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

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 15× less training data on high-resolution inputs compared to the tiny resolution ($64\times 256$) 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 256× larger than the coarse model. On four test geometries and eight flow configurations unseen during training, we observe a consistent 2–2.1× speedup over the OpenFOAM physics solver independent of the test geometry and the resolution size (up to $2048 \times 2048$), demonstrating both resolution-invariance and generalization capabilities. Moreover, compared to the baseline model (aka oracle) that collects large training data at $256 \times 256$ and $512 \times 512$ grid resolutions, SURFNet achieves the same performance gain while reducing the combined data collection and training time by 3.6× and 10.2×, respectively. Our approach addresses the challenge of reconstructing high-resolution solutions from coarse grid models trained using low-resolution inputs (i.e., super-resolution) without loss of accuracy and requiring limited computational resources.