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1/10
Machine-Learning for Turbulence
Modelling
August 31, 2023
2/10
Motivation/Objective
Ï To improve the GEP-RANS simulations
Ï To improve the agreement with experimental data
Research Questions
Ï What features are useful for clustering turbulence data?
Ï Can continuous statistical field data be clustered?
Ï Can dataset be decomposed into partitions, each encoding a
particular type of turbulence physics
Ï Are machine-learned clusters consistent with our human
understanding of turbulent flows?
Ï Can we automatically identify a relatively small number of
"exemplars" or "prototypes", from each cluster?
Hypothesis: Unsupervised learning algorithms can be applied to
turbulence data to produce an automated partitioning of data that
reconciles with our understanding of turbulence.
3/10
4/10
Technical challenges
Ï Find a physical-aware feature
space (clustering)
Ï Any turbulent state is
approximately a combination of
3 limiting states
Ï Clustering with Gaussian
Mixture Modeling (GMM)
Ï A greedy feature search is
wrapped around GMM
Ï Cluster extent set as a
threshold on the
Mahalanobis distance of
each data point
Turbulence-derived feature space
+ greedy clustering
+ dM thresholds
= interpretable clusters
5/10
Ï Qualitative understanding of turbulence’s type revealed by clustering
Ï Quantitative understanding requires prototypes and analysis
Ï Incremental classification of complex dataset using learned clusters1
1Feature Selection, Clustering, and Prototype Placement for Turbulence
Datasets, https://doi.org/10.2514/6.2021-1750
6/10
7/10
8/10
The good news ...
Figure: A curated dataset for data-driven turbulence modelling,
https://doi.org/10.1038/s41597-021-01034-2
9/10
10/10
Unsupervised Semantic Segmentation
https://paperswithcode.com/task/
unsupervised-semantic-segmentation
https://github.com/janghyuncho/PiCIE
https://github.com/xu-ji/IIC
https://github.com/facebookresearch/dino
https://github.com/mhamilton723/STEGO
They often use "transformers" but based on pre-trained traditional
backbones, like ResNet, U-Net, etc., which possibly implies the necessity
to have some labels and relatively big database.
The availability of a dedicated database simplifies the pre-training stage.

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MLMM_28_06_2022.pdf