Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-aware Matchings

TL;DR

This paper introduces a topological data analysis framework for automatically evaluating and ranking viscous finger simulations against a reference, improving the selection of physically relevant models in porous media flow.

Contribution

The novel framework uses persistence diagrams and optimal transport metrics to compare simulation runs, providing a quantitative and qualitative ranking method.

Findings

Our approach outperforms traditional ranking methods in accuracy.

The web interface facilitates expert exploration of rankings.

The in-situ implementation enhances performance in parametric studies.

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.