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MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework

arXiv 2005.01463 ↗First posted 1 May 2020cs.LG eess.IV physics.flu-dyncited by 78

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Abstract (arXiv)

We propose MeshfreeFlowNet, a novel deep learning-based super-resolution framework to generate continuous (grid-free) spatio-temporal solutions from the low-resolution inputs. While being computationally efficient, MeshfreeFlowNet accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet allows for: (i) the output to be sampled at all spatio-temporal resolutions, (ii) a set of Partial Differential Equation (PDE) constraints to be imposed, and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal domains owing to its fully convolutional encoder. We empirically study the performance of MeshfreeFlowNet on the task of super-resolution of turbulent flows in the Rayleigh-Benard convection problem. Across a diverse set of evaluation metrics, we show that MeshfreeFlowNet significantly outperforms existing baselines. Furthermore, we provide a large scale implementation of MeshfreeFlowNet and show that it efficiently scales across large clusters, achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of less than 4 minutes.

Key facts. Cited by 78 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 May 2020.

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Citing papers per year: 2020: 1; 2021: 10; 2022: 21; 2023: 21; 2024: 15; 2025: 7; 2026: 3.

78 papers.

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  1. 2021Neural Fields in Visual Computing and Beyondcited by 539
  2. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  3. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 218
  4. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  5. 2023Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEscited by 66
  6. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  7. 2023Super-Resolution Neural Operatorcited by 48
  8. 2021Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domainscited by 37
  9. 2022Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal datacited by 37
  10. 2022Learning to Solve PDE-constrained Inverse Problems with Graph Networkscited by 37
  11. 2021Meta-Auto-Decoder for Solving Parametric Partial Differential Equationscited by 36
  12. 2023Foundation Models for Weather and Climate Data Understanding: A Comprehensive Surveycited by 32
38 more
  1. 2023Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flowscited by 30
  2. 2022Hard-Constrained Deep Learning for Climate Downscalingcited by 29
  3. 2021Variational Data Assimilation with a Learned Inverse Observation Operatorcited by 28
  4. 2022MAgNet: Mesh Agnostic Neural PDE Solvercited by 28
  5. 2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
  6. 2024Wavelet Diffusion Neural Operatorcited by 28
  7. 2022Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learningcited by 24
  8. 2022Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustrationcited by 21
  9. 2022Guiding continuous operator learning through Physics-based boundary constraintscited by 21
  10. 2025DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic predictioncited by 21
  11. 2023SuperBench: A Super-Resolution Benchmark Dataset for Scientific Machine Learningcited by 18
  12. 2024Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networkscited by 18
  13. 2020Physics-Informed Neural Network Super Resolution for Advection-Diffusion Modelscited by 16
  14. 2022SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domaincited by 16
  15. 2023Inducing Point Operator Transformer: A Flexible and Scalable Architecture for Solving PDEscited by 16
  16. 2023OpenForest: A data catalogue for machine learning in forest monitoringcited by 15
  17. 2023Improving day-ahead Solar Irradiance Time Series Forecasting by Leveraging Spatio-Temporal Contextcited by 13
  18. 2023WeatherGNN: Exploiting Meteo- and Spatial-Dependencies for Local Numerical Weather Prediction Bias-Correctioncited by 13
  19. 2022A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEscited by 11
  20. 2024Uncertainty Quantification of Surrogate Models using Conformal Predictioncited by 11
  21. 2021S3RP: Self-Supervised Super-Resolution and Prediction for Advection-Diffusion Processcited by 9
  22. 2022Physics-informed Deep Super-resolution for Spatiotemporal Datacited by 9
  23. 2021SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasetscited by 8
  24. 2022AtmoDist: Self-supervised Representation Learning for Atmospheric Dynamicscited by 8
  25. 2023Latent assimilation with implicit neural representations for unknown dynamicscited by 8
  26. 2025Calibrated Physics-Informed Uncertainty Quantificationcited by 8
  27. 2022PhySRNet: Physics informed super-resolution network for application in computational solid mechanicscited by 7
  28. 2024Observation-Guided Meteorological Field Downscaling at Station Scale: A Benchmark and a New Methodcited by 7
  29. 2021Machine Learning-Accelerated Computational Solid Mechanics: Application to Linear Elasticitycited by 6
  30. 2022Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equationscited by 6
  31. 2023Multi-variable Hard Physical Constraints for Climate Model Downscalingcited by 6
  32. 2025F-INR: Functional Tensor Decomposition for Implicit Neural Representationscited by 6
  33. 2022Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networkscited by 5
  34. 2023RANS-PINN based Simulation Surrogates for Predicting Turbulent Flowscited by 5
  35. 2024Neural Network Emulator for Atmospheric Chemical ODEcited by 5
  36. 2021BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learningcited by 4
  37. 2022Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networkscited by 4
  38. 2022Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networkscited by 3

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