Estimating the Execution Time of the Coupled Stage in Multiscale Numerical Simulations

Abstract

Estimating the execution time of high-performance computing (HPC) applications is an issue that affects both shared computing infrastructures and their users. The goal of the present work is to estimate the execution time of simulation applications driven by multiscale numerical methods. In computational terms, these methods induce a two-stage simulation process. Fundamentally, the number of possibilities for configuring this two-stage process tends to be much larger than that of classical, one-stage numerical methods. This scenario makes it harder to provide accurate estimates of the execution time of multiscale simulations by using classical regression techniques. We propose a methodology that explores the idiosyncrasies of multiscale simulators to reduce the uncertainty of predictions. We applied it in this paper to the specific challenge of estimating the execution time of these simulators based on knowledge about the influence of each parameter of the numerical method they employ. We consider the multiscale hybrid-mixed (MHM) finite element method as a specific multiscale method to validate our methodology. We compared our proposed technique with 3 well-known regression approaches: a model-based tree (M5P), a bayesian nonparametric method (GPR), and a state-of-the-art ensemble method (Random Forest). We found that the root-mean-square error (RMSE) of the test dataset for our technique was considerably less than that obtained by these 3 approaches. We conclude that an educated consideration of the numerical parameters of the MHM method to estimate the execution time of the simulations helps to obtain more accurate models. We believe such conclusion can be easily generalized to other multiscale numerical methods.