Online Bayesian Optimization of Polynomial-Multigrid Cycles for Flux Reconstruction

Abstract

In this study, we present a novel strategy for dynamically optimizing polynomial multigrid cycles to accelerate convergence within the dual-time-stepping formulation of the artificial compressibility method. To accomplish this, a Gaussian process model is developed using Bayesian optimization to efficiently sample possible cycles to minimize run-time. To allow the use of conventional optimization methods, we developed fractional smoothing steps, moving the optimization from a discrete space to a continuous space. Initially, a static, offline, approach was developed, and optimal cycles were found for two flow past cylinder test cases with [Formula: see text] and [Formula: see text]; however, when exchanging optimal cycles between the different test cases, there was significant degradation in speedup. Toward this, a dynamic, online, approach was developed where cycles are optimized during a simulation. The performance of the resulting optimal cycles gave a similar speedup to the offline approach while achieving a net reduction in run-time. Again testing the optimization strategy on the flow past a cylinder, this yielded candidates with mean speedups of [Formula: see text] and [Formula: see text], respectively. Finally, testing online optimization on a turbulent flow past a cylinder at [Formula: see text] resulted in an overall speedup of [Formula: see text].