems, including high dimensional Volterra type integral equations, hypersingular integral equations and nonlocal PDEs, to demonstrate the effectiveness of our approach.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 14 of its 35 references that are in the map. First posted on arXiv 26 Dec 2022.

Builds on

14 of 35 references.

References · 14

  1. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  3. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
  4. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  5. 2019Machine Learning for Fluid Mechanicscited by 385
  6. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  7. 2017Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanicscited by 214
  8. 2018Discovering physical concepts with neural networkscited by 117
  9. 2020nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applicationscited by 36
  10. 2021Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow modelscited by 35
  11. 2020Machine Learning and Computational Mathematicscited by 22
  12. 2022Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equationscited by 20
2 more
  1. 2020Numerical methods for nonlocal and fractional modelscited by 12
  2. 2021An augmented Lagrangian deep learning method for variational problems with essential boundary conditionscited by 11

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Cited by year

Citing papers per year: 2024: 1.

1 paper.

  1. 2024Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networkscited by 5