Learning Data-Efficient and Generalizable Neural Operators via Fundamental Physics Knowledge
Not on the map. Why?
Abstract (arXiv)
Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While existing approaches focus primarily on learning simulations from the target PDE, they often overlook more fundamental physical principles underlying these equations. Inspired by how numerical solvers are compatible with simulations of different settings of PDEs, we propose a multiphysics training framework that jointly learns from both the original PDEs and their simplified basic forms. Our framework enhances data efficiency, reduces predictive errors, and improves out-of-distribution (OOD) generalization, particularly in scenarios involving shifts of physical parameters and synthetic-to-real transfer. Our method is architecture-agnostic and demonstrates consistent improvements in normalized root mean square error (nRMSE) across a wide range of 1D/2D/3D PDE problems. Through extensive experiments, we show that explicit incorporation of fundamental physics knowledge significantly strengthens the generalization ability of neural operators. We will release models and codes at https://sites.google.com/view/sciml-fundemental-pde.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 45 of its 74 references that are in the map. First posted on arXiv 16 Feb 2026.
Builds on
45 of 74 references.
References · 45
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2022VideoMAE: Masked Autoencoders are Data-Efficient Learners for Self-Supervised Video Pre-Trainingcited by 1,305
- 2017An Overview of Multi-Task Learning in Deep Neural Networkscited by 791
- 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 537
- 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 516
- 2021Machine learning accelerated computational fluid dynamicscited by 461
- 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
- 2020Multi-Task Learning with Deep Neural Networks: A Surveycited by 374
- 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
- 2019Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Datacited by 261
33 more
- 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 237
- 2022U-NO: U-shaped Neural Operatorscited by 219
- 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 207
- 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
- 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 173
- 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 144
- 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 137
- 2023Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behaviorcited by 128
- 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 127
- 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 118
- 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
- 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
- 2021Improved architectures and training algorithms for deep operator networkscited by 85
- 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
- 2014Curriculum Learning of Multiple Taskscited by 65
- 2023Learning Physical Models that Can Respect Conservation Lawscited by 58
- 2021Seismic wave propagation and inversion with Neural Operatorscited by 51
- 2022Generative Adversarial Neural Operatorscited by 51
- 2023LNO: Laplace Neural Operator for Solving Differential Equationscited by 47
- 2020Automated Synthetic-to-Real Generalizationcited by 35
- 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
- 2021Contrastive Syn-to-Real Generalizationcited by 32
- 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
- 2024Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learningcited by 32
- 2023Koopman neural operator as a mesh-free solver of non-linear partial differential equationscited by 29
- 2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
- 2022Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equationscited by 28
- 2024Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEscited by 14
- 2024Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Lawscited by 10
- 2019Auxiliary Learning for Deep Multi-task Learningcited by 4
- 2023Hyena Neural Operator for Partial Differential Equationscited by 4
- 2024Data-Efficient Inference of Neural Fluid Fields via SciML Foundation Modelcited by 4
- 2023Meta-Learning for Airflow Simulations with Graph Neural Networkscited by 1
Built on by
Citing papers per year: 2026: 2.
2 papers.