arXiv subjects

Michael C. Brennan

Publications and source records attributed to Michael C. Brennan.

4 recordsLinked to original sources

arXiv2022

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.

physics.ins-det↗

arXiv2022

Analytical Methods for Superresolution Dislocation Identification in Dark-Field X-ray Microscopy

In this work, we develop several inference methods to estimate the position of dislocations from images generated using dark-field X-ray microscopy (DFXM) -- achieving superresolution accuracy and principled uncertainty quantification. Using the framework of Bayesian inference, we incorporate models of the DFXM contrast mechanism and detector measurement noise, along with initial position estimates, into a statistical model coupling DFXM images with the dislocation position of interest. We motivate several position estimation and uncertainty quantification algorithms based on this model. We then demonstrate the accuracy of our primary estimation algorithm on synthetic realistic DFXM images of edge dislocations in single crystal aluminum. We conclude with a discussion of our methods' impact on future dislocation studies and possible future research avenues.

cond-mat.mtrl-sci↗

arXiv2020

Contour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theoretic Approach

Contour integral methods for nonlinear eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algorithms, establishing a relationship to system realization techniques in control theory. This connection motivates a new general framework for contour integral methods (for linear and nonlinear eigenvalue problems), building on recent developments in multi-point rational interpolation of dynamical systems. These new techniques, which replace the usual Hankel matrices with Loewner matrix pencils, incorporate general interpolation schemes and permit ready recovery of eigenvectors. Because the main computations (the solution of linear systems associated with contour integration) are identical for these Loewner methods and the traditional Hankel approach, a variety of new eigenvalue approximations can be explored with modest additional work. Numerical examples illustrate the potential of this approach. We also discuss how the concept of filter functions can be employed in this new framework, and show how contour methods enable a data-driven modal truncation method for model reduction.

math.NA↗

arXiv2020

Greedy inference with structure-exploiting lazy maps

We propose a framework for solving high-dimensional Bayesian inference problems using \emph{structure-exploiting} low-dimensional transport maps or flows. These maps are confined to a low-dimensional subspace (hence, lazy), and the subspace is identified by minimizing an upper bound on the Kullback--Leibler divergence (hence, structured). Our framework provides a principled way of identifying and exploiting low-dimensional structure in an inference problem. It focuses the expressiveness of a transport map along the directions of most significant discrepancy from the posterior, and can be used to build deep compositions of lazy maps, where low-dimensional projections of the parameters are iteratively transformed to match the posterior. We prove weak convergence of the generated sequence of distributions to the posterior, and we demonstrate the benefits of the framework on challenging inference problems in machine learning and differential equations, using inverse autoregressive flows and polynomial maps as examples of the underlying density estimators.

stat.CO↗