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

Helmholtz-Hodge Decomposition of vector fields on 2-manifolds

posterA Morse-like Decomposition ? - Morse-Smale decomposition for gradient (of scalar) fields is an interesting way of decomposing the domain into regions of unidirectional flow (from a source to a sink ). - But works for gradient fields, which are conservative (irrotational), only. - Can such a decomposition and analysis be extended to generic (consisting rotational component) vector fields ? - Can we extract the rotational component out from generic vector fields ? Feature Identification ? - Analysis on the decomposed components of fields is simpler. eg Identification of critical points in the potentials of the two components is easy. Topological Consistency ? - Is there any relation between the topology of the components and the topology of the original field ? Limitation - So far, HH Decomposition exists only for piece-wise constant vector fields. Such a decomposition for piece-wise linear fields is desirable

Flow visualization with quantified spatial and temporal errors using edge maps

pre-printRobust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures

The natural Helmholtz-Hodge decomposition for open-boundary flow analysis

pre-printThe Helmholtz-Hodge decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions

Local, Smooth, and Consistent Jacobi Set Simplification

The relation between two Morse functions defined on a common domain can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces have shown to be useful in various applications. Unfortunately, in practice functions often contain noise and discretization artifacts causing their Jacobi set to become unmanageably large and complex. While there exist techniques to simplify Jacobi sets, these are unsuitable for most applications as they lack fine-grained control over the process and heavily restrict the type of simplifications possible. In this paper, we introduce a new framework that generalizes critical point cancellations in scalar functions to Jacobi sets in two dimensions. We focus on simplifications that can be realized by smooth approximations of the corresponding functions and show how this implies simultaneously simplifying contiguous subsets of the Jacobi set. These extended cancellations form the atomic operations in our framework, and we introduce an algorithm to successively cancel subsets of the Jacobi set with minimal modifications according to some user-defined metric. We prove that the algorithm is correct and terminates only once no more local, smooth and consistent simplifications are possible. We disprove a previous claim on the minimal Jacobi set for manifolds with arbitrary genus and show that for simply connected domains, our algorithm reduces a given Jacobi set to its simplest configuration.Comment: 24 pages, 19 figure

AMM: Adaptive Multilinear Meshes

We present Adaptive Multilinear Meshes (AMM), a new framework that significantly reduces the memory footprint compared to existing data structures. AMM uses a hierarchy of cuboidal cells to create continuous, piecewise multilinear representation of uniformly sampled data. Furthermore, AMM can selectively relax or enforce constraints on conformity, continuity, and coverage, creating a highly adaptive and flexible representation to support a wide range of use cases. AMM supports incremental updates in both spatial resolution and numerical precision establishing the first practical data structure that can seamlessly explore the tradeoff between resolution and precision. We use tensor products of linear B-spline wavelets to create an adaptive representation and illustrate the advantages of our framework. AMM provides a simple interface for evaluating the function defined on the adaptive mesh, efficiently traversing the mesh, and manipulating the mesh, including incremental, partial updates. Our framework is easy to adopt for standard visualization and analysis tasks. As an example, we provide a VTK interface, through efficient on-demand conversion, which can be used directly by corresponding tools, such as VisIt, disseminating the advantages of faster processing and a smaller memory footprint to a wider audience. We demonstrate the advantages of our approach for simplifying scalar-valued data for commonly used visualization and analysis tasks using incremental construction, according to mixed resolution and precision data streams

Data-driven model for divertor plasma detachment prediction

We present a fast and accurate data-driven surrogate model for divertor plasma detachment prediction leveraging the latent feature space concept in machine learning research. Our approach involves constructing and training two neural networks. An autoencoder that finds a proper latent space representation (LSR) of plasma state by compressing the multi-modal diagnostic measurements, and a forward model using multi-layer perception (MLP) that projects a set of plasma control parameters to its corresponding LSR. By combining the forward model and the decoder network from autoencoder, this new data-driven surrogate model is able to predict a consistent set of diagnostic measurements based on a few plasma control parameters. In order to ensure that the crucial detachment physics is correctly captured, highly efficient 1D UEDGE model is used to generate training and validation data in this study. Benchmark between the data-driven surrogate model and UEDGE simulations shows that our surrogate model is capable to provide accurate detachment prediction (usually within a few percent relative error margin) but with at least four orders of magnitude speed-up, indicating that performance-wise, it has the potential to facilitate integrated tokamak design and plasma control. Comparing to the widely used two-point model and/or two-point model formatting, the new data-driven model features additional detachment front prediction and can be easily extended to incorporate richer physics. This study demonstrates that the complicated divertor and scrape-off-layer plasma state has a low-dimensional representation in latent space. Understanding plasma dynamics in latent space and utilizing this knowledge could open a new path for plasma control in magnetic fusion energy research.Comment: 24 pages, 15 figure

Identifying Orientation-specific Lipid-protein Fingerprints using Deep Learning

Improved understanding of the relation between the behavior of RAS and RAF proteins and the local lipid environment in the cell membrane is critical for getting insights into the mechanisms underlying cancer formation. In this work, we employ deep learning (DL) to learn this relationship by predicting protein orientational states of RAS and RAS-RAF protein complexes with respect to the lipid membrane based on the lipid densities around the protein domains from coarse-grained (CG) molecular dynamics (MD) simulations. Our DL model can predict six protein states with an overall accuracy of over 80%. The findings of this work offer new insights into how the proteins modulate the lipid environment, which in turn may assist designing novel therapies to regulate such interactions in the mechanisms associated with cancer development

Computational Lipidomics of the Neuronal Plasma Membrane

Membrane lipid composition varies greatly within submembrane compartments, different organelle membranes, and also between cells of different cell stage, cell and tissue types, and organisms. Environmental factors (such as diet) also influence membrane composition. The membrane lipid composition is tightly regulated by the cell, maintaining a homeostasis that, if disrupted, can impair cell function and lead to disease. This is especially pronounced in the brain, where defects in lipid regulation are linked to various neurological diseases. The tightly regulated diversity raises questions on how complex changes in composition affect overall bilayer properties, dynamics, and lipid organization of cellular membranes. Here, we utilize recent advances in computational power and molecular dynamics force fields to develop and test a realistically complex human brain plasma membrane (PM) lipid model and extend previous work on an idealized, "average" mammalian PM. The PMs showed both striking similarities, despite significantly different lipid composition, and interesting differences. The main differences in composition (higher cholesterol concentration and increased tail unsaturation in brain PM) appear to have opposite, yet complementary, influences on many bilayer properties. Both mixtures exhibit a range of dynamic lipid lateral inhomogeneities ("domains"). The domains can be small and transient or larger and more persistent and can correlate between the leaflets depending on lipid mixture, Brain or Average, as well as on the extent of bilayer undulations