# SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasets

arXiv: https://arxiv.org/abs/2108.07667 · HTML: https://mlsanity.com/paper/2108.07667/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 52 references that are in the map.
- First posted on arXiv 17 Aug 2021.

## Builds on (most cited first, 19 of 19)

- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [A Survey on Deep Transfer Learning](https://mlsanity.com/paper/1808.01974/) (2018)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Deep Learning for Single Image Super-Resolution: A Brief Review](https://mlsanity.com/paper/1808.03344/) (2018)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [SciANN: A Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks](https://mlsanity.com/paper/2005.08803/) (2020)
- [Adaptive Neural Network-Based Approximation to Accelerate Eulerian Fluid Simulation](https://mlsanity.com/paper/2008.11832/) (2020)

## Built on by (most cited first, 8 of 8)

- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations](https://mlsanity.com/paper/2212.04663/) (2022)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [Breaking Boundaries: Distributed Domain Decomposition with Scalable Physics-Informed Neural PDE Solvers](https://mlsanity.com/paper/2308.14258/) (2023)
- [NUNet: Deep Learning for Non-Uniform Super-Resolution of Turbulent Flows](https://mlsanity.com/paper/2203.14154/) (2022)
- [Redefining Super-Resolution: Fine-mesh PDE predictions without classical simulations](https://mlsanity.com/paper/2311.09740/) (2023)
- [Patch-Based 3D Variational Autoencoder for Super-Resolution of Turbulent Channel Flow](https://mlsanity.com/paper/2507.22082/) (2025)
- [Learning Mappings in Mesh-based Simulations](https://mlsanity.com/paper/2506.12652/) (2025)

## Abstract (arXiv)

Deep Learning (DL) algorithms are emerging as a key alternative to computationally expensive CFD simulations. However, state-of-the-art DL approaches require large and high-resolution training data to learn accurate models. The size and availability of such datasets are a major limitation for the development of next-generation data-driven surrogate models for turbulent flows. This paper introduces SURFNet, a transfer learning-based super-resolution flow network. SURFNet primarily trains the DL model on low-resolution datasets and transfer learns the model on a handful of high-resolution flow problems - accelerating the traditional numerical solver independent of the input size. We propose two approaches to transfer learning for the task of super-resolution, namely one-shot and incremental learning. Both approaches entail transfer learning on only one geometry to account for fine-grid flow fields requiring 15x less training data on high-resolution inputs compared to the tiny resolution (64x256) of the coarse model, significantly reducing the time for both data collection and training. We empirically evaluate SURFNet's performance by solving the Navier-Stokes equations in the turbulent regime on input resolutions up to 256x larger than the coarse model. On four test geometries and eight flow configurations unseen during training, we observe a consistent 2-2.1x speedup over the OpenFOAM physics solver independent of the test geometry and the resolution size (up to 2048x2048), demonstrating both resolution-invariance and generalization capabilities. Our approach addresses the challenge of reconstructing high-resolution solutions from coarse grid models trained using low-resolution inputs (super-resolution) without loss of accuracy and requiring limited computational resources.