mlsanityData to 7 Oct 2026

Physics-Informed Geometry-Aware Neural Operator

arXiv 2408.01600 ↗First posted 2 Aug 2024cs.LG cs.NA math.NAcited by 18

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Abstract (arXiv)

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly predicting the PDE solutions. However, training these neural operators typically requires large datasets, the acquisition of which can be prohibitively expensive. To overcome this, physics-informed training offers an alternative way of building neural operators, eliminating the high computational costs associated with Finite Element generation of training data. Nevertheless, current physics-informed neural operators struggle with limitations, either in handling varying domain geometries or varying PDE parameters. In this research, we introduce a novel method, the Physics-Informed Geometry-Aware Neural Operator (PI-GANO), designed to simultaneously generalize across both PDE parameters and domain geometries. We adopt a geometry encoder to capture the domain geometry features, and design a novel pipeline to integrate this component within the existing DCON architecture. Numerical results demonstrate the accuracy and efficiency of the proposed method. All the codes and data related to this work are available on GitHub: https://github.com/WeihengZ/Physics-informed-Neural-Foundation-Operator.

Key facts. Cited by 18 papers in the map (data through 7 Oct 2026). Builds on 21 of its 34 references that are in the map. First posted on arXiv 2 Aug 2024.

Builds on

21 of 34 references.

References · 21

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  4. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
  5. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  6. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
  7. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  8. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  9. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  10. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  11. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  12. 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
9 more
  1. 2021Improved architectures and training algorithms for deep operator networkscited by 85
  2. 2022Wavelet neural operator: a neural operator for parametric partial differential equationscited by 77
  3. 2020Pooling Methods in Deep Neural Networks, a Reviewcited by 52
  4. 2023Physics informed WNOcited by 26
  5. 2018Automatic differentiation in ML: Where we are and where we should be goingcited by 20
  6. 2023Inducing Point Operator Transformer: A Flexible and Scalable Architecture for Solving PDEscited by 16
  7. 2024Diffeomorphism Neural Operator for various domains and parameters of partial differential equationscited by 15
  8. 2023Multi-scale Time-stepping of Partial Differential Equations with Transformerscited by 14
  9. 2024MPIPN: A Multi Physics-Informed PointNet for solving parametric acoustic-structure systemscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 9; 2026: 9.

18 papers.

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  1. 2025DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulationscited by 26
  2. 2025Geometry-Informed Neural Operator Transformercited by 8
  3. 2025DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modelingcited by 5
  4. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 5
  5. 2025RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equationscited by 4
  6. 2026Topological Neural Operatorscited by 2
  7. 2026A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modelingcited by 2
  8. 2025Transferable Foundation Models for Geometric Tasks on Point Cloud Representations: Geometric Neural Operatorscited by 1
  9. 2025Variational Rank Reduction Autoencoders for Generative Thermal Designcited by 1
  10. 2025Learning Nonlinear Responses in PET Bottle Buckling with a Hybrid DeepONet-Transolver Frameworkcited by 0
  11. 2025GIMLET: Generalizable and Interpretable Model Learning through Embedded Thermodynamicscited by 0
  12. 2026Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structurescited by 0
6 more
  1. 2026Investigating Nonlinear Quenching Effects on Polar Field Buildup in the Sun Using Physics-Informed Neural Networkscited by 0
  2. 2026Resolution-free neural surrogates for geometric parameterization and mapping with spatially varying fieldscited by 0
  3. 2026GA-VINO: A Geometry-Aware Variational Physics-informed Neural Operator for Mindlin-Reissner Platescited by 0
  4. 2026Latent PDE mapping for efficient physics-informed learning across geometries with limited datacited by 0
  5. 2026Learning PDE Dynamics between Submanifolds Using Green's Observation Operatorscited by 0
  6. 2026Transferability of Learned States in Neural PDE Solverscited by 0