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

arXiv: https://arxiv.org/abs/2005.01463 · HTML: https://mlsanity.com/paper/2005.01463/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2020.

## Built on by (most cited first, 30 of 78)

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- [Super-Resolution Neural Operator](https://mlsanity.com/paper/2303.02584/) (2023)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Learning to Solve PDE-constrained Inverse Problems with Graph Networks](https://mlsanity.com/paper/2206.00711/) (2022)
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- [Foundation Models for Weather and Climate Data Understanding: A Comprehensive Survey](https://mlsanity.com/paper/2312.03014/) (2023)
- [Hard-Constrained Deep Learning for Climate Downscaling](https://mlsanity.com/paper/2208.05424/) (2022)
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- [Wavelet Diffusion Neural Operator](https://mlsanity.com/paper/2412.04833/) (2024)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [MAgNet: Mesh Agnostic Neural PDE Solver](https://mlsanity.com/paper/2210.05495/) (2022)
- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning](https://mlsanity.com/paper/2201.12354/) (2022)
- [Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration](https://mlsanity.com/paper/2205.14249/) (2022)
- [Guiding continuous operator learning through Physics-based boundary constraints](https://mlsanity.com/paper/2212.07477/) (2022)
- [DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction](https://mlsanity.com/paper/2504.19496/) (2025)
- [Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks](https://mlsanity.com/paper/2401.11611/) (2024)
- [SuperBench: A Super-Resolution Benchmark Dataset for Scientific Machine Learning](https://mlsanity.com/paper/2306.14070/) (2023)
- [Inducing Point Operator Transformer: A Flexible and Scalable Architecture for Solving PDEs](https://mlsanity.com/paper/2312.10975/) (2023)
- [Physics-Informed Neural Network Super Resolution for Advection-Diffusion Models](https://mlsanity.com/paper/2011.02519/) (2020)
- [SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain](https://mlsanity.com/paper/2210.14044/) (2022)
- [OpenForest: A data catalogue for machine learning in forest monitoring](https://mlsanity.com/paper/2311.00277/) (2023)
- [WeatherGNN: Exploiting Meteo- and Spatial-Dependencies for Local Numerical Weather Prediction Bias-Correction](https://mlsanity.com/paper/2310.05517/) (2023)
- [Improving day-ahead Solar Irradiance Time Series Forecasting by Leveraging Spatio-Temporal Context](https://mlsanity.com/paper/2306.01112/) (2023)

## 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.