mlsanityData to 7 Oct 2026

Neural Operators for Accelerating Scientific Simulations and Design

arXiv 2309.15325 ↗First posted 27 Sep 2023cs.LG physics.comp-phcited by 218

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Abstract (arXiv)

Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise. Numerical simulations present an alternative to physical experiments but are usually infeasible for complex real-world domains due to the computational requirements of existing numerical methods. Artificial intelligence (AI) presents a potential paradigm shift by developing fast data-driven surrogate models. In particular, an AI framework, known as Neural Operators, presents a principled framework for learning mappings between functions defined on continuous domains, e.g., spatiotemporal processes and partial differential equations (PDE). They can extrapolate and predict solutions at new locations unseen during training, i.e., perform zero-shot super-resolution. Neural Operators can augment or even replace existing simulators in many applications, such as computational fluid dynamics, weather forecasting, and material modeling, while being 4-5 orders of magnitude faster. Further, Neural Operators can be integrated with physics and other domain constraints enforced at finer resolutions to obtain high-fidelity solutions and good generalization. Since Neural Operators are differentiable, they can directly optimize parameters for inverse design and other inverse problems. We believe that Neural Operators present a transformative approach to simulation and design, enabling rapid research and development.

Key facts. Cited by 218 papers in the map (data through 7 Oct 2026). Builds on 75 of its 137 references that are in the map. First posted on arXiv 27 Sep 2023.

Builds on

75 of 137 references.

References · 75

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38 more
  1. 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
  2. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
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50 most cited of 75 All 75 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 50; 2025: 84; 2026: 84.

218 papers.

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  1. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
  2. 2024Neural Operators with Localized Integral and Differential Kernelscited by 59
  3. 2024Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEscited by 58
  4. 2024CViT: Continuous Vision Transformer for Operator Learningcited by 47
  5. 2024A Library for Learning Neural Operatorscited by 31
  6. 2025Generative Latent Neural PDE Solver using Flow Matchingcited by 28
  7. 2024Zero-shot forecasting of chaotic systemscited by 25
  8. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  9. 2024Positional Knowledge is All You Need: Position-induced Transformer (PiT) for Operator Learningcited by 17
  10. 2024RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operatorscited by 16
  11. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  12. 2025Operator Learning: A Statistical Perspectivecited by 14
38 more
  1. 2025Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learningcited by 14
  2. 2024AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamicscited by 13
  3. 2024Solving Poisson Equations using Neural Walk-on-Spherescited by 11
  4. 2024Linearization Turns Neural Operators into Function-Valued Gaussian Processescited by 11
  5. 2025Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learningcited by 11
  6. 2025Mesh-Informed Neural Operator : A Transformer Generative Approachcited by 11
  7. 2024Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flowscited by 10
  8. 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
  9. 2025Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulationscited by 10
  10. 2025Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Trainingcited by 10
  11. 2025CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operatorscited by 10
  12. 2024Universal Functional Regression with Neural Operator Flowscited by 9
  13. 2024Neural Operators for Predictor Feedback Control of Nonlinear Delay Systemscited by 9
  14. 2025DUE: A Deep Learning Framework and Library for Modeling Unknown Equationscited by 8
  15. 2025Solving engineering eigenvalue problems with neural networks using the Rayleigh quotientcited by 8
  16. 2025An Agentic Framework for Autonomous Metamaterial Modeling and Inverse Designcited by 8
  17. 2025The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operatorscited by 8
  18. 2026GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Trainingcited by 8
  19. 2024A Unified Model for Compressed Sensing MRI Across Undersampling Patternscited by 7
  20. 2025Guaranteed prediction sets for functional surrogate modelscited by 7
  21. 2025Enabling Automatic Differentiation with Mollified Graph Neural Operatorscited by 6
  22. 2025When is a System Discoverable from Data? Discovery Requires Chaoscited by 6
  23. 2024How more data can hurt: Instability and regularization in next-generation reservoir computingcited by 5
  24. 2024Scalable Mechanistic Neural Networks for Differential Equations and Machine Learningcited by 5
  25. 2024BI-EqNO: Generalized Approximate Bayesian Inference with an Equivariant Neural Operator Frameworkcited by 5
  26. 2024Projected Neural Differential Equations for Learning Constrained Dynamicscited by 5
  27. 2025TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Trainingcited by 5
  28. 2025A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometriescited by 5
  29. 2025Geometry aware inference of steady state PDEs using Equivariant Neural Fields representationscited by 5
  30. 2025Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programscited by 5
  31. 2024Global-local Fourier Neural Operator for Accelerating Coronal Magnetic Field Modelcited by 4
  32. 2024Solving Partial Differential Equations in Different Domains by Operator Learning method Based on Boundary Integral Equationscited by 4
  33. 2024Understanding complex crowd dynamics with generative neural simulatorscited by 4
  34. 2025Continuous Representation Methods, Theories, and Applications: An Overview and Perspectivescited by 4
  35. 2025PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modelingcited by 4
  36. 2025A Physics-informed Multi-resolution Neural Operatorcited by 4
  37. 2026Out-of-Distribution Generalization for Neural Physics Solverscited by 4
  38. 2026Simple yet Effective: Low-Rank Spatial Attention for Neural Operatorscited by 4

50 most cited of 218 All 218 (JSON)