رئاسـة البـحث : Julien TIERNY

تأطـير مـشـترك : PLAINCHAULT Mélanie (Total)

Large Data Reduction and Structure Comparison with Topological Data Analysis

In this thesis, we propose different methods, based on Topological Data Analysis, in order to address modern problematics concerning the increasing difficulty in the analysis of scientific data. In the case of scalar data defined on geometrical domains, extracting meaningful knowledge from static data, then time-varying data, then ensembles of time-varying data proves increasingly challenging. Our approaches for the reduction and analysis of such data are based on the idea of defining structures of interest in scalar fields as topological features. In a first effort to address data volume growth, we propose a new lossy compression scheme which offers strong topological guarantees, allowing topological features to be preserved throughout compression. The approach is shown to yield high compression factors in practice. Extensions are proposed to offer additional control over the geometrical error. We then target time-varying data by designing a new method for tracking topological features over time, based on topological metrics. We extend the metrics in order to overcome robustness and performance limitations. We propose a new efficient way to compute them, gaining orders of magnitude speedups over state-of-the-art approaches. Finally, we apply and adapt our methods to ensemble data related to reservoir simulation, for modeling viscous fingering in porous media. We show how to capture viscous fingers with topological features, adapt topological metrics for capturing discrepancies between simulation runs and a ground truth, evaluate the proposed metrics with feedback from experts, then implement an in-situ ranking framework for rating the fidelity of simulation runs.

إصدارات 2018-2019