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At least 271 records · Page 15

Edge detection - Image-plane versus digital processing

To optimize edge detection with the familiar Laplacian-of-Gaussian operator, it has become common to implement this operator with a large digital convolution mask followed by some interpolation of the processed data to determine the zero crossings that locate edges. It is generally recognized that this large mask causes substantial blurring of fine detail. It is shown that the spatial detail can be improved by a factor of about four with either the Wiener-Laplacian-of-Gaussian filter or an image-plane processor. The Wiener-Laplacian-of-Gaussian filter minimizes the image-gathering degradations if the scene statistics are at least approximately known and also serves as an interpolator to determine the desired zero crossings directly. The image-plane processor forms the Laplacian-of-Gaussian response by properly combining the optical design of the image-gathering system with a minimal three-by-three lateral-inhibitory processing mask. This approach, which is suggested by Marr's model of early processing in human vision, also reduces data processing by about two orders of magnitude and data transmission by up to an order of magnitude.

Huck, Friedrich O.↗

Exploration with Scalable Gaussian Process Reinforcement Learning

Exploration is a challenging problem in reinforcement learning (RL), especially in environments with sparse rewards. Quantifying and utilizing the parametric uncertainty has been shown to be paramount for successful exploration [Osband et al., 2018]. Bayesian, or approximately Bayesian, methods present a principled means of estimating the parametric uncertainty in RL problems. Gaussian processes, nonparametric Bayesian models, are often impractical due to poor scalability and computational bottlenecks. We introduce a scalable Gaussian process RL (GPRL) method which directly induces sparsity in the covariance matrix to facilitate faster computation. This is a departure from previous GPRL methods which instead rely on data reduction and subsampling. We compare various covariance-based exploration techniques (Thompson sampling, upper confidence bound, and probabilistic maximum variance) which leverage our scalable GP framework in sparse reward environments. Finally, we show favorable comparison against the bootstrapped deep Q-Network.

97 MATHEMATICS AND COMPUTING↗

Characterization of Ring Wave Spectra for Natural Rain: Measurements and Model for Remote Sensing Applications

Ring waves generated by natural rains from 1 to 100 mm/hr were measured in a small tank located in a field. Time series were obtained: (a) from a wire capacitance probe that measured surface elevation, (b) from an optical gauge that measured rain rates R, (c) from an anemometer that measured wind speeds and (d) from a 13.5 GHz scatterometer (w polarization, and 30 degree incidence angle). Ring wave frequency spectra are computed from the surface elevation data for each minute of rain. All the spectra have a similar shape, with a maximum near 5 Hz, and with a more rapid decay towards higher frequencies than towards lower frequencies. A log-Gaussian spectral model provides a useful representation of these data and analysis of the model coefficients shows that the peak frequency and bandwidth are approximately constant, but the magnitude increases as R increases, Additionally, the normalized radar cross section from the scatterometer varies approximately linearly with the spectral line corresponding to the Bragg-wavelength, so together the log-Gaussian ring wave model and the Bragg scattering theory should be useful for a broad range of applications. These findings can be used to help interpret remote sensing data during rain events and to guide model development for radar scattering from rain roughened seas.

Bliven, L.↗

Two Suzaku Observations of the Cyclotron Line Source 4U 1907+09

Suzaku observed the accreting pulsar 4U 1907+09 in May 2006 and in April 2007. We present and compare the light curves and broad band spectra of both observations. The approximately 10 mCrab source is strongly variable and shows a rich phenomenology. While the 2006 observation is dominated by typical, non-absorption-related dipping behavior, the 2007 observation shows equally typical flaring behavior in both the XIS and PIN light curves. Above 2 keV the average combined XIS and PIN broad band spectrum can be well described by standard pulsar continuum models, modified by the fundamental cyclotron resonant scattering feature at approximately 19 keV. We model the cyclotron line using the standard phenomenological Gaussian model as well as a new physically motivated Green's functions based approach (Schoenherr et al., 2007, A&A 472, 353). Below 2 keV the XIS spectra allow for the first detection of a soft excess in this source, in addition to providing the best determination of the parameters of the weak iron line at 6.4 keV (EW approximately 70 eV) to date.

Pottschmidt, Katja↗

Uncertainty-aware molecular dynamics from Bayesian active learning for phase transformations and thermal transport in SiC

Abstract Machine learning interatomic force fields are promising for combining high computational efficiency and accuracy in modeling quantum interactions and simulating atomistic dynamics. Active learning methods have been recently developed to train force fields efficiently and automatically. Among them, Bayesian active learning utilizes principled uncertainty quantification to make data acquisition decisions. In this work, we present a general Bayesian active learning workflow, where the force field is constructed from a sparse Gaussian process regression model based on atomic cluster expansion descriptors. To circumvent the high computational cost of the sparse Gaussian process uncertainty calculation, we formulate a high-performance approximate mapping of the uncertainty and demonstrate a speedup of several orders of magnitude. We demonstrate the autonomous active learning workflow by training a Bayesian force field model for silicon carbide (SiC) polymorphs in only a few days of computer time and show that pressure-induced phase transformations are accurately captured. The resulting model exhibits close agreement with both ab initio calculations and experimental measurements, and outperforms existing empirical models on vibrational and thermal properties. The active learning workflow readily generalizes to a wide range of material systems and accelerates their computational understanding.

36 MATERIALS SCIENCE↗

Merged interaction regions and large-scale magnetic field fluctuations during 1991: Voyager 2 observations

This paper analyzes Voyager 2 observations of the magnetic field between 33.6 AU and 36.2 AU during 1991 when extraordinary events were observed on the Sun and in the heliosphere. The magnetic field strength signal B(t) has the unusual form of two large transient merged interaction regions (MIRs) on a fluctuating background. The two MIRs moved past the spacecraft in 32 days and 18 days, respectively. The mean field strength in each transient MIR was approx. equals 2.6 times the mean field during the remaining part of the year (0.11 nT). Each of the MIRs is related to a fast stream. The magnetic field is strong throughout each stream, suggesting that the strong fields are carried by the streams as well as produced by shock and stream compression. The fluctuations in B(t) during 1991 are not multifractal, and the MIRs cannot be approximated as multifractal clusters of intense magnetic fields. The distribution of the hour-averaged magnetic field strengths is approximately lognormal over 90% of its intermediate range, and it has an exponential tail for B greater than the average magnetic field strength. The elevation angles of B have a normal distribution with a standard deviation of 16 deg +/- 4 deg. The distributions of the azimuthal angles of B in the ranges 1 deg - 180 deg and 180 deg - 360 deg are approximately normal over a more limited range, and non-Gaussian tails associated with nearly radial magnetic fields; the standard deviations are approx. equal to 40 deg. Individual sectors are present throughout most of the interval, even in the MIRs, but there is no recurrent sector pattern. A model of the large-scale fluctuations in 1991 will have to include both determinaistic and statistical factors.

Burlaga, L. F.↗

Capacity of Pulse-Position Modulation (PPM) on Gaussian and Webb Channels

This article computes the capacity of various idealized soft-decision channels modeling an optical channel using an avalanche photodiode detector (APD) and pulse-position modulation (PPM). The capacity of this optical channel depends in a complicated way on the physical parameters of the APD and the constraints imposed by the PPM orthogonal signaling set. This article attempts to identify and separate the effects of several fundamental parameters on the capacity of the APD-detected optical PPM channel. First, an overall signal-to-noise ratio (SNR) parameter is de ned such that the capacity as a function of a bit-normalized version of this SNR drops precipitously toward zero at quasi-brick-wall limits on bit SNR that are numerically the same as the well-understood brick-wall limits for the standard additive white Gaussian noise (AWGN) channel. A second parameter is used to quantify the effects on capacity of one unique facet of the optical PPM channel (as compared with the standard AWGN channel) that causes the noise variance to be higher in signal slots than in nonsignal slots. This nonuniform noise variance yields interesting capacity effects even when the channel model is AWGN. A third parameter is used to measure the effects on capacity of the difference between an AWGN model and a non-Gaussian model proposed by Webb (see reference in [2]) for approximating the statistics of the APD-detected optical channel. Finally, a fourth parameter is used to quantify the blending of a Webb model with a pure AWGN model to account for thermal noise. Numerical results show that the capacity of M-ary orthogonal signaling on the Webb channel exhibits the same brick-wall Shannon limit, (M ln 2)=(M 1), as on the AWGN channel ( 1:59 dB for large M). Results also compare the capacity obtained by hard- and soft-output channels and indicate that soft-output channels o er a 3-dB advantage.

Dolinar, S.↗

A comparison of Gaussian processes and neural networks for computer model emulation and calibration

The Department of Energy relies on complex physics simulations for prediction in domains like cosmology, nuclear theory, and materials science. These simulations are often extremely computationally intensive, with some requiring days or weeks for a single simulation. In order to assure their accuracy, these models are calibrated against observational data in order to estimate inputs and systematic biases. Because of their great computational complexity, this process typically requires the construction of an emulator, a fast approximation to the simulation. In this paper, two emulator approaches are compared: Gaussian process regression and neural networks. Their emulation accuracy and calibration performance on three real problems of Department of Energy interest is considered. On these problems, the Gaussian process emulator tends to be more accurate with narrower, but still well-calibrated uncertainty estimates. The neural network emulator is accurate, but tends to have large uncertainty on its predictions. Finally, as a result, calibration with the Gaussian process emulator produces more constrained posteriors that still perform well in prediction.

97 MATHEMATICS AND COMPUTING↗

Shear and compression buckling analysis for anisotropic panels with centrally located elliptical cutouts

An approximate analysis for buckling of biaxial- and shear-loaded anisotropic panels with centrally located elliptical cutouts is presented in the present paper. The analysis is composed of two parts, a prebuckling analysis and a buckling analysis. The prebuckling solution is determined using Lekhnitskii's complex variable equations of plane elastostatics combined with a Laurent series approximation and a boundary collocation method. The buckling solution is obtained using the principle of minimum potential energy. A by-product of the minimum potential energy equation is an integral equation which is solved using Gaussian quadrature. Comparisons with documented experimental results and finite element analyses indicate that the approximate analysis accurately predicts the buckling loads of square biaxial- and shear-loaded panels having elliptical cutouts with major axes up to sixty percent of the panel width. Results of a parametric study are presented for shear- and compression-loaded rectangular anisotropic panels with elliptical cutouts. The effects of panel aspect ratio, cutout shape, cutout size, cutout orientation, laminate anisotropy, and combined loading on the buckling load are examined.

Britt, V. O.↗

Ionospheric scintillation by a random phase screen Spectral approach

The theory developed by Briggs and Parkin, given in terms of an anisotropic gaussian correlation function, is extended to a spectral description specified as a continuous function of spatial wavenumber with an intrinsic outer scale as would be expected from a turbulent medium. Two spectral forms were selected for comparison: (1) a power-law variation in wavenumber with a constant three-dimensional index equal to 4, and (2) Gaussian spectral variation. The results are applied to the F-region ionosphere with an outer-scale wavenumber of 2 per km (approximately equal to the Fresnel wavenumber) for the power-law variation, and 0.2 per km for the Gaussian spectral variation. The power-law form with a small outer-scale wavenumber is consistent with recent F-region in-situ measurements, whereas the gaussian form is mathematically convenient and, hence, mostly used in the previous developments before the recent in-situ measurements. Some comparison with microwave scintillation in equatorial areas is made.

Rufenach, C. L.↗

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

We present a model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structures. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents, followed by (b) pruning of the shells according to their contributions to the 2- body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-ζ quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree−Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 μE h per electron, respectively.

Approximation↗

Structural behavior of scientific balloons - Finite element simulation and verification

An off-the-shelf nonlinear finite element code was used to analyze fully inflated scientific balloons. The thin balloon film was modeled by shell bending elements. Numerical difficulties caused by insignificant bending stiffness terms were overcome by introducing some artificial bending stiffness. This approximation is justified by the fact that in thin shells with nonzero Gaussian curvature the membrane solution component is essentially independent of the bending solution component. Perturbation of the coveraged solution by increasing the bending stiffness by a full decade verified this assertion. This analytical approach was experimentally verified. As a result of this verification process it was discovered that the generally accepted linearly visco-elastic model for polyethylene film is inappropriate for a significant planar (as opposed to uniaxial) stress state. A linear elastic model presents a good approximation for planar stress states.

Schur, Willi W.↗

On the statistical uncertainties associated with line profile fitting

The paper considers the statistical uncertainties in the best-fit parameters associated with the fitting of observational data by model line profiles of specific form. The parameters involved are amplitude, center, and width. A general procedure is described for any profile type of parametric form. The case of Gaussian profiles is treated in detail, and numerical solutions are presented for equally spaced data of equal weight. Approximate analytical solutions are derived that give good general agreement with the numerical solutions over the whole range of interest. Approximate solutions are also obtained for the case of Lorentzian profiles. It is shown that the Lorentzian results can be used in conjunction with the Gaussian results to estimate the corresponding parameter uncertainties in the case of the general Voigt profile.

Landman, D. A.↗

Gaussian processes for autonomous data acquisition at large-scale synchrotron and neutron facilities

The execution and analysis of complex experiments are challenged by the vast dimensionality of the underlying parameter spaces. Although an increase in data-acquisition rates should allow broader querying of the parameter space, the complexity of experiments and the subtle dependence of the model function on input parameters remains daunting owing to the sheer number of variables. New strategies for autonomous data acquisition are being developed, with one promising direction being the use of Gaussian process regression (GPR). GPR is a quick, non-parametric and robust approximation and uncertainty quantification method that can be applied directly to autonomous data acquisition. We review GPR-driven autonomous experimentation and illustrate its functionality using real-world examples from large experimental facilities in the USA and France. We introduce the basics of a GPR-driven autonomous loop with a focus on Gaussian processes, and then shift the focus to the infrastructure that needs to be built around GPR to create a closed loop. Finally, the case studies we discuss show that Gaussian-process-based autonomous data acquisition is a widely applicable method that can facilitate the optimal use of instruments and facilities by enabling the efficient acquisition of high-value datasets.

36 MATERIALS SCIENCE↗

coh3

CoH3 (CoH ver.3) is an optical model, exciton pre-equilibrium, and Hauser-Feshbach statistical model code, which calculates nuclear reaction cross sections for medium to heavy targets in the keV to MeV energy region. This program is written in standard C++, divided into approximately 200 source and header files. CoH solves the Schroedinger equation for optical potentials defined in the code, and calculates differential elastic scattering, reaction, and total cross sections, for neutron, proton, deuteron, triton, 3He, and alpha-particle. Deformed optical potentials are solved with the coupled-channels method, in which the ground state rotational band members, or vibrational phonon states are coupled. The optical model gives particle transmission coefficients that are fed into the statistical model calculations. CoH includes the pre-equilibrium model (exciton model), the direct/semidirect capture model, and the multi-stage Hauser-Feshbach statistical decay with width fluctuation correction based on the Gaussian orthogonal ensemble. For weakly coupled levels, the DWBA (distorted wave Born approximation) method is used to calculate the direct inelastic scattering process to the excited states.

Kawano, Toshihiko↗

O'Hare Airport roadway traffic prediction via data fusion and Gaussian process regression

This study proposes an approach of leveraging information gathered from multiple traffic data sources at different resolutions to obtain approximate inference on the traffic distribution of Chicago's O'Hare Airport area. Specifically, it proposes the ingestion of traffic datasets at different resolutions to build spatiotemporal models for predicting the distribution of traffic volume on the road network. Due to its good adaptability and flexibility for spatiotemporal data, the Gaussian process (GP) regression was employed to provide short-term forecasts using data collected by loop detectors (sensors) and supplemented by telematics data. The GP regression is used to make predictions of the distribution of the proportion of sensor data traffic volume represented by the telematics data for each location of the sensors. Consequently, the fitted GP model can be used to determine the approximate traffic distribution for a testing location outside of the training points. Policymakers in the transportation sector can find the results of this work helpful for making informed decisions relating to current and future transportation conditions in the area.

42 ENGINEERING↗

Exact Gaussian processes for massive datasets via non-stationary sparsity-discovering kernels

Abstract A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. Its success is largely attributed to the GP’s analytical tractability, robustness, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $$O(N^3)$$ O ( N 3 ) in computation and $$O(N^2)$$ O ( N 2 ) in storage. All existing methods addressing this issue utilize some form of approximation—usually considering subsets of the full dataset or finding representative pseudo-points that render the covariance matrix well-structured and sparse. These approximate methods can lead to inaccuracies in function approximations and often limit the user’s flexibility in designing expressive kernels. Instead of inducing sparsity via data-point geometry and structure, we propose to take advantage of naturally-occurring sparsity by allowing the kernel to discover—instead of induce—sparse structure. The premise of this paper is that the data sets and physical processes modeled by GPs often exhibit natural or implicit sparsities, but commonly-used kernels do not allow us to exploit such sparsity. The core concept of exact, and at the same time sparse GPs relies on kernel definitions that provide enough flexibility to learn and encode not only non-zero but also zero covariances. This principle of ultra-flexible, compactly-supported, and non-stationary kernels, combined with HPC and constrained optimization, lets us scale exact GPs well beyond 5 million data points.

97 MATHEMATICS AND COMPUTING↗