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At least 433 records · Page 24

The correspondence of surface climate parameters with satellite and terrain data

One of the goals of the research was to develop a ground sampling stragegy for calibrating remotely sensed measurements of surface climate parameters. The initial sampling strategy involved the stratification of the terrain based on important ancillary surface variables such as slope, exposure, insolation, geology, drainage, fire history, etc. For a spatially heterogeneous population, sampling error is reduced and efficiency increased by stratification of the landscape into more homogeneous sub-areas and by employing periodic random spacing of samples. These concepts were applied in the initial stratification of the study site for the purpose of locating and allocating instrumentation.

Dozier, Jeff↗

Coarse-Grained Density Functional Theory Predictions via Deep Kernel Learning

Scalable electronic predictions are critical for soft materials design. Recently, the Electronic Coarse-Graining (ECG) method was introduced to renormalize all-atom quantum chemical (QC) predictions to coarse-grained (CG) resolutions using deep neural networks (DNNs). While DNNs can learn complex representations that prove challenging for kernel-based methods, they are susceptible to overfitting and the overconfidence of uncertainty estimations. Here, we develop ECG within a GPU-accelerated Deep Kernel Learning (DKL) framework to enable CG QC predictions using range-separated hybrid density functional theory (DFT), obtaining a 107 speedup relative to naive all-atom QC. By treating the predicted electronic properties as random Gaussian Processes, DKL incorporates CG mapping degeneracy by learning the distribution of electronic energies as a function of CG configuration. DKL-ECG accurately reproduces molecular orbital energies from range-separated DFT while facilitating efficient training via active learning using the uncertainties provided by DKL. Further, we show that while active learning algorithms enable efficient sampling of a more diverse configurational space relative to random sampling, all explored query methods exhibit comparable performance for the examined system. We attribute this result to the significant overlap of the feature space and output property distributions across multiple temperatures.

97 MATHEMATICS AND COMPUTING↗

Compositional inhomogeneities in a single Icelandic tholeiite flow

New trace element analyses of 25 basalt samples from a vertical traverse in an 11 m thick flow of Icelandic tholeiite show compositional differences which exceed analytical uncertainties and are random with respect to height. These variations suggest a short-range segregation model in which the amounts of phenocrysts, groundmass materials, and residual liquid vary randomly in different samples of the flow; a least-squares method is applied to determine if these variations reflect different proportions of crystallizing phases and residual liquid. Monte Carlo computations indicate that short-range segregation results in inhomogeneity of a magnitude of interflow compositional differences; this causes incoherence in elements with different geochemical behaviors while preserving coherence in elements of similar behavior.

Lindstrom, M. M.↗

Changes in the Optical Properties of Simulated Shuttle Waste Water Deposits: Urine Darkening

Manned spacecraft have historically dumped the crew generated waste water overboard, into the environment in which the spacecraft operates, sometimes depositing the waste water on the external spacecraft surfaces. The change in optical properties of wastewater deposited on spacecraft external surfaces, from exposure to space environmental effects, is not well understood. This study used nonvolatile residue (NVR) from Human Urine to simulate wastewater deposits and documents the changes in the optical properties of the NVR deposits after exposure to ultra violet(UV)radiation. Twenty four NVR samples of, 0-angstromes/sq cm to 1000-angstromes/sq cm, and one sample contaminated with 1 to 2-mg/sq cm were exposed to UV radiation over the course of approximately 6151 equivalent sun hours (ESH). Random changes in sample mass, NVR, solar absorbance, and infrared emission were observed during the study. Significant changes in the UV transmittance were observed for one sample contaminated at the mg/sq cm level.

Albyn, Keith↗

Changes in the Optical Properties of Simulated Shuttle Waste Water Deposits- Urine Darkening

Manned spacecraft have historically dumped the crew generated waste waster overboard, into the environment in which the spacecraft operates, sometimes depositing the waste water on the external spacecraft surfaces. The change in optical properties of wastewater deposited on spacecraft external surfaces, from exposure to space environmental effects, is not well understood. This study used nonvolatile residue (NVR) from Human Urine to simulate wastewater deposits and documents the changes in the optical properties of the NVR deposits after exposure to ultra violet (UV) radiation. Twenty NVR samples of, 0-angstromes/sq cm to 1000-angstromes/sq cm, and one sample contaminated with 1 to 2-mg/sq cm were exposed to UV radiation over the course of approximately 6151 equivalent sun hours (ESH). Random changes in sample mass, NVR, solar absorbance, and infrared emission were observed during the study. Significant changes in the UV transmittance were observed for one sample contaminated at the mg/sq cm level.

Albyn, Keith↗

Rapid Identification of X-ray Diffraction Patterns Based on Very Limited Data by Interpretable Convolutional Neural Networks

Large volumes of data from material characterizations call for rapid and automatic data analysis to accelerate materials discovery. Herein, we report a convolutional neural network (CNN) that was trained based on theoretical data and very limited experimental data for fast identification of experimental X-ray diffraction (XRD) patterns of metal–organic frameworks (MOFs). To augment the data for training the model, noise was extracted from experimental data and shuffled; then it was merged with the main peaks that were extracted from theoretical spectra to synthesize new spectra. For the first time, one-to-one material identification was achieved. Theoretical MOFs patterns (1012) were augmented to a whole data set of 72 864 samples. It was then randomly shuffled and split into training (58 292 samples) and validation (14 572 samples) data sets at a ratio of 4:1. For the task of discriminating, the optimized model showed the highest identification accuracy of 96.7% for the top 5 ranking on a test data set of 30 hold-out samples. Neighborhood component analysis (NCA) on the experimental XRD samples shows that the samples from the same material are clustered in groups in the NCA map. Analysis on the class activation maps of the last CNN layer further discloses the mechanism by which the CNN model successfully identifies individual MOFs from the XRD patterns. Furthermore, this CNN model trained by the data augmentation technique would not only open numerous potential applications for identifying XRD patterns for different materials, but also pave avenues to autonomously analyze data by other characterization tools such as FTIR, Raman, and NMR spectroscopies.

36 MATERIALS SCIENCE↗

A methodology for small scale rural land use mapping in semi-arid developing countries using orbital imagery. Part 5: Experimental and operational techniques of mapping land use

The author has identified the following significant results. Scope of the preprocessing techniques was restricted to standard material from the EROS Data Center accompanied by some enlarging procedures and the use of the diazo process. Investigation has shown that the most appropriate sampling strategy for this study is the stratified random technique. A viable sampling procedure, together with a method for determining minimum number of sample points in order to test results of any interpretation are presented.

Vangenderen, J. L.↗

A data based random number generator for a multivariate distribution (using stochastic interpolation)

Let X be a K-dimensional random variable serving as input for a system with output Y (not necessarily of dimension k). given X, an outcome Y or a distribution of outcomes G(Y/X) may be obtained either explicitly or implicity. The situation is considered in which there is a real world data set X sub j sub = 1 (n) and a means of simulating an outcome Y. A method for empirical random number generation based on the sample of observations of the random variable X without estimating the underlying density is discussed.

Thompson, J. R.↗

The Effect of Homogenization Heat Treatment on the Texture Evolution in U-10Mo Alloy

Uranium alloyed with 10 wt% Mo (U-10Mo) undergoes discontinuous precipitation (DP) when subjected to sub-eutectoid heat-treatment. It is hypothesized that the crystallographic texture of the U-10Mo can be modified to minimize the degree of DP, however the evolution of texture throughout the manufacturing process is not well understood. Crystallographic textures of two U-10Mo samples homogenized at 900°C and 1000°C were studied after uniaxial rolling and annealing. A total of 6 samples were analyzed upon rolling using a combination of hot and cold rolling conditions to strains of 83%, 90% and 97% and subsequently annealed at 700°C for one hour. Microstructures and textures were analyzed via electron backscatter diffraction (EBSD) for each homogenization, strain and post-annealed states. Results show that the U-10Mo exhibits typical rolling textures seen in body-centered cubic materials with increasing intensities of both a- and ?-fibers with increasing strain. After recrystallization, the texture appeared to be effectively randomized in all samples. Homogenization temperature showed no effect on the rolling and recrystallization behavior. Potential factors leading to the randomization of texture are discussed along with the implications of textures on the minimization of DP.

nuclear fuel, texture, rolling↗

Monte-Carlo analysis of rarefied-gas diffusion including variance reduction using the theory of Markov random walks

Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.

Perlmutter, M.↗

Lunar Meteorites: A Global Geochemical Dataset

To date, the world's meteorite collections contain over 260 lunar meteorite stones representing at least 120 different lunar meteorites. Additionally, there are 20-30 as yet unnamed stones currently in the process of being classified. Collectively these lunar meteorites likely represent 40-50 distinct sampling locations from random locations on the Moon. Although the exact provenance of each individual lunar meteorite is unknown, collectively the lunar meteorites represent the best global average of the lunar crust. The Apollo sites are all within or near the Procellarum KREEP Terrane (PKT), thus lithologies from the PKT are overrepresented in the Apollo sample suite. Nearly all of the lithologies present in the Apollo sample suite are found within the lunar meteorites (high-Ti basalts are a notable exception), and the lunar meteorites contain several lithologies not present in the Apollo sample suite (e.g., magnesian anorthosite). This chapter will not be a sample-by-sample summary of each individual lunar meteorite. Rather, the chapter will summarize the different types of lunar meteorites and their relative abundances, comparing and contrasting the lunar meteorite sample suite with the Apollo sample suite. This chapter will act as one of the introductory chapters to the volume, introducing lunar samples in general and setting the stage for more detailed discussions in later more specialized chapters. The chapter will begin with a description of how lunar meteorites are ejected from the Moon, how deep samples are being excavated from, what the likely pairing relationships are among the lunar meteorite samples, and how the lunar meteorites can help to constrain the impactor flux in the inner solar system. There will be a discussion of the biases inherent to the lunar meteorite sample suite in terms of underrepresented lithologies or regions of the Moon, and an examination of the contamination and limitations of lunar meteorites due to terrestrial weathering. The bulk of the chapter will use examples from the lunar meteorite suite to examine important recent advances in lunar science, including (but not limited to the following: (1) Understanding the global compositional diversity of the lunar surface; (2) Understanding the formation of the ancient lunar primary crust; (3) Understanding the diversity and timing of mantle melting, and secondary crust formation; (4) Comparing KREEPy lunar meteorites to KREEPy Apollo samples as evidence of variability within the PKT; and (5) A better understanding of the South Pole Aitken Basin through lunar meteorites whose provenance are within that Terrane.

Zeigler, R. A.↗

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Engineering↗

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

Deepak, A.↗

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗

Operator Relaxation and the Optimal Depth of Classical Shadows

Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via “shallow shadows,” a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. Here we show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing (“twirling”) circuit—namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t~log⁡(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗