mlsanityData to 7 Oct 2026

Physics informed WNO

arXiv 2302.05925 ↗First posted 12 Feb 2023stat.ML cs.LGcited by 26

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Abstract (arXiv)

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict solutions of PDEs for varying initial or boundary conditions and different inputs. A recently proposed Wavelet Neural Operator (WNO) is one such operator that harnesses the advantage of time-frequency localization of wavelets to capture the manifolds in the spatial domain effectively. While WNO has proven to be a promising method for operator learning, the data-hungry nature of the framework is a major shortcoming. In this work, we propose a physics-informed WNO for learning the solution operators of families of parametric PDEs without labeled training data. The efficacy of the framework is validated and illustrated with four nonlinear spatiotemporal systems relevant to various fields of engineering and science.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 16 of its 50 references that are in the map. First posted on arXiv 12 Feb 2023.

Builds on

16 of 50 references.

References · 16

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  3. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  4. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  6. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  7. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  8. 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
  9. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  10. 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
  11. 2019Transfer learning enhanced physics informed neural network for phase-field modeling of fracturecited by 116
  12. 2020Transfer learning based multi-fidelity physics informed deep neural networkcited by 68
4 more
  1. 2019Data-Driven Deep Learning of Partial Differential Equations in Modal Spacecited by 46
  2. 2018Machine Learning for semi linear PDEscited by 28
  3. 2022Stochastic projection based approach for gradient free physics informed learningcited by 15
  4. 2022Multi-fidelity wavelet neural operator with application to uncertainty quantificationcited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 9; 2025: 8; 2026: 2.

26 papers.

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  1. 2024Physics-Informed Geometry-Aware Neural Operatorcited by 18
  2. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  3. 2023A foundational neural operator that continuously learns without forgettingcited by 10
  4. 2025Physics-Informed Latent Neural Operator for Real-time Predictions of time-dependent parametric PDEscited by 9
  5. 2024Physics-informed Discretization-independent Deep Compositional Operator Networkcited by 6
  6. 2024Quantitative Approximation for Neural Operators in Nonlinear Parabolic Equationscited by 5
  7. 2025DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modelingcited by 5
  8. 2024Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularizationcited by 3
  9. 2024Towards Gaussian Process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanicscited by 3
  10. 2023Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operatorcited by 2
  11. 2023How important are specialized transforms in Neural Operators?cited by 2
  12. 2023DPA-WNO: A gray box model for a class of stochastic mechanics problemcited by 2
14 more
  1. 2023Waveformer for modelling dynamical systemscited by 2
  2. 2024Generative flow induced neural architecture search: Towards discovering optimal architecture in wavelet neural operatorcited by 2
  3. 2024M2M: Learning controllable Multi of experts and multi-scale operators are the Partial Differential Equations needcited by 2
  4. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  5. 2025Geometric Laplace Neural Operatorcited by 2
  6. 2023Neuroscience inspired scientific machine learning (Part-2): Variable spiking wavelet neural operatorcited by 1
  7. 2024Harnessing physics-informed operators for high-dimensional reliability analysis problemscited by 1
  8. 2025A unified physics-informed generative operator framework for general inverse problemscited by 1
  9. 2026Physics-Informed Laplace Neural Operator for Solving Partial Differential Equationscited by 1
  10. 2024LE-PDE++: Mamba for accelerating PDEs Simulationscited by 0
  11. 2025Deep Muscle EMG construction using A Physics-Integrated Deep Learning approachcited by 0
  12. 2025From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systemscited by 0
  13. 2025Event-driven physics-informed operator learning for reliability analysiscited by 0
  14. 2026Multi-Fidelity Learning with Shallow Recurrent Decoders for Multi-Physics Applicationscited by 0