Jacobi Fiber Surfaces for Bivariate Reeb Space Computation

This paper presents an efficient algorithm for the computation of the Reeb space of an input bivariate piecewise linear scalar function f defined on a tetrahedral mesh. By extending and generalizing algorithmic concepts from the univariate case to the bivariate one, we report the first practical, output-sensitive algorithm for the exact computation of such a Reeb space. The algorithm starts by identifying the Jacobi set of f , the bivariate analogs of critical points in the univariate case. Next, the Reeb space is computed by segmenting the input mesh along the new notion of Jacobi Fiber Surfaces, the bivariate analog of critical contours in the univariate case. We additionally present a simplification heuristic that enables the progressive coarsening of the Reeb space. Our algorithm is simple to implement and most of its computations can be trivially parallelized. We report performance numbers demonstrating orders of magnitude speedups over previous approaches, enabling for the first time the tractable computation of bivariate Reeb spaces in practice. Moreover, unlike range-based quantization approaches (such as the Joint Contour Net), our algorithm is parameter-free. We demonstrate the utility of our approach by using the Reeb space as a semi-automatic segmentation tool for bivariate data. In particular, we introduce continuous scatterplot peeling, a technique which enables the reduction of the cluttering in the continuous scatterplot, by interactively selecting the features of the Reeb space to project. We provide a VTK-based C++ implementation of our algorithm that can be used for reproduction purposes or for the development of new Reeb space based visualization techniques

voxel2vec: A Natural Language Processing Approach to Learning Distributed Representations for Scientific Data

Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and ensemble data, are intricate and complex. This paper presents voxel2vec, a novel unsupervised representation learning model, which is used to learn distributed representations of scalar values/scalar-value combinations in a low-dimensional vector space. Its basic assumption is that if two scalar values/scalar-value combinations have similar contexts, they usually have high similarity in terms of features. By representing scalar values/scalar-value combinations as symbols, voxel2vec learns the similarity between them in the context of spatial distribution and then allows us to explore the overall association between volumes by transfer prediction. We demonstrate the usefulness and effectiveness of voxel2vec by comparing it with the isosurface similarity map of univariate data and applying the learned distributed representations to feature classification for multivariate data and to association analysis for time-varying and ensemble data.Comment: Accepted by IEEE Transaction on Visualization and Computer Graphics (TVCG

Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles

We present the first neural network that has learned to compactly represent and can efficiently reconstruct the statistical dependencies between the values of physical variables at different spatial locations in large 3D simulation ensembles. Going beyond linear dependencies, we consider mutual information as a measure of non-linear dependence. We demonstrate learning and reconstruction with a large weather forecast ensemble comprising 1000 members, each storing multiple physical variables at a 250 x 352 x 20 simulation grid. By circumventing compute-intensive statistical estimators at runtime, we demonstrate significantly reduced memory and computation requirements for reconstructing the major dependence structures. This enables embedding the estimator into a GPU-accelerated direct volume renderer and interactively visualizing all mutual dependencies for a selected domain point

Doctor of Philosophy

dissertationRay tracing presents an efficient rendering algorithm for scientific visualization using common visualization tools and scales with increasingly large geometry counts while allowing for accurate physically-based visualization and analysis, which enables enhanced rendering and new visualization techniques. Interactivity is of great importance for data exploration and analysis in order to gain insight into large-scale data. Increasingly large data sizes are pushing the limits of brute-force rasterization algorithms present in the most widely-used visualization software. Interactive ray tracing presents an alternative rendering solution which scales well on multicore shared memory machines and multinode distributed systems while scaling with increasing geometry counts through logarithmic acceleration structure traversals. Ray tracing within existing tools also provides enhanced rendering options over current implementations, giving users additional insight from better depth cues while also enabling publication-quality rendering and new models of visualization such as replicating photographic visualization techniques

Multifield-based modeling of material failure in high performance reinforced cementitious composites

Cementitious materials such as mortar or concrete are brittle and have an inherent weakness in resisting tensile stresses. The addition of discontinuous fibers to such matrices leads to a dramatic improvement in their toughness and remedies their deficiencies. It is generally agreed that the fibers contribute primarily to the post-cracking response of the composite by bridging the cracks and providing resistance to crack opening. On the other hand, the multifield theory is a mathematical tool able to describe materials which contain a complex substructure. This substructure is endowed with its own properties and it interacts with the macrostructure and influences drastically its behavior. Under this mathematical framework, materials such as cement composites can be seen as a continuum with a microstructure. Therefore, the whole continuum damage mechanics theory, incorporating a new microstructure, is still applicable. A formulation, initially based on the theory of continua with microstructure Capriz, has been developed to model the mechanical behavior of the high perfor-mance fiber cement composites with arbitrarily oriented fibers. This formulation approaches a continuum with microstructure, in which the microstructure takes into account the fiber-matrix interface bond/slip processes, which have been recognized for several authors as the principal mechanism increasing the ductility of the quasi-brittle cement response. In fact, the interfaces between the fiber and the matrix become a limiting factor in improving mechanical properties such as the tensile strength. Particularly, in short fiber composites is desired to have a strong interface to transfer effectively load from the matrix to the fiber. However, a strong interface will make difficult to relieve fiber stress concentration in front of the approaching crack. According to Naaman, in order to develop a better mechanical bond between the fiber and the matrix, the fiber should be modified along its length by roughening its surface or by inducing mechanical defor-mations. Thus, the premise of the model is to take into account this process considering a micro field that represents the slipping fiber-cement displacement. The conjugate generalized stress to the gradient of this micro-field verifies a balance equation and has a physical meaning. This contribution includes the computational modeling aspects of the high fiber rein-forced cement composites (HFRCC) model. To simulate the composite material, a finite element discretization is used to solve the set of equations given by the multifield approach for this particular case. A two field discretization: the standard macroscopic and the micro-scopic displacements, is proposed through a mixed finite element methodology. Furthermore, a splitting procedure for uncoupling both fields is proposed, which provides a more convenient numerical treatment of the discrete equation system. The initiation of failure in HPFRCC at the constitutive level identified as the onset of strain localization depends on the mechanical properties of the all compounds and not only on the matrix ones. As localization criteria is considered the bifurcation analysis in combination with the localized strain injection technique presented by Oliver et al. It consists of injecting a specific localization mode during the localization stage, via mixed finite element formulations, to the path of elements that are going to capture the cracks, and, in this way, the spurious mesh orientation dependence is removed. Model validation was performed using a selected set of experiments that proves the via-bility of this approach. The numerical examples of the proposed formulation illustrated two relevant aspects, namely: 1) the role of the bonding mechanism in the strain hardening be-havior after cracking in the HPFRCC and 2) the role that plays the finite element formulation in capturing the displacement localization in the localization stage

Multivariate relationship specification and visualization

In this dissertation, we present a novel method for multivariate visualization that focuses on multivariate relationshipswithin scientific datasets. Specifically, we explore the considerations of such a problem, i.e. we develop an appropriate visualization approach, provide a framework for the specification of multivariate relationships and analyze the space of such relationships for the purpose of guiding the user toward desired visualizations. The visualization approach is derived from a point classification algorithm that summarizes many variables of a dataset into a single image via the creation of attribute subspaces. Then, we extend the notion of attribute subspaces to encompass multivariate relationships. In addition, we provide an unconstrained framework for the user to define such relationships. Althoughwe intend this approach to be generally applicable, the specification of complicated relationships is a daunting task due to the increasing difficulty for a user to understand and apply these relationships. For this reason, we explore this relationship space with a common information visualization technique well suited for this purpose, parallel coordinates. In manipulating this space, a user is able to discover and select both complex and logically informative relationship specifications