Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning

Abstract

In this study, the numerical solutions to the Elder problem are analyzed using Big Data technologies and data-driven approaches. The steady-state solutions to the Elder problem are investigated with regard to Rayleigh numbers ((Formula presented.)), grid sizes, perturbations, and other parameters of the system studied. The complexity analysis is carried out for the datasets containing different solutions to the Elder problem, and the time of the highest complexity of numerical solutions is estimated. An approach to the identification of transient fingers and the visualization of large ensembles of solutions is proposed. Predictive models are developed to forecast steady states based on early-time observations. These models are classified into three possible types depending on the features (predictors) used in a model. The numerical results of the prediction accuracy are given, including the estimated confidence intervals for the accuracy, and the estimated time of 95% predictability. Different solutions, their averages, principal components, and other parameters are visualized.