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Scientific visualizations: A bridge to knowledge - Part 2

What are some further examples of effective collaborations between visualization researchers and domain experts?

The second example is work done by my colleagues Professors Ross Whitaker and Valerio Pascucci, former Ph.D. student Samuel Gerber, who is now at the University of Oregon, and collaborator Peer-Timo Bremer from Lawrence Livermore National Laboratory.  

The team of visualization researchers worked with domain experts in combustion simulation to create a new visual analysis method for exploring high dimensional scalar field data.

From their paper, “An important goal of scientific data analysis is to understand the behavior of a system or process based on a sample of the system. In many instances it is possible to observe both input parameters and system outputs, and characterize the system as a high-dimensional function. Such data sets arise, for instance, in large numerical simulations, as energy landscapes in optimization problems, or in the analysis of image data relating to biological or medical parameters.” 

In this example, the combustion application problem is trying to understand the relationship between the composition of chemical species in a turbulent combustion process and its efficiency in terms of fuel consumption and pollutants generated.  The data to analyze consists of 700K samples of chemical composition and temperature extracted pointwise (samples in space and time) from temporal jet simulations of turbulent CO/H2-air flames.  A common way that domain experts visualize high dimensional scalar field data is to break the high dimensional data into a series of two-dimensional plots. 

<strong>Influencing the longwave flux. </strong>Chemical composition in relation to heat released during a jet flame combustion simulation. The three distinct minima correspond to pure fuel, pure oxidizer and extinction/re-ignition. Graphs of chemical composition plotted against temperature for the crystals corresponding to extinction (a) pure oxidizer, (b) pure fuel, and (c) minima compositions. Courtesy Whitaker, Pascucci, et al.

In this example, one could break up the data into ten two-dimensional graphs of temperature versus chemical species; for example temperature versus: H2 and O2 and H02 and CO and HCO, etc.  Domain experts then look at pairs or triples of the two-dimensional graphs over to time to try to infer underlying relationships.  As one can imagine, as the number of dimensions increases, the high dimensional data in a coherent way becomes more difficult.  I have not met anyone yet who can reason about 10-dimensional spaces.

To help visualize this 10-dimensional space, Gerber, Bremer, Pascucci, and Whitaker create a method that combines topological and geometric techniques to provide interactive visualizations of discretely sampled high-dimensional scalar fields.  

As described in their paper, “the method relies on a segmentation of the parameter space using an approximate Morse-Smale complex on the cloud of point samples. For each crystal of the Morse-Smale complex, a regression of the system parameters with respect to the output yields a curve in the parameter space. The result is a simplified geometric representation of the Morse-Smale complex in the high dimensional input domain. Finally, the geometric representation is embedded in 2D, using dimension reduction, to provide a visualization platform. The geometric properties of the regression curves enable the visualization of additional information about each crystal such as local and global shape, width, length, and sampling densities.”

The figure above shows the result of their new visualization technique along with numerous two-dimensional graphs at one instant in time. Their analysis confirmed the expectation of the domain experts of four distinct modes of combustion. In a different analysis they applied the methodology to climate simulation data. The visualization uncovered a novel relationship of different cloud formation regimes on longwave flux that are not made apparent through traditional statistical analysis methods.

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