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

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.

Topologically Controlled Lossy Compression

This paper presents a new algorithm for the lossy compression of scalar data defined on 2D or 3D regular grids, with topological control. Certain techniques allow users to control the pointwise error induced by the compression. However, in many scenarios it is desirable to control in a similar way the preservation of higher-level notions, such as topological features , in order to provide guarantees on the outcome of post-hoc data analyses. This paper presents the first compression technique for scalar data which supports a strictly controlled loss of topological features. It provides users with specific guarantees both on the preservation of the important features and on the size of the smaller features destroyed during compression. In particular, we present a simple compression strategy based on a topologically adaptive quantization of the range. Our algorithm provides strong guarantees on the bottleneck distance between persistence diagrams of the input and decompressed data, specifically those associated with extrema. A simple extension of our strategy additionally enables a control on the pointwise error. We also show how to combine our approach with state-of-the-art compressors, to further improve the geometrical reconstruction. Extensive experiments, for comparable compression rates, demonstrate the superiority of our algorithm in terms of the preservation of topological features. We show the utility of our approach by illustrating the compatibility between the output of post-hoc topological data analysis pipelines, executed on the input and decompressed data, for simulated or acquired data sets. We also provide a lightweight VTK-based C++ implementation of our approach for reproduction purposes.