Mathematics

In this presentation, I will share the work I've been conducting in the last year in collaboration with the Fluids & Flows group, based in the Eindhoven University of Technology. We investigated the capability of Artificial Neural Networks to build turbulence subgrid closure for a Shell Model of turbulence. Shell Models are reduced dynamical systems of Ordinary Differential Equations that have been shown to rather faithfully mimic the phenomenology of the energy cascade in of the Naver Stokes Equations in Fourier space. Our method employs a novel custom-made Neural Network architecture comprising a classical integrator (Runge Kutta 4th order) for the large scales of turbulence, augmented with LSTM cells to obtain the values of the fluxes to the small scales. We are able to reproduce, within statistical errors, the intermittent behavior found in the full model, obtaining the correct scaling laws for eulerian and lagrangian structure functions and outperforming classical physics-based methods. This work demonstrates the capability of Machine Learning to capture complex multiscale dynamics and reproduce complex multi-scale and multi-time non-gaussian behaviors.