mlsanityData to 7 Oct 2026

Applications of physics informed neural operators

arXiv 2203.12634 ↗First posted 23 Mar 2022physics.comp-ph astro-ph.IM cs.AIcited by 33

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Abstract (arXiv)

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential equations that are ubiquitous in the study and modeling of physics phenomena. We first demonstrate that our methods reproduce the accuracy and performance of other neural operators published elsewhere in the literature to learn the 1D wave equation and the 1D Burgers equation. Thereafter, we apply our physics-informed neural operators to learn new types of equations, including the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we show that our approach is also applicable to learn the physics of the 2D linear and nonlinear shallow water equations, which involve three coupled partial differential equations. We release our artificial intelligence surrogates and scientific software to produce initial data and boundary conditions to study a broad range of physically motivated scenarios. We provide the source code, an interactive website to visualize the predictions of our physics informed neural operators, and a tutorial for their use at the Data and Learning Hub for Science.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). Builds on 23 of its 67 references that are in the map. First posted on arXiv 23 Mar 2022.

Builds on

23 of 67 references.

References · 23

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2016Gaussian Error Linear Units (GELUs)cited by 3,431
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  5. 2017Towards A Rigorous Science of Interpretable Machine Learningcited by 1,400
  6. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  7. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  8. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  9. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  10. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  11. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  12. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
11 more
  1. 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 158
  2. 2021Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Controlcited by 24
  3. 2020Accelerated, Scalable and Reproducible AI-driven Gravitational Wave Detectioncited by 20
  4. 2019Enabling real-time multi-messenger astrophysics discoveries with deep learningcited by 18
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 6; 2024: 7; 2025: 11; 2026: 8.

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  1. 2023Plasma Surrogate Modelling using Fourier Neural Operatorscited by 29
  2. 2023Neural Spectral Methods: Self-supervised learning in the spectral domaincited by 14
  3. 2025TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolationcited by 14
  4. 2022FAIR for AI: An interdisciplinary and international community building perspectivecited by 13
  5. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  6. 2024Masked Autoencoders are PDE Learnerscited by 11
  7. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  8. 2023Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific MLcited by 8
  9. 2025PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulationscited by 8
  10. 2024Component Fourier Neural Operator for Singularly Perturbed Differential Equationscited by 7
  11. 2023Magnetohydrodynamics with Physics Informed Neural Operatorscited by 6
  12. 2025Enabling Automatic Differentiation with Mollified Graph Neural Operatorscited by 6
21 more
  1. 2024Large-scale flood modeling and forecasting with FloodCastcited by 5
  2. 2025Physics-Informed DeepONet Coupled with FEM for Convective Transport in Porous Media with Sharp Gaussian Sourcescited by 3
  3. 2025Generalized Lie Symmetries in Physics-Informed Neural Operatorscited by 2
  4. 2025An effective physics-informed neural operator framework for predicting wavefieldscited by 2
  5. 2025Data-Efficient Time-Dependent PDE Surrogates: Graph Neural Simulators vs. Neural Operatorscited by 2
  6. 2025Chaos into Order: Neural Framework for Expected Value Estimation of Stochastic Partial Differential Equationscited by 1
  7. 2025Bridging ocean wave physics and deep learning: Physics-informed neural operators for nonlinear wavefield reconstruction in real-timecited by 1
  8. 2026Physics-Informed Laplace Neural Operator for Solving Partial Differential Equationscited by 1
  9. 2026Learning Physical Operators using Neural Operatorscited by 1
  10. 2026Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolutioncited by 1
  11. 2026Debiased neural operators for estimating functionalscited by 1
  12. 2026On the training of physics-informed neural operators for solving parametric partial differential equationscited by 1
  13. 2023Number Theoretic Accelerated Learning of Physics-Informed Neural Networkscited by 0
  14. 2024Equation identification for fluid flows via physics-informed neural networkscited by 0
  15. 2024LE-PDE++: Mamba for accelerating PDEs Simulationscited by 0
  16. 2024How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observationcited by 0
  17. 2025Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Datacited by 0
  18. 2025ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marchingcited by 0
  19. 2026General Explicit Network (GEN): A novel deep learning architecture for solving partial differential equationscited by 0
  20. 2026Physics-informed neural operators for the in situ characterization of locally reacting sound absorberscited by 0
  21. 2026LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamicscited by 0