SISSA had a secondment to Virginia Tech in November 2023. The purpose is to investigate machine learning methods and optimization algorithms to find theoptimal filtering and relaxation parameters in the Evolve-Filter-Relax (EFR) regularization technique. This technique is applied to a benchmark in convection-dominated CFD simulations, in particular, the flow past a circular cylinder, discretized with the Finite Element Method.
The aim of the work is to provide an algorithm able to find the optimal parameters such that the
regularized solution is as close as possible to a reference solution, computed on a grid with a more
refined resolution.
The transfer of knowledge concerned:
- Investigation of the optimal relaxation parameter, taking the filtering parameter fixed. We
considered different cases: a space and time-dependent parameter, a time-dependent
parameter. The optimization is done using a feed-forward neural network minimizing the
discrepancy between the EFR solution (both velocity and pressure) and the reference solution.
- Investigation of the optimal filtering parameter in the EF algorithm, without the relaxation part.
The optimization is done using a standard gradient method.