%0 Journal Article %1 scillitoe2020uncertainty %A Scillitoe, Ashley %A Seshadri, Pranay %A Girolami, Mark %D 2020 %K bayesian readings uncertainty %T Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests %U http://arxiv.org/abs/2003.01968 %X Data-driven turbulence modelling approaches are gaining increasing interest from the CFD community. Such approaches generally aim to improve the modelled Reynolds stresses by leveraging data from high fidelity turbulence resolving simulations. However, the introduction of a machine learning (ML) model introduces a new source of uncertainty, the ML model itself. Quantification of this uncertainty is essential since the predictive capability of data-driven models diminishes when predicting physics not seen during training. In this work, we explore the suitability of Mondrian forests (MF's) for data-driven turbulence modelling. MF's are claimed to possess many of the advantages of the commonly used random forest (RF) machine learning algorithm, whilst offering principled uncertainty estimates. On a manufactured test case these claims are substantiated, providing feature selection is first performed to remove irrelevant features from the training data. A data-driven turbulence modelling test case is then constructed, with a turbulence anisotropy constant derived from high fidelity data the quantity to predict. A number of flows at several Reynolds numbers are used for training and testing. Irrelevant features are not found to be a problem here. MF predictions are found to be superior to those obtained from a commonly used linear eddy viscosity model. Shapley values, borrowed from game theory, are used to interpret the MF predictions. Predictive uncertainty is found to be large in regions where the training data is not representative. Additionally, the MF predictive uncertainty is compared to the uncertainty estimated from applying jackknifing to random forest predictions, and to an a priori statistical distance measure. In both cases the MF uncertainty is found to exhibit stronger correlation with predictive errors, which indicates it is a better measure of prediction confidence.

@article{scillitoe2020uncertainty, abstract = {Data-driven turbulence modelling approaches are gaining increasing interest from the CFD community. Such approaches generally aim to improve the modelled Reynolds stresses by leveraging data from high fidelity turbulence resolving simulations. However, the introduction of a machine learning (ML) model introduces a new source of uncertainty, the ML model itself. Quantification of this uncertainty is essential since the predictive capability of data-driven models diminishes when predicting physics not seen during training. In this work, we explore the suitability of Mondrian forests (MF's) for data-driven turbulence modelling. MF's are claimed to possess many of the advantages of the commonly used random forest (RF) machine learning algorithm, whilst offering principled uncertainty estimates. On a manufactured test case these claims are substantiated, providing feature selection is first performed to remove irrelevant features from the training data. A data-driven turbulence modelling test case is then constructed, with a turbulence anisotropy constant derived from high fidelity data the quantity to predict. A number of flows at several Reynolds numbers are used for training and testing. Irrelevant features are not found to be a problem here. MF predictions are found to be superior to those obtained from a commonly used linear eddy viscosity model. Shapley values, borrowed from game theory, are used to interpret the MF predictions. Predictive uncertainty is found to be large in regions where the training data is not representative. Additionally, the MF predictive uncertainty is compared to the uncertainty estimated from applying jackknifing to random forest predictions, and to an a priori statistical distance measure. In both cases the MF uncertainty is found to exhibit stronger correlation with predictive errors, which indicates it is a better measure of prediction confidence.}, added-at = {2020-03-06T15:06:02.000+0100}, author = {Scillitoe, Ashley and Seshadri, Pranay and Girolami, Mark}, biburl = {https://www.bibsonomy.org/bibtex/2985d493b441350655a19fc5ec5ff6db2/kirk86}, description = {[2003.01968] Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests}, interhash = {4dde84122f6526ee63ee2eff9e774876}, intrahash = {985d493b441350655a19fc5ec5ff6db2}, keywords = {bayesian readings uncertainty}, note = {cite arxiv:2003.01968Comment: 24 pages, 21 figures, submitted to Journal of Computational Physics}, timestamp = {2020-03-06T15:06:02.000+0100}, title = {Uncertainty Quantification for Data-driven Turbulence Modelling with Mondrian Forests}, url = {http://arxiv.org/abs/2003.01968}, year = 2020 }