# ELLIIT LU P09: Visual Feature Based Data Reduction

Project: Research

### Description

The goal of this project is to enable the exploration of results from large-scale scientific simulations on different scales with high accuracy. To achieve this we propose a “feature based data reduction and storage strategy” using methods from topological data analysis. The key idea relies on the observation that many data sets consist of a large number of similar structures with typical temporal behavior. In this case it is not important to store each individual feature in high detail but store a few “typical features” with high spatio-temporal resolution and represent the large-scale structure as “feature skeleton”.

Solutions to driving scientific and technologic questions rely more and more on simulations—e.g. computational fluid dynamics, material sciences, climate predictions. Nowadays it is possible to run simulations with an incredible high accuracy. The limiting factor is not the computational power anymore but the space to store the data. A common practice is to store a reasonable height spatial resolution for a coarse number of temporal snapshots. While a low spatial sampling rate only results in data smoothing and thus limits the scale of detectable features, a low temporal sampling rate makes feature tracking unreliable with uncontrollable errors even for large-scale features. The error accumulates over time and is hard to estimate.

To tackle this problem we plan to develop a feature based data reduction and storage strategy. It is planned to move essential data analysis steps from post-processing into the simulation. The analysis results can then be used to store the most important information for accurate visualization and data exploration. Thereby we will focus on features that are related to extremal structures, which are line-like structures where some key measures are especially strongly expressed. From a mathematical point of view such features are part of the topological skeleton of the respective scalar field. Steps towards this goal include (i) The development of application-specific importance measures, which can be used to filter the data for overview representations: Although there exist some importance measures for topology features, which provide valuable mathematical guarantees with respect to changes in the fields, they do not always match the intuitive notion of importance of physical properties. (ii) Robust tracking of topological structures over time. (iii) The comparison of topological structures and the development of meaningful distance metrics. (iv) The identification of typical or representative features and detecting atypical behavior. This question is closely linked to finding symmetries in the data. Such features can also provide the basis for a feature statistics. (v) Building a visualization system exploiting this information to support a seamless zooming from overview representations to detailed close-ups.

Solutions to driving scientific and technologic questions rely more and more on simulations—e.g. computational fluid dynamics, material sciences, climate predictions. Nowadays it is possible to run simulations with an incredible high accuracy. The limiting factor is not the computational power anymore but the space to store the data. A common practice is to store a reasonable height spatial resolution for a coarse number of temporal snapshots. While a low spatial sampling rate only results in data smoothing and thus limits the scale of detectable features, a low temporal sampling rate makes feature tracking unreliable with uncontrollable errors even for large-scale features. The error accumulates over time and is hard to estimate.

To tackle this problem we plan to develop a feature based data reduction and storage strategy. It is planned to move essential data analysis steps from post-processing into the simulation. The analysis results can then be used to store the most important information for accurate visualization and data exploration. Thereby we will focus on features that are related to extremal structures, which are line-like structures where some key measures are especially strongly expressed. From a mathematical point of view such features are part of the topological skeleton of the respective scalar field. Steps towards this goal include (i) The development of application-specific importance measures, which can be used to filter the data for overview representations: Although there exist some importance measures for topology features, which provide valuable mathematical guarantees with respect to changes in the fields, they do not always match the intuitive notion of importance of physical properties. (ii) Robust tracking of topological structures over time. (iii) The comparison of topological structures and the development of meaningful distance metrics. (iv) The identification of typical or representative features and detecting atypical behavior. This question is closely linked to finding symmetries in the data. Such features can also provide the basis for a feature statistics. (v) Building a visualization system exploiting this information to support a seamless zooming from overview representations to detailed close-ups.

Status | Not started |
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