Source-linked AI summary
Super-resolution reconstruction of turbulent flows with machine learning
Kai Fukami, Koji Fukagata, Kunihiko Taira
TL;DR
Grossly under-resolved flow data limits access to high-resolution turbulent structures, motivating data reconstruction methods. The paper develops CNN and hybrid DSC/MS super-resolution models and tests them on cylinder wakes and homogeneous turbulence. Both models reconstruct laminar and turbulent flows accurately, with some cases requiring as few as 50 training snapshots, while performance depends on input preparation and resolution.
Problem
Increasingly coarse or under-resolved flow data creates a need for machine-learning methods that reconstruct high-resolution flow fields and potentially support subgrid-scale analysis.
Method
The study uses CNN and hybrid DSC/MS models for super-resolution, preparing inputs by average or max pooling at medium, low, and super-low resolutions.
Results
Both models reconstruct laminar and turbulent flows, accurately reproduce kinetic energy spectra, and can in some cases be learned from as few as 50 training snapshots.
Takeaways & Limitations
The models can reconstruct turbulent velocity and vorticity fields from extremely low-resolution inputs, supporting extraction of subgrid flow information.
Takeaways & Limitations
Reconstruction accuracy depends on input-data characteristics and coarsening: max pooling can produce unstable staircased results, while larger inputs increase training cost.
Abstract
from arXiv · showhide
We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machine-learning models are developed; namely the convolutional neural network (CNN) and the hybrid Downsampled Skip-Connection Multi-Scale (DSC/MS) models. These machine-learning models are applied to two-dimensional cylinder wake as a preliminary test and show remarkable ability to reconstruct laminar flow from low-resolution flow field data. We further assess the performance of these models for two-dimensional homogeneous turbulence. The CNN and DSC/MS models are found to reconstruct turbulent flows from extremely coarse flow field images with remarkable accuracy. For the turbulent flow problem, the machine-leaning based super-resolution analysis can greatly enhance the spatial resolution with as little as 50 training snapshot data, holding great potential to reveal subgrid-scale physics of complex turbulent flows. With the growing availability of flow field data from high-fidelity simulations and experiments, the present approach motivates the development of effective super-resolution models for a variety of fluid flows.
1. Introduction
Machine learning is positioned as a way to reconstruct high-resolution flow fields from increasingly abundant but coarse flow data. This study applies CNN and hybrid DSC/MS models to laminar and turbulent test cases.
- High-resolution flow data remains a central pursuit in experimental and computational fluid dynamics as measurement and simulation capabilities advance.Miniaturized hot wires, particle image velocimetry, and finer computational grids expose increasingly intricate turbulent structures.
- The growing volume of fluid-flow data motivates using machine learning to complement experimental and computational approaches.
- Traditional bicubic interpolation is easy to implement but its low-pass characteristics limit reconstruction of high-frequency image content.
- The study develops CNN and hybrid DSC/MS super-resolution models and tests them on two-dimensional cylinder wake and homogeneous turbulence.
- The work targets reconstruction of high-resolution flow fields from low-resolution images, including unsteady laminar and turbulent flows.
2. Methodology
The methodology reconstructs high-resolution flow fields from coarse data using machine-learned nonlinear regression, comparing CNN and hybrid DSC/MS architectures across pooling and flow-field inputs.
- Machine-learned reconstruction: The model learns a nonlinear mapping from low-resolution input x to high-resolution output F(x; w) by minimizing the L2 error against desired data y.After training, the optimized model is used to reconstruct flow fields from low-resolution data.
- Input preparation: Average and max pooling downsample DNS fields using M × M windows, with M = 8, 16, and 32 representing medium-, low-, and super-low-resolution inputs.Average pooling smooths the field, whereas max pooling retains regions with large velocity magnitudes.
- CNN model: The CNN processes flow data iteratively through layers, transforming q^(0) = x until q^(lmax) = F(x; w).The architecture uses convolutional filters and activation functions to generate the reconstructed output.
- Flow-field inputs: Velocity vectors and vorticity fields are supplied separately, using K = 2 and K = 1 input channels, respectively, to assess their influence on reconstruction accuracy.The two inputs differ both in whether they are vector or scalar fields and in their spectral content.
- Hybrid DSC/MS model: The hybrid DSC/MS model combines compression, skip connections, and differently sized CNN filters to capture large- and small-scale turbulent structures.Compression improves robustness to translation and rotation, skip connections address convergence issues, and multi-scale filters span a range of scales.
- Evaluation setup: Both models use early stopping after 20 learning iterations and are compared with bicubic interpolation on cylinder-wake and decaying homogeneous-turbulence fields.The cylinder wake provides a laminar preliminary test, while homogeneous turbulence evaluates reconstruction of multi-scale flow structure.
3. Results
The CNN and hybrid DSC/MS models reconstruct laminar and turbulent flow fields from coarse inputs, with DSC/MS generally providing the strongest turbulent-flow performance. Accuracy depends on pooling type, resolution, training snapshots, and flow-field spectral content.
- 3.1. Example 1: Two-dimensional cylinder wake: 1000 snapshots are sufficient to recover the laminar cylinder-wake flow field from coarse data.The reconstructed vorticity agrees well with reference DNS data, including its probability density function, on held-out test data.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: 0.659 is the bicubic velocity error for medium-resolution input, compared with 1.08 for medium-resolution vorticity input.Further coarsening oversmooths both fields, while average pooling yields approximately five-fold lower bicubic error than max pooling.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: The CNN reduces reconstruction errors for max-pooled turbulent inputs but performs comparably to bicubic interpolation for average-pooled inputs.These trends hold for both velocity and vorticity fields.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: The hybrid DSC/MS model generally achieves significant error reduction over bicubic interpolation and CNN reconstruction for turbulent flows.Its main difficulty occurs with super-low-resolution max-pooled inputs; with 4 × 4 average-pooled inputs, it recovers general velocity and vorticity distributions on a 128 × 128 grid.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: 2000 held-out test snapshots show that DSC/MS almost always outperforms the other models, while vorticity reconstruction is less accurate than velocity reconstruction.The higher vorticity error is attributed to spectral content extending toward high wavenumbers.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: 50 training snapshots can produce a reliable DSC/MS model for velocity reconstruction, although reconstruction errors generally decrease as snapshot count increases.The study evaluates 50–10 000 snapshots selected at even time intervals.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: The hybrid DSC/MS model reproduces kinetic-energy spectra accurately over resolved wavenumbers, but cannot predict spectra below E(k) ≈ 10^-5.Average-pooled inputs improve spectral recovery over max-pooled inputs, while the limitation is attributed to lost large-to-small-scale data correlation.
- 3.2. Example 2: Two-dimensional decaying isotropic turbulence: The recovered spectral range extends over five fold for some max-pooled cases and over two fold for average-pooled inputs relative to the cutoff wavenumber.The original max-pooled error level is high despite its larger recovery ratio.
4. Conclusion
The study develops CNN and hybrid DSC/MS approaches for reconstructing coarse flow fields, accurately recovering laminar and turbulent structures. The hybrid model reconstructs turbulent velocity and vorticity fields from extremely low-resolution inputs, with accurate kinetic-energy spectra and, in some cases, only 50 training snapshots.
- Two machine-learning approaches reconstruct coarse flow fields: a standard CNN and an improved hybrid DSC/MS model designed for multi-scale flows.
- Both models reconstruct laminar and turbulent flows, with the cylinder wake demonstrating the super-resolution process on laminar data.
- The hybrid DSC/MS model accurately reconstructs turbulent velocity and vorticity fields from extremely low-resolution input data.
- The kinetic energy spectra can also be accurately reproduced.
- 50 training snapshots can suffice for learning the model in some cases, while average pooling is more robust than max pooling.