Integration-free Learning of Flow Maps

We present a method for learning neural representations of flow maps from time-varying vector field data. The flow map is pervasive within the area of flow visualization, as it is foundational to numerous visualization techniques, e.g. integral curve computation for pathlines or streaklines, as well as computing separation/attraction structures within the flow field. Yet bottlenecks in flow map computation, namely the numerical integration of vector fields, can easily inhibit their use within interactive visualization settings. In response, in our work we seek neural representations of flow maps that are efficient to evaluate, while remaining scalable to optimize, both in computation cost and data requirements. A key aspect of our approach is that we can frame the process of representation learning not in optimizing for samples of the flow map, but rather, a self-consistency criterion on flow map derivatives that eliminates the need for flow map samples, and thus numerical integration, altogether. Central to realizing this is a novel neural network design for flow maps, coupled with an optimization scheme, wherein our representation only requires the time-varying vector field for learning, encoded as instantaneous velocity. We show the benefits of our method over prior works in terms of accuracy and efficiency across a range of 2D and 3D time-varying vector fields, while showing how our neural representation of flow maps can benefit unsteady flow visualization techniques such as streaklines, and the finite-time Lyapunov exponent

Doctor of Philosophy

dissertationWith modern computational resources rapidly advancing towards exascale, large-scale simulations useful for understanding natural and man-made phenomena are becoming in- creasingly accessible. As a result, the size and complexity of data representing such phenom- ena are also increasing, making the role of data analysis to propel science even more integral. This dissertation presents research on addressing some of the contemporary challenges in the analysis of vector fields--an important type of scientific data useful for representing a multitude of physical phenomena, such as wind flow and ocean currents. In particular, new theories and computational frameworks to enable consistent feature extraction from vector fields are presented. One of the most fundamental challenges in the analysis of vector fields is that their features are defined with respect to reference frames. Unfortunately, there is no single ""correct"" reference frame for analysis, and an unsuitable frame may cause features of interest to remain undetected, thus creating serious physical consequences. This work develops new reference frames that enable extraction of localized features that other techniques and frames fail to detect. As a result, these reference frames objectify the notion of ""correctness"" of features for certain goals by revealing the phenomena of importance from the underlying data. An important consequence of using these local frames is that the analysis of unsteady (time-varying) vector fields can be reduced to the analysis of sequences of steady (time- independent) vector fields, which can be performed using simpler and scalable techniques that allow better data management by accessing the data on a per-time-step basis. Nevertheless, the state-of-the-art analysis of steady vector fields is not robust, as most techniques are numerical in nature. The residing numerical errors can violate consistency with the underlying theory by breaching important fundamental laws, which may lead to serious physical consequences. This dissertation considers consistency as the most fundamental characteristic of computational analysis that must always be preserved, and presents a new discrete theory that uses combinatorial representations and algorithms to provide consistency guarantees during vector field analysis along with the uncertainty visualization of unavoidable discretization errors. Together, the two main contributions of this dissertation address two important concerns regarding feature extraction from scientific data: correctness and precision. The work presented here also opens new avenues for further research by exploring more-general reference frames and more-sophisticated domain discretizations

Doctor of Philosophy

dissertationVisualizing surfaces is a fundamental technique in computer science and is frequently used across a wide range of fields such as computer graphics, biology, engineering, and scientific visualization. In many cases, visualizing an interface between boundaries can provide meaningful analysis or simplification of complex data. Some examples include physical simulation for animation, multimaterial mesh extraction in biophysiology, flow on airfoils in aeronautics, and integral surfaces. However, the quest for high-quality visualization, coupled with increasingly complex data, comes with a high computational cost. Therefore, new techniques are needed to solve surface visualization problems within a reasonable amount of time while also providing sophisticated visuals that are meaningful to scientists and engineers. In this dissertation, novel techniques are presented to facilitate surface visualization. First, a particle system for mesh extraction is parallelized on the graphics processing unit (GPU) with a red-black update scheme to achieve an order of magnitude speed-up over a central processing unit (CPU) implementation. Next, extending the red-black technique to multiple materials showed inefficiencies on the GPU. Therefore, we borrow the underlying data structure from the closest point method, the closest point embedding, and the particle system solver is switched to hierarchical octree-based approach on the GPU. Third, to demonstrate that the closest point embedding is a fast, flexible data structure for surface particles, it is adapted to unsteady surface flow visualization at near-interactive speeds. Finally, the closest point embedding is a three-dimensional dense structure that does not scale well. Therefore, we introduce a closest point sparse octree that allows the closest point embedding to scale to higher resolution. Further, we demonstrate unsteady line integral convolution using the closest point method

Introduction to Vector Field Visualization

Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation

Surface-based flow visualization

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/computers-and-graphics/.With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing\ud data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of\ud flow visualization over the last two decades, a number of challenges remain. Whilst the visualization of 2D flow has many good\ud solutions, the visualization of 3D flow still poses many problems. Challenges such as domain coverage, speed of computation, and\ud perception remain key directions for further research. Flow visualization with a focus on surface-based techniques forms the basis\ud of this literature survey, including surface construction techniques and visualization methods applied to surfaces. We detail our\ud investigation into these algorithms with discussions of their applicability and their relative strengths and drawbacks. We review the\ud most important challenges when considering such visualizations. The result is an up-to-date overview of the current state-of-the-art\ud that highlights both solved and unsolved problems in this rapidly evolving branch of research

Multi-touch 3D Exploratory Analysis of Ocean Flow Models

Modern ocean flow simulations are generating increasingly complex, multi-layer 3D ocean flow models. However, most researchers are still using traditional 2D visualizations to visualize these models one slice at a time. Properly designed 3D visualization tools can be highly effective for revealing the complex, dynamic flow patterns and structures present in these models. However, the transition from visualizing ocean flow patterns in 2D to 3D presents many challenges, including occlusion and depth ambiguity. Further complications arise from the interaction methods required to navigate, explore, and interact with these 3D datasets. We present a system that employs a combination of stereoscopic rendering, to best reveal and illustrate 3D structures and patterns, and multi-touch interaction, to allow for natural and efficient navigation and manipulation within the 3D environment. Exploratory visual analysis is facilitated through the use of a highly-interactive toolset which leverages a smart particle system. Multi-touch gestures allow users to quickly position dye emitting tools within the 3D model. Finally, we illustrate the potential applications of our system through examples of real world significance

Generalizing Deep Learning Methods for Particle Tracing Using Transfer Learning

Particle tracing is a very important method for scientific visualization of vector fields, but it is computationally expensive. Deep learning can be used to speed up particle tracing, but existing deep learning models are domain-specific. In this work, we present a methodology to generalize the use of deep learning for particle tracing using transfer learning. We demonstrate the performance of our approach through a series of experimental studies that address the most common simulation design scenarios: varying time span, Reynolds number, and problem geometry. The results show that our methodology can be effectively used to generalize and accelerate the training and practical use of deep learning models for visualization of unsteady flows

Numerical Evaluation of Pathline Predicates of the Benguela Upwelling System

Using simulation data of a regional ocean model, Nardini et al. applied pathline predicates for a detailed post-hoc analysis of the Benguela upwelling system. In this work, we evaluate the accuracy of this technique. Using different temporal samplings, we aim at finding minimum requirements for the temporal resolution of the flow data in the context of retroactive particle pathline techniques. Besides the flow field, our simulation data contains synthetic tracer fields for different tracer source regions. Using the flow data, dense trajectories are computed to enable deriving ”emulated tracer fields” based on the local ratio of pathline particles originating from tracer source regions to other ones, which can then be compared to the original tracer fields. We find that the emulated tracer concentrations are overestimated in comparison to the original ones. However, the shape of the regions with high tracer concentration can be reproduced