Data Complexity and Dimensionality Reduction for Numerical Solution of the Elder Problem

In this study, we use Big Data and Machine Learning methods and techniques for the analysis of numerical solutions of Partial Differential Equations (PDEs). In particular, we have applied these methods to the large ensembles of numerical solutions of the Elder problem. Different dimensionality reduction (DR) approaches have been considered for the studied problem, both linear and non-linear. We compared DR methods from the perspective of Data Complexity (DC) and predictability of steady states of the Elder problem. Based on the studied approaches, we re-estimated the limit of high-accuracy predictability for the Elder problem. We developed a feature selection method for monitoring and predicting real-life fluid processes. Additionally, we proposed our own DC measure for the ensemble of perturbed solutions of the Elder problem. Uncertainty estimates are provided for all results presented in this study.