Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-Aware Matchings
2019 IEEE 9th Symposium on Large Data Analysis and Visualization (LDAV)
Figure 1 : Overview of the ranking framework. An ensemble of viscous fingering simulation runs S 1 , S 2 , S 3 is launched, and the persistence diagram of newly available time-steps can be computed in-situ (left). Only persistence diagrams for which there is a matching ground truth image (center, top) are computed. Diagrams of every simulation are compared with the diagrams of the ground truth (center, bottom) at matching time-steps. This comparison, based on a metric W 2 combining the notions
... f persistence and geometry, outputs a distance measurement, which can be integrated over time to form the metric d W 2 . This produces a final ranking (right) which characterizes the quality of simulations, allowing experts to select and explore best performing runs automatically. ABSTRACT This application paper presents a novel framework based on topological data analysis for the automatic evaluation and ranking of viscous finger simulation runs in an ensemble with respect to a reference acquisition. Individual fingers in a given time-step are associated with critical point pairs in the distance field to the injection point, forming persistence diagrams. Different metrics, based on optimal transport, for comparing time-varying persistence diagrams in this specific applicative case are introduced. We evaluate the relevance of the rankings obtained with these metrics, both qualitatively thanks to a lightweight web visual interface, and quantitatively by studying the deviation from a reference ranking suggested by experts. Extensive experiments show the quantitative superiority of our approach compared to traditional alternatives. Our web interface allows experts to conveniently explore the produced rankings. We show a complete viscous fingering case study demonstrating the utility of our approach in the context of porous media fluid flow, where our framework can be used to automatically discard physically-irrelevant simulation runs from the ensemble and rank the most plausible ones. We document an in-situ implementation to lighten I/O and performance constraints arising in the context of parametric studies. 2. Metrics: new topological metrics for comparing time-varying viscous fingers are introduced, based on the Wasserstein matching of persistence diagrams, specifically tuned for the viscous fingering phenomenon and integrated over time. 3. Case study: a complete case study of a viscous fingering simulation ensemble is documented, along with a proof-ofconcept in-situ implementation of our approach. 4. Evaluation: the metrics and ranking framework are qualitatively evaluated with feedback from domain experts. The quantitative performance of our approach is also analyzed and its superiority over traditional alternatives is demonstrated.