mlsanityData to 13 Oct 2026

Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equations

arXiv 2303.02304 ↗First posted 4 Mar 2023cs.LGcited by 11

Not on the map. Why?

Abstract (arXiv)

Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet space, so the difficulty for solving the coupled PDEs depends on dealing with the coupled mappings between the functions. Towards this end, we propose a textitcoupled multiwavelets neural operator (CMWNO) learning scheme by decoupling the coupled integral kernels during the multiwavelet decomposition and reconstruction procedures in the Wavelet space. The proposed model achieves significantly higher accuracy compared to previous learning-based solvers in solving the coupled PDEs including Gray-Scott (GS) equations and the non-local mean field game (MFG) problem. According to our experimental results, the proposed model exhibits a 2× ~ 4× improvement relative L2 error compared to the best results from the state-of-the-art models.

Key facts. Cited by 11 papers in the map (data through 13 Oct 2026). Builds on 20 of its 62 references that are in the map. First posted on arXiv 4 Mar 2023.

Builds on

20 of 62 references.

References · 20

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,857
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,989
  3. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 786
  4. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 766
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  11. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
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8 more
  1. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  2. 2020A physics-informed operator regression framework for extracting data-driven continuum modelscited by 60
  3. 2021Spectral Temporal Graph Neural Network for Trajectory Predictioncited by 36
  4. 2022Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Mediacited by 20
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  8. 2022DSLOB: A Synthetic Limit Order Book Dataset for Benchmarking Forecasting Algorithms under Distributional Shiftcited by 6

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 2; 2026: 4.

11 papers.

  1. 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Modelcited by 33
  2. 2024BENO: Boundary-embedded Neural Operators for Elliptic PDEscited by 23
  3. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  4. 2024Multi-scale Conditional Generative Modeling for Microscopic Image Restorationcited by 2
  5. 2025COMPOL: A Unified Neural Operator Framework for Scalable Multi-Physics Simulationscited by 1
  6. 2025Fast 3D Surrogate Modeling for Data Center Thermal Managementcited by 1
  7. 2026Adaptive Mamba Neural Operatorscited by 1
  8. 2026Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEscited by 1
  9. 2023Neuro-Inspired Hierarchical Multimodal Learningcited by 0
  10. 2026Theory Guided and Interpretable Neural Operator Design for Partial Differential Equation Learningcited by 0
  11. 2026A Generative Model of Complex Networks Using Graphons and Neural Inverse Operatorscited by 0