Computational Methods for Support Vector Machine Classification and Large-Scale Kalman Filtering

The first half of this dissertation focuses on computational methods for solving the constrained quadratic program (QP) within the support vector machine (SVM) classifier. One of the SVM formulations requires the solution of bound and equality constrained QPs. We begin by describing an augmented Lagrangian approach which incorporates the equality constraint into the objective function, resulting in a bound constrained QP. Furthermore, all constraints may be incorporated into the objective function to yield an unconstrained quadratic program, allowing us to apply the conjugate gradient (CG) method. Lastly, we adapt the scaled gradient projection method of [10] to the SVM QP and compare the performance of these methods with the state-of-the-art sequential minimal optimization algorithm and MATLAB\u27s built in constrained QP solver, quadprog. The augmented Lagrangian method outperforms other state-of-the-art methods on three image test cases. The second half of this dissertation focuses on computational methods for large-scale Kalman filtering applications. The Kalman filter (KF) is a method for solving a dynamic, coupled system of equations. While these methods require only linear algebra, standard KF is often infeasible in large-scale implementations due to the storage requirements and inverse calculations of large, dense covariance matrices. We introduce the use of the CG and Lanczos methods into various forms of the Kalman filter for low-rank approximations of the covariance matrices, with low-storage requirements. We also use CG for efficient Gaussian sampling within the ensemble Kalman filter method. The CG-based KF methods perform similarly in root-mean-square error when compared to the standard KF methods, when the standard implementations are feasible, and outperform the limited-memory Broyden-Fletcher-Goldfarb-Shanno approximation method

Statistical Interpolation for Surface Reconstruction of PDV and BLR data

Author Institution: Nevada National Security Site; Lawrence Livermore National LaboratorySlides presented at the 2018 Photonic Doppler Velocimetry (PDV) Users Workshop, Drury Plaza Hotel, Santa Fe, New Mexico, May 16-18, 2018

Optical Ranging Overview and Analysis of Calibration Data

Author Institution: Lawrence Livermore National Laboratory; National Security Technologies, LLCSlides presented at the 2016 Photonic Doppler Velocimetry (PDV) unclassified program, Bankhead Theater, Livermore, California, June 7 - 9, 2016. Morning program, June 9, 2016

In-Situ Visualization of Long-Range Defect Interactions at the Edge of Melting

Connecting a bulk material's microscopic defects to its macroscopic properties is an age-old problem in materials science. Long-range interactions between dislocations (line defects) are known to play a key role in how materials deform or melt, but we lack the tools to connect these dynamics to the macroscopic properties. We introduce time-resolved dark-field X-ray microscopy to directly visualize how dislocations move and interact over hundreds of micrometers, deep inside bulk aluminum. With real-time movies, we reveal the thermally-activated motion and interactions of dislocations that comprise a boundary, and show how weakened binding forces inhomogeneously destabilize the structure at 99% of the melting temperature. Connecting dynamics of the microstructure to its stability, we provide important opportunities to guide and validate multiscale models that are yet untested

An Online Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics

High-brightness X-ray pulses, as generated at synchrotrons and X-ray free electron lasers (XFEL), are used in a variety of scientific experiments. Many experimental testbeds require optical equipment, e.g Compound Refractive Lenses (CRLs), to be precisely aligned and focused. The lateral alignment of CRLs to a beamline requires precise positioning along four axes: two translational, and the two rotational. At a synchrotron, alignment is often accomplished manually. However, XFEL beamlines present a beam brightness that fluctuates in time, making manual alignment a time-consuming endeavor. Automation using classic stochastic methods often fail, given the errant gradient estimates. We present an online correction based on the combination of a generalized finite difference stencil and a time-dependent sampling pattern. Error expectation is analyzed, and efficacy is demonstrated. We provide a proof of concept by laterally aligning optics on a simulated XFEL beamline

Simultaneous Bright- and Dark-Field X-ray Microscopy at X-ray Free Electron Lasers

The structures, strain fields, and defect distributions in solid materials underlie the mechanical and physical properties across numerous applications. Many modern microstructural microscopy tools characterize crystal grains, domains and defects required to map lattice distortions or deformation, but are limited to studies of the (near) surface. Generally speaking, such tools cannot probe the structural dynamics in a way that is representative of bulk behavior. Synchrotron X-ray diffraction based imaging has long mapped the deeply embedded structural elements, and with enhanced resolution, Dark Field X-ray Microscopy (DFXM) can now map those features with the requisite nm-resolution. However, these techniques still suffer from the required integration times due to limitations from the source and optics. This work extends DFXM to X-ray free electron lasers, showing how the $10^{12}$ photons per pulse available at these sources offer structural characterization down to 100 fs resolution (orders of magnitude faster than current synchrotron images). We introduce the XFEL DFXM setup with simultaneous bright field microscopy to probe density changes within the same volume. This work presents a comprehensive guide to the multi-modal ultrafast high-resolution X-ray microscope that we constructed and tested at two XFELs, and shows initial data demonstrating two timing strategies to study associated reversible or irreversible lattice dynamics