Online Bayesian Optimization of Polynomial-Multigrid Cycles for Flux Reconstruction

We introduce an innovative approach to optimise polynomial multigrid cycles to enhance convergence acceleration of incompressible flow simulations. To achieve this, we apply the Bayesian Optimisation approach to efficiently sample possible cycles to minimise runtime. To allow the use of traditional optimisation methods, we developed fractional smoothing steps for multigrid cycles to perform optimisation in a continuous domain. Initially we explored a static offline optimisation strategy and identified optimal cycles. However the performance of the cycles was not transferable across different simulations.

This observation led us to develop a dynamic online optimisation strategy where cycles are continuously optimised with simulation progress. The performance of the optimal cycles determined through this approach gave similar speed up to the offline approach, with the added advantage of continuous progression during the simulation. Tests were performed on three case setups of flow past cylinder at Reynolds numbers 200, 500 and 3900 to give speedups of $3.0\times$, $2.1\times$ and $1.9\times$ respectively.