Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Coupling of deep neural networks and physical invariants for turbulent flow surrogate modeling

Prof. Dr. Didier Lucor talk

**Date:** 01.04.20 **Time:** 16.15 - 17.45 **Room:** Y27H46

The development of data-driven surrogate models for the prediction and compression of complex fluid phenomena, in place of more standard numerical simulations may help when many query and/or real-time simulations are required in such fields as uncertainty quantification, data assimilation, control. In this work, we rely on deep neural networks (DNN) which are known to be performant in capturing transient and intermittent phenomenon with the possibility of handling translations, rotations and other invariances. More specifically, the approach retained is the one of training a DNN by leveraging some underlying physical laws of the system. In particular, a natural approach is to incorporate (some of) the governing partial differential equations of the physical model (e.g. mass/momentum/energy conservation) at the core of the DNN, i.e. in the loss/likelihood functions. We propose to investigate how this additional information allows for the recovery of hidden variables and effectively regularizes the minimization procedure in the training of DNN, and enables them to generalize well. More specifically, we will report on the influence of the choice and the dimensionality of the domain of interest for data acquisition as well as subsequent training and predictions, in relation to the problem geometry, initial/boundary conditions and flow regimes. Finally, we will report on the DNN training attempt on large direct numerical simulations database acquired for mildly turbulent convective flow in rectangular three dimensional cavity with buoyant effects.