Talk A machine learning approach to designing subgrid closures for fluid flows.


The problem of subgrid closure in computational fluid mechanics is particularly prominent for environmental fluids where very coarse discretization are usually used. Within the frame of Large Eddy Simulation methods (LES), correlations between non-linear terms at scales smaller that the discretization grid (subgrid scales) should be approximated from resolved scales of motion. A typical subgrid closure problem is associated with the discretization of convective terms in tracer transport equations as eg. in ocean or atmosphere circulation models.

The approach we propose here uses machine learning methods for estimating effective subgrid closures for use in low resolution ocean model simulations on the basis of high resolution ocean model simulations.
In practice, we build a statistical regression problem covering a wide range of possible local
realizations of fluid flow at high resolution. The regression is formulated in order to estimate
weights on a predefined decomposition basis, using the Least Angle Regression (LARS) method. This approach enables to compare existing subgrid closures and to define new
subgrid closures which are shown to improve significantly existing subgrid closures.

In this poster, we will describe how python, numpy, scipy and scikit.learn have been successfully applied in this study. A hierarchy of scripts and modules, which will be detailed here, enables to formulate a regression problem in a very compact code describing high level operation (900 lines). With a given high resolution ocean model simulation
database, a statistical learning problem of ~100,000 members is shaped and solved in a few tens of
seconds on a personal computer. This study illustrates the great potential of high level scripting languages and
scientific modules for designing and implementing new approaches to tackle longstanding scientific problems.

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