Entropy guided visualization and analysis of multivariate spatio-temporal data generated by physically based simulation

Flow fields produced by physically based simulations are subsets of multivariate spatiotemporal data, and have been in interest of many researchers for visualization, since the data complexity makes it difficult to extract representative views for the interpretation of fluid behavior. In this thesis, we utilize Information Theory to find entropy maps for vector flow fields, and use entropy maps to aid visualization and analysis of the flow fields. Our major contribution is to use Principal Component Analyses (PCA) to find a projection that has the maximal directional variation in polar coordinates for each sampling window in order to generate histograms according to the projected 3D vector field, producing results with fewer artifacts than the traditional methods. Entropy guided visualization of different data sets are presented to evaluate proposed method for the generation of entropy maps. High entropy regions and coherent directional components of the flow fields are visible without cluttering to reveal fluid behavior in rendered images. In addition to using data sets those are available for research purposes, we have developed a fluid simulation framework using Smoothed Particle Hydrodynamics (SPH) to produce flow fields. SPH is a widely used method for fluid simulations, and used to generate data sets that are difficult to interpret with direct visualization techniques. A moderate improvement for the performance and stability of SPH implementations is also proposed with the use of fractional derivatives, which are known to be useful for approximating particle behavior immersed in fluids

Analysis of spatiotemporal ensemble data using machine learning

Simulations of physical processes are of great importance in many areas of research. Typically, time-dependent volume data with high resolution are generated in this context. Simulations are often repeated multiple times with different setup parameters, creating an ensemble data set containing several instances of volumetric data. The high-dimensional nature of ensemble data prevents the application of direct visualization methods and motivates automated techniques that support the visualization of the simulation results. This thesis deals with the analysis of spatiotemporal velocity data of a liquid flowing through a channel containing a cylinder. We present a method for the extraction of characteristic representations based on artificial neural networks. For this purpose two different types of representations are studied: time steps which contain the velocity vector field of the liquid flow at a specific point in time and isolines which mark velocity vectors of a certain length. In addition, results from different simulation runs are compared pairwise and their similarity is evaluated with a distance metric. Subsets of the simulation data, in form of the two representations, and the calculated distance values serve as input and target output for the supervised learning of the neural networks. For learning the distance metric, we present a convolutional neural network whose architecture is adapted to the significant size of the input data, the use of different amounts of representations and the symmetry of the metric. The trained networks are used to predict the distances between simulations of a separate evaluation data set. The resulting prediction accuracy serves as measure for the information content of the representations that were used for the training. In addition to the technique of extracting characteristic representations, we present methods for visualizing time steps and isolines over the entire time series of a simulation. The effectiveness of the extraction method is discussed in a comparison of visualizations resulting from those representations, which have achieved the highest and lowest prediction accuracy