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DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

SANE: strategic autonomous non-smooth exploration for multiple optima discovery in multi-modal and non-differentiable black-box functions

Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and multimodal parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, material structure image spaces, and molecular embedding spaces. Often these systems are black-boxes and time-consuming to evaluate, which resulted in strong interest towards active learning methods such as Bayesian optimization (BO). However, these systems are often noisy which make the black box function severely multi-modal and non-differentiable, where a vanilla BO can get overly focused near a single or faux optimum, deviating from the broader goal of scientific discovery. To address these limitations, here we developed Strategic Autonomous Non-Smooth Exploration (SANE) to facilitate an intelligent Bayesian optimized navigation with a proposed cost-driven probabilistic acquisition function to find multiple global and local optimal regions, avoiding the tendency to becoming trapped in a single optimum. To distinguish between a true and false optimal region due to noisy experimental measurements, a human (domain) knowledge driven dynamic surrogate gate is integrated with SANE. We implemented the gate-SANE into pre-acquired piezoresponse spectroscopy data of a ferroelectric combinatorial library with high noise levels in specific regions, and piezoresponse force microscopy (PFM) hyperspectral data. SANE demonstrated better performance than classical BO to facilitate the exploration of multiple optimal regions and thereby prioritized learning with higher coverage of scientific values in autonomous experiments. Our work showcases the potential application of this method to real-world experiments, where such combined strategic and human intervening approaches can be critical to unlocking new discoveries in autonomous research.

Biswas, Arpan [University of Tennessee, Knoxville,↗

DOE OSTI2023

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Revealing the Predominant Surface Facets of Rough Cu Electrodes under Electrochemical Conditions

Metal electrodes with rough surfaces are frequently found to convert CO or CO 2 to hydrocarbons and oxygenates with high selectivity and at high reaction rates in comparison with their smooth counterparts. The atomic-level morphology of a rough electrode is likely one key factor responsible for its comparatively high catalytic selectivity and activity. However, few methods are capable of probing the atomic-level structure of rough metal electrodes under electrocatalytic conditions. As a result, the nuances in the atomic-level surface morphology that control the catalytic characteristics of these electrodes have remained largely unexplored. Because the C≡O stretching frequency of atop-bound CO (CO atop ) depends on the coordination of the underlying metal atom, the IR spectrum of this reaction intermediate on the copper electrode could, in principle, provide structural information about the catalytic surface during electrolysis. However, other effects, such as dynamic dipole coupling, easily obscure the dependence of the frequency on the surface morphology. Further, in the limit of low CO atop coverage, where coupling effects are small, the C≡O stretching frequencies of CO atop on Cu(111) and Cu(100) facets are virtually identical. Therefore, on the basis of the C≡O stretching frequency, it is not straightforward to distinguish between these two ubiquitous surface facets, which exhibit vastly different CO reduction activities. Herein, we show that key features of the atomic-level surface morphology of rough copper electrodes can be inferred from the potential dependence of the line shape of the C≡O stretching band of CO atop . Specifically, we compared two types of rough copper thin-film electrodes that are routinely employed in the context of surface-enhanced infrared absorption spectroscopy (SEIRAS). We found that copper films that are electrochemically deposited on Si-supported Au films (CuAu–Si) are poor catalysts for the reduction of CO to ethylene in comparison to copper films (Cu–Si) that are electrolessly deposited onto Si crystals. As quantified by differential electrochemical mass spectrometry (DEMS), the onset potential for ethylene is ~200 ± 65 mV more cathodic for CuAu–Si than that for Cu–Si. To reveal the origin of the disparate catalytic properties of Cu–Si and CuAu–Si, we probed the surfaces of the electrodes with cyclic voltammetry (CV) and SEIRAS. The CV characterization suggests that the (111) surface facet predominates on CuAu–Si, whereas the (100) facet is more common on Cu–Si. SEIRAS reveals that the line shape of the C≡O stretching of CO atop is composed of two bands that are attributable to CO atop on terrace and defect sites. The different surface structures manifest themselves in the form of starkly different potential dependences of the line shape of the C≡O stretching mode of CO atop on the two types of electrodes. With a simple Boltzmann model that considers the different adsorption energies of CO atop on terrace and defect sites, and the resulting CO atop populations on terrace and defect sites, we deduced that the observed electrode-specific potential dependence of the line shape is consistent with the presence of different predominant terrace sites on the two types of films. This strategy for assessing the atomic-level morphology is not restricted to SEIRAS but could also be applied to the C≡O stretching bands recorded with surface-enhanced Raman spectroscopy (SERS), which is suitable for probing a wide range of rough copper electrodes. Therefore, with this work, we establish the potential dependence of the C≡O stretching band of CO atop as a probe of the atomic-level surface structure of rough metal electrodes under electrochemical conditions. When it is coupled with complementary techniques, this methodology provides essential structural information for further improvement in the reaction selectivity of rough metal electrodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1974

Sticking probabilities for the adsorption of hydrogen on clean Ni/111/, Ni/100/, Ni sheet and evaporated Ni films

Determination of the sticking probability for hydrogen adsorption on clean Ni(111), Ni(100), polycrystalline nickel sheet, and polycrystalline evaporated nickel films, using a modification of the reflection detector technique of Horgan and King (1970) for metal films. The initial sticking probability for hydrogen adsorption on a nickel film at 300 K by the proposed method is found to be 0.25 in comparison to 0.35 for hydrogen adsorption on a nickel film using the reflection detector technique. Also, the sticking probabilities on smooth single-crystal (111) and (100) planes and polycrystalline sheets are found to be lower than those on the rougher polycrystalline nickel films.

Horgan, A. M.↗

NASA NTRS1984

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Roberts, G. O.↗

NASA NTRS1984

Applications of a conservative zonal scheme to transient and geometrically complex problems

A conservative zoning technique, wherein the flow field for a finite-difference calculation is divided into several regions to simplify grid generation, is discussed and is applied in the solution of a two-dimensional problem of complex topology. Calculations are performed on two zonal, or patched, grid systems for the supersonic flow over a double-airfoil configuration. The solution is smooth and continuous across the zonal interfaces, and shock waves pass through the boundaries without distortion. In addition, the time-accuracy of the zonal-boundary method is verified by a two-zone cyclinder calculation with a stationary inner and a rotating outer mesh.The feasibility of the zonal approach for use in the solution of geometrically complex and unsteady problems is thus demonstrated.

Hessenius, K. A.↗

NASA NTRS1985

Numerical simulation of a turbulent flame stabilized behind a rearward-facing step

Flow of combustible mixtures in a plane channel past a smooth contraction followed by an abrupt expansion, in a typical dump combustor configuration, is modeled by a two-dimensional numerical technique based on the random vortex method. Both the inert and the reacting case are considered. In the latter, the flame is treated as an interface, self-advancing at a prescribed normal burning speed, while the dynamic effects of expansion due to the exothermicity of combustion are expressed by volumetric source lines delineated by its front. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and the reattachment length. The stochastic turbulent velocity components manifest interesting differences, especially near the walls where three-dimensional effects of turbulence are expected to be of importance.

Hsiao, C. C.↗

NASA NTRS2006

Terrestrial Water Mass Load Changes from Gravity Recovery and Climate Experiment (GRACE)

Recent studies show that data from the Gravity Recovery and Climate Experiment (GRACE) is promising for basin- to global-scale water cycle research. This study provides varied assessments of errors associated with GRACE water storage estimates. Thirteen monthly GRACE gravity solutions from August 2002 to December 2004 are examined, along with synthesized GRACE gravity fields for the same period that incorporate simulated errors. The synthetic GRACE fields are calculated using numerical climate models and GRACE internal error estimates. We consider the influence of measurement noise, spatial leakage error, and atmospheric and ocean dealiasing (AOD) model error as the major contributors to the error budget. Leakage error arises from the limited range of GRACE spherical harmonics not corrupted by noise. AOD model error is due to imperfect correction for atmosphere and ocean mass redistribution applied during GRACE processing. Four methods of forming water storage estimates from GRACE spherical harmonics (four different basin filters) are applied to both GRACE and synthetic data. Two basin filters use Gaussian smoothing, and the other two are dynamic basin filters which use knowledge of geographical locations where water storage variations are expected. Global maps of measurement noise, leakage error, and AOD model errors are estimated for each basin filter. Dynamic basin filters yield the smallest errors and highest signal-to-noise ratio. Within 12 selected basins, GRACE and synthetic data show similar amplitudes of water storage change. Using 53 river basins, covering most of Earth's land surface excluding Antarctica and Greenland, we document how error changes with basin size, latitude, and shape. Leakage error is most affected by basin size and latitude, and AOD model error is most dependent on basin latitude.

Seo, K.-W.↗

NASA NTRS2014

Smooth Pursuit of Flicker-Defined Motion

We examined the pursuit response to stimuli defined by space-variant flicker of a dense random dot carrier pattern. On each frame, every element of the pattern could change polarity, with a probability given by a two-dimensional Gaussian distribution. A normal distribution produces a circular region of twinkle, while inverting the distribution results in a spot of static texture in a twinkling surround. In this latter case, the carrier texture could be stationary, or could move with the twinkle modulator,thereby producing first-order motion in the region of the spot. While the twinkle-defined spot produces a strong sensation of motion, the complementary stimulus defined by the absence of twinkle does not;when viewed peripherally, it appears to move in steps even when the generating distribution moves smoothly. We examined pursuit responses to these stimuli using two techniques: 1) the eye movement correlogram, obtained by cross-correlating eye velocity with the velocity of a randomly-moving stimulus; and 2) delayed visual feedback, where transient stabilization of a target can produce spontaneous oscillations of the eye, with a period empirically observed to vary linearly with the applied delay. Both techniques provide an estimate of the internal processing time, which can be as short as100 milliseconds for a first-order target. Assessed by the correlogram method, the response to flicker defined motion is delayed by more than 100 milliseconds, and significantly weaker (especially in the vertical dimension). When initially presented in the delayed feedback condition, purely saccadic oscillation is observed. One subject eventually developed smooth oscillations (albeit with significant saccadic intrusions), showing a period-versus-delay slope similar to that observed for first-order targets. This result is somewhat surprising, given that we interpret the slope of the period-versus-delayfunction as reflecting the balance between position- and velocity-sensitive inputs to pursuit.

smooth pursuit↗

NASA NTRS1975

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies was generated from coordinates of points in several cross sections. Since these points may not be on smooth curves, they are divided into groups forming segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction through longitudinal curves. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines or specifying slopes at selected points. This method was used to surface fit a 70 deg slab delta wing and the HL-10 Lifting Body. The results for the delta wing were very close to the exact geometry. Although there is no exact solution for the lifting body, the surface fit generated a smooth surface with cross-sectional planes very close to prescribed coordinate points.

Dejarnette, F. R.↗

DOE OSTI2022

Deblurring galaxy images with Tikhonov regularization on magnitude domain

Abstract We propose a regularization-based deblurring method that works efficiently for galaxy images. The spatial resolution of a ground-based telescope is generally limited by seeing conditions and is much worse than space-based telescopes. This circumstance has generated considerable research interest in the restoration of spatial resolution. Since image deblurring is a typical inverse problem and often ill-posed, solutions tend to be unstable. To obtain a stable solution, much research has adopted regularization-based methods for image deblurring, but the regularization term is not necessarily appropriate for galaxy images. Although galaxies have an exponential or Sérsic profile, the conventional regularization assumes the image profiles to behave linearly in space. The significant deviation between the assumption and real situations leads to blurring of the images and smoothing out the detailed structures. Clearly, regularization on logarithmic domain, i.e., magnitude domain, should provide a more appropriate assumption, which we explore in this study. We formulate a problem of deblurring galaxy images by an objective function with a Tikhonov regularization term on a magnitude domain. We introduce an iterative algorithm minimizing the objective function with a primal–dual splitting method. We investigate the feasibility of the proposed method using simulation and observation images. In the simulation, we blur galaxy images with a realistic point spread function and add both Gaussian and Poisson noise. For the evaluation with the observed images, we use galaxy images taken by the Subaru HSC-SSP. Both of these evaluations show that our method successfully recovers the spatial resolution of the deblurred images and significantly outperforms the conventional methods. The code is publicly available from the GitHub 〈https://github.com/kzmurata-astro/PSFdeconv_amag〉.

Murata, Kazumi↗

NASA NTRS2014

Smooth Pursuit of Flicker-Defined Motion

We examined the pursuit response to stimuli defined by space-variant flicker of a dense random dot carrier pattern. On each frame, every element of the pattern could change polarity, with a probability given by a two-dimensional Gaussian distribution. A normal distribution produces a circular region of twinkle, while inverting the distribution results in a spot of static texture in a twinkling surround. In this latter case, the carrier texture could be stationary, or could move with the twinkle modulator, thereby producing first-order motion in the region of the spot. While the twinkle-defined spot produces a strong sensation of motion, the complementary stimulus defined by the absence of twinkle does not, when viewed peripherally, it appears to move in steps even when the generating distribution moves smoothly. We examined pursuit responses to these stimuli using two techniques: 1) the eye movement correlogram, obtained by cross-correlating eye velocity with the velocity of a randomly-moving stimulus; and 2) delayed visual feedback, where transient stabilization of a target can produce spontaneous oscillations of the eye, with a period empirically observed to vary linearly with the applied delay. Both techniques provide an estimate of the internal processing time, which can be as short as 100 milliseconds for a first-order target. Assessed by the correlogram method, the response to flicker-defined motion is delayed by more than 100 milliseconds, and significantly weaker (especially in the vertical dimension). When initially presented in the delayed feedback condition, purely saccadic oscillation is observed. One subject eventually developed smooth oscillations (albeit with significant saccadic intrusions), showing a period-versus-delay slope similar to that observed for first-order targets. This result is somewhat surprising, given that we interpret the slope of the period-versus-delay-function as reflecting the balance between position- and velocity-sensitive inputs to pursuit.

eye movements↗

DOE OSTI2024

E-PVT: enhanced position-velocity-time scheduler for computer-controlled optical finishing with comprehensive considerations of dynamics constraints, continuity and efficiency

Deterministic computer-controlled optical finishing is an essential approach for achieving high-quality optical surfaces. Its determinism and convergence rely heavily on precise and smooth motion control to guide the machine tool over an optical surface to correct residual errors. One widely supported and smooth motion control model is position-velocity-time (PVT), which employs piecewise cubic polynomials to describe positions. Our prior research introduced a PVT-based velocity scheduling method, demonstrating sub-nanometer level convergence in ion beam figuring (IBF) processes. However, three challenges remained. Firstly, this method relies on quadratic programming, resulting in computational intensiveness for dense tool paths. Secondly, the dynamics constraints and velocity and acceleration continuities are not comprehensively considered, limiting the full potential of PVT-based control. Thirdly, no compensation mechanism existed when dynamics constraints are exceeded. In this study, in response to these challenges, we proposed the Enhanced PVT (E-PVT) method, reducing the time complexity from O ( n 3 ) to O ( n ) while fully addressing dynamics constraints and continuities. A novel compensation method utilizing particle swarm optimization was proposed to address situations where dynamics constraints might be exceeded while maintaining the overall processing efficiency. Validation through simulation and experimentation confirmed the improved performance of E-PVT.

36 MATERIALS SCIENCE↗

NASA NTRS1978

Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions

A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

NASA NTRS1980

Geometric methods in computational fluid dynamics

General methods for the construction of geometric computational fluid dynamic algorithms are presented which simulate a variety of flow fields in various nontrivial regions. Included are: basic developments with tensors; various forms for the equations of motion; generalized numerical methods and boundary conditions; and methods for mesh generation to meet the strong geometric constraints of turbomachines. Coordinate generation is shown generally to yield mesh descriptions from one or more transformations that are smoothly joined together to form a composite mesh.

Eiseman, P. R.↗

NASA NTRS1981

Optimum structural design with plate bending elements - A survey

A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.

Haftka, R. T.↗

NASA NTRS1982

High spatial resolution Mg/Al maps of the western Crisium and Sulpicius Gallus regions

High spatial resolution Mg/Al ratio maps of the western Crisium and Sulpicius Gallus regions of the moon are presented. The data is from the X-ray fluorescence experiment and the image enhancement technique in the Laplacian subtraction method using a special least-squares version of the Laplacian to reduce noise amplification. In the highlands region west of Mare Crisium several relatively small patches of smooth material have high local Mg/Al ratio similar to values found in mare sites, suggesting volcanism in the highlands. In the same highland region there were other smooth areas with no high Mg/Al local values and they are probably Cayley Formation material produced by impact mass wasting. The Sulpicius Gallus region has variable Mg/Al ratios. In this region there are several high Mg/Al ratio spots, two of which occur at the highland-mare interface. Another high Mg/Al ratio area corresponds to the Sulpicius Gallus Rima I region. The high Mg/Al ratio material in the Sulpicius Gallus region is probably pyroclastic.

Schonfeld, E.↗