Gaussian Processes for Uncertainty Visualization

Data is virtually always uncertain in one way or another. Yet, uncertainty information is not routinely included in visualizations and, outside of simple 1D diagrams, there is no established way to do it. One big issue is to find a method that shows the uncertainty without completely cluttering the display. A second important question that needs to be solved, is how uncertainty and interpolation interact. Interpolated values are inherently uncertain, because they are heuristically estimated values – not measurements. But how much more uncertain are they? How can this effect be modeled? In this thesis, we introduce Gaussian processes, a statistical framework that allows for the smooth interpolation of data with heteroscedastic uncertainty through regression. Its theoretical background makes it a convincing method to analyze uncertain data and create a model of the underlying phenomenon and, most importantly, the uncertainty at and in-between the data points. For this reason, it is already popular in the GIS community where it is known as Kriging but has applications in machine learning too. In contrast to traditional interpolation methods, Gaussian processes do not merely create a surface that runs through the data points, but respect the uncertainty in them. This way, noise, errors or outliers in the data do not disturb the model inappropriately. Most importantly, the model shows the variance in the interpolated values, which can be higher but also lower than that of its neighboring data points, providing us with a lot more insight into the quality of our data and how it influences our uncertainty! This enables us to use uncertainty information in algorithms that need to interpolate between data points, which includes almost all visualization algorithms

Visualization and Simulation of Laser-Induced Fullerene Fragmentation

The benefit from the research of carbon, an element with one of the highest variety of binding possibilities that is essential for life, has a strong impact in many fields in science as well as in industry. A molecule that is suited to explore more complex systems of carbon atoms due to its highly symmetrical hollow sphere-like structure is C60, one of the best known fullerenes. Still, its dynamics is far from being understood, especially its interaction with ultrashort and strong laser pulses. Simulations can help us to get insights into the dynamics of molecules. In combination with visualization, these dynamics can be analyzed and understood. Leaned to laser experiments with fullerene, performed at LCLS to get further insights into the dynamics of fullerene, this work examines some of their experiments by means of molecular dynamics simulations, which we analyze by our developed visualization techniques. The focus is on the fragmentation dynamics, induced by laser pulses that are used in the experiments. The contribution of this work can be summarized into simulation and visualization. Simulations are required to imitate the experiment, including the modeling of C60 by the choice of force field potentials, the modeling of laser pulses, and their intensities. The results of our simulations are adapted based on results from the experiments. Goals in the visualization are the development of novel analysis techniques. These techniques are for the fragmentation process of fullerene, the fragmentation dynamics by exibility methods, the reconstruction of diffraction images, which can be used as additional medium for the physical analysis, as well as the analysis of the achieved results of this work