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“Explainable & Efficient Learning of Turbulence”

Mathematics Colloquium

“Explainable & Efficient Learning of Turbulence”
Series: Mathematics Colloquium
Location: MATH 501
Presenter: Misha Chertkov, University of Arizona
Abstract: In this colloquium we describe progress made towards developing and applying to the classic problem of Naiver-Stocks turbulence  novel methodology which bridges the two complementary poles --  application agnostic modern machine learning (in particular deep learning), computationally efficient but lacking interpretability,  and science based tuning, highly interpretable but lacking automatization and implementation efficiency.
 
The presentation will be split in two parts.  
 
First, we discuss acceleration and automation of hydrodynamic codes in the regime of developed turbulence by Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics of turbulence explicitly, are impressively good overall when it comes to qualitative description of important features of turbulence. However, the early tests have also uncovered some caveats of the DL approaches. We observe that DL schemes trained on spatial snapshots of turbulence, fails to reproduce intermittency of turbulent fluctuations at small scales and details of the turbulence geometry at large scales. We show that dynamic NN schemes trained on a temporal sequence of turbulence snapshots are capable to correct for the caveats of the static NN. We discuss path forward towards improving tractability of the DL-NN models of turbulence. 
 
Second, we review work in progress towards developing, training over a rich family of interpretable parameters, and then validating against DNS physics-informed reduced, Lagrangian models of turbulence.  Models of the following two flavours are considered: (a) minimal stochastic model describing self-consistent dynamics of a fluid element; (b) multi-particle model combining elements of Molecular Dynamics (MD) and Smooth Particle Hydrodynamics (SPH). 
 
We conclude discussing future research directions and challenges. 
(Refreshments will be served in the Math Commons Room at 3:30 PM)