# Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates

In the combustion community, the determination of the sub-grid scale contribution to the filtered reaction rate in reacting flows Large Eddy Simulation is an example of closure problem that has been daunting for a long time. We propose a new approach for premixed turbulent combustion modeling based on convolutional neural networks by reformulating the problem of subgrid flame surface density estimation as a machine learning task.

In order to train a neural network for this task, a Direct Numerical Simulation and the equivalent LES obtained by a spatial filtering of this DNS (more details can be found in the paper) is needed.

• In a first step, two DNS of a methane-air slot burner are run and then filtered to create the training dataset. Models are trained on this data in a supervised manner.
• In a second step, a new, unseen and more difficult case was used to ensure network capabilities. This third DNS is a short-term transient started from the last field of the second DNS, where inlet velocity is doubled, going from 10 to 20 m/s for 1 ms, and then set back to its original value for 2 more ms.

## Description of the dataset

The dataset can be downloaded here. Each of these files corresponds to a time step of a simulation and contains 3 fields :

Filt_8 is the filtered progress variable $\overline{c}$,
Filt_grad_8 is the DNS field $\overline{\Sigma}$,
Grad_filt_8 is the LES field $\lvert&space;\mathbf{\nabla}&space;\overline{c}&space;\lvert$.