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At least 775 records · Page 43

Model's sparse representation based on reduced mixed GMsFE basis methods

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. A typical application for the elliptic PDEs is the flow in heterogeneous random porous media. Mixed generalized multiscale finite element method (GMsFEM) is one of the accurate and efficient approaches to solve the flow problem in a coarse grid and obtain the velocity with local mass conservation. When the inputs of the PDEs are parameterized by the random variables, the GMsFE basis functions usually depend on the random parameters. This leads to a large number degree of freedoms for the mixed GMsFEM and substantially impacts on the computation efficiency. In order to overcome the difficulty, we develop reduced mixed GMsFE basis methods such that the multiscale basis functions are independent of the random parameters and span a low-dimensional space. To this end, a greedy algorithm is used to find a set of optimal samples from a training set scattered in the parameter space. Reduced mixed GMsFE basis functions are constructed based on the optimal samples using two optimal sampling strategies: basis-oriented cross-validation and proper orthogonal decomposition. Although the dimension of the space spanned by the reduced mixed GMsFE basis functions is much smaller than the dimension of the original full order model, the online computation still depends on the number of coarse degree of freedoms. To significantly improve the online computation, we integrate the reduced mixed GMsFE basis methods with sparse tensor approximation and obtain a sparse representation for the model's outputs. The sparse representation is very efficient for evaluating the model's outputs for many instances of parameters. To illustrate the efficacy of the proposed methods, we present a few numerical examples for elliptic PDEs with multiscale and random inputs. In particular, a two-phase flow model in random porous media is simulated by the proposed sparse representation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Carbon Monitoring System Flux Estimation and Attribution: Impact of ACOS-GOSAT X(CO2) Sampling on the Inference of Terrestrial Biospheric Sources and Sinks

Using an Observing System Simulation Experiment (OSSE), we investigate the impact of JAXA Greenhouse gases Observing SATellite 'IBUKI' (GOSAT) sampling on the estimation of terrestrial biospheric flux with the NASA Carbon Monitoring System Flux (CMS-Flux) estimation and attribution strategy. The simulated observations in the OSSE use the actual column carbon dioxide (X(CO2)) b2.9 retrieval sensitivity and quality control for the year 2010 processed through the Atmospheric CO2 Observations from Space algorithm. CMS-Flux is a variational inversion system that uses the GEOS-Chem forward and adjoint model forced by a suite of observationally constrained fluxes from ocean, land and anthropogenic models. We investigate the impact of GOSAT sampling on flux estimation in two aspects: 1) random error uncertainty reduction and 2) the global and regional bias in posterior flux resulted from the spatiotemporally biased GOSAT sampling. Based on Monte Carlo calculations, we find that global average flux uncertainty reduction ranges from 25% in September to 60% in July. When aggregated to the 11 land regions designated by the phase 3 of the Atmospheric Tracer Transport Model Intercomparison Project, the annual mean uncertainty reduction ranges from 10% over North American boreal to 38% over South American temperate, which is driven by observational coverage and the magnitude of prior flux uncertainty. The uncertainty reduction over the South American tropical region is 30%, even with sparse observation coverage. We show that this reduction results from the large prior flux uncertainty and the impact of non-local observations. Given the assumed prior error statistics, the degree of freedom for signal is approx.1132 for 1-yr of the 74 055 GOSAT X(CO2) observations, which indicates that GOSAT provides approx.1132 independent pieces of information about surface fluxes. We quantify the impact of GOSAT's spatiotemporally sampling on the posterior flux, and find that a 0.7 gigatons of carbon bias in the global annual posterior flux resulted from the seasonally and diurnally biased sampling when using a diagonal prior flux error covariance.

biased sampling↗

Effective pair potential for random fcc CoCrFeMnNi alloys

The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C 12 - C 44 , which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.

Materials Science↗

Sampling Errors in Monthly Rainfall Totals for TRMM and SSM/I, Based on Statistics of Retrieved Rain Rates and Simple Models

Estimates from TRMM satellite data of monthly total rainfall over an area are subject to substantial sampling errors due to the limited number of visits to the area by the satellite during the month. Quantitative comparisons of TRMM averages with data collected by other satellites and by ground-based systems require some estimate of the size of this sampling error. A method of estimating this sampling error based on the actual statistics of the TRMM observations and on some modeling work has been developed. "Sampling error" in TRMM monthly averages is defined here relative to the monthly total a hypothetical satellite permanently stationed above the area would have reported. "Sampling error" therefore includes contributions from the random and systematic errors introduced by the satellite remote sensing system. As part of our long-term goal of providing error estimates for each grid point accessible to the TRMM instruments, sampling error estimates for TRMM based on rain retrievals from TRMM microwave (TMI) data are compared for different times of the year and different oceanic areas (to minimize changes in the statistics due to algorithmic differences over land and ocean). Changes in sampling error estimates due to changes in rain statistics due 1) to evolution of the official algorithms used to process the data, and 2) differences from other remote sensing systems such as the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I), are analyzed.

Bell, Thomas L.↗

Efficient Probabilistic Prediction and Uncertainty Quantification of Tropical Cyclone–Driven Storm Tides and Inundation

Abstract This study proposes and assesses a methodology to obtain high-quality probabilistic predictions and uncertainty information of near-landfall tropical cyclone–driven (TC-driven) storm tide and inundation with limited time and resources. Forecasts of TC track, intensity, and size are perturbed according to quasi-random Korobov sequences of historical forecast errors with assumed Gaussian and uniform statistical distributions. These perturbations are run in an ensemble of hydrodynamic storm tide model simulations. The resulting set of maximum water surface elevations are dimensionality reduced using Karhunen–Loève expansions and then used as a training set to develop a polynomial chaos (PC) surrogate model from which global sensitivities and probabilistic predictions can be extracted. The maximum water surface elevation is extrapolated over dry points incorporating energy head loss with distance to properly train the surrogate for predicting inundation. We find that the surrogate constructed with third-order PCs using elastic net penalized regression with leave-one-out cross validation provides the most robust fit across training and test sets. Probabilistic predictions of maximum water surface elevation and inundation area by the surrogate model at 48-h lead time for three past U.S. landfalling hurricanes (Irma in 2017, Florence in 2018, and Laura in 2020) are found to be reliable when compared to best track hindcast simulation results, even when trained with as few as 19 samples. The maximum water surface elevation is most sensitive to perpendicular track-offset errors for all three storms. Laura is also highly sensitive to storm size and has the least reliable prediction. Significance Statement The purpose of this study is to develop and evaluate a methodology that can be used to provide high-quality probabilistic predictions of hurricane-induced storm tide and inundation with limited time and resources. This is important for emergency management purposes during or after the landfall of hurricanes. Our results show that sampling forecast errors using quasi-random sequences combined with machine learning techniques that fit polynomial functions to the data are well suited to this task. The polynomial functions also have the benefit of producing exact sensitivity indices of storm tide and inundation to the forecasted hurricane properties such as path, intensity, and size, which can be used for uncertainty estimation. The code implementing the presented methodology is publicly available on GitHub.

54 ENVIRONMENTAL SCIENCES↗

Generating log-normal mock catalog of galaxies in redshift space

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear bias relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.

79 ASTRONOMY AND ASTROPHYSICS↗

A Numerical Theory for Impedance Education in Three-Dimensional Normal Incidence Tubes

A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance.

Watson, Willie R.↗

Disk Density Tuning of a Maximal Random Packing

We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations.

97 MATHEMATICS AND COMPUTING↗

Detector Calibration to Quantify Random Summing in HPGe Spectroscopy

While calibrating a High Purity Germanium (HPGe) Radiation Detector for Xenon-133 (133Xe) the process of random summing occurs which leads to excess counts in the 160.6keV peak from random summing of the 81keV photons at the 162keV energy. Multiple samples of 133Xe with varying levels of radioactivity were assayed to determine a relationship between the occurrence of random summing and the net area of the 160.6keV peak. When the calculated efficiencies in the 160.6keV peak were compared to the theoretical efficiency obtained from a multi-energy calibration at 160.6keV, the amount of random summing could be estimated as excess observed efficiency and correlated to the sample activity. While a trend is apparent in the data, the mechanisms that contribute to the trend are still being studied so the data can be accurately correlated.

07 ISOTOPE AND RADIATION SOURCES↗

Observational needs for estimating Alaskan soil carbon stocks under current and future climate

Abstract Representing land surface spatial heterogeneity when designing observation networks is a critical scientific challenge. Here we present a geospatial approach that utilizes the multivariate spatial heterogeneity of soil‐forming factors—namely, climate, topography, land cover types, and surficial geology—to identify observation sites to improve soil organic carbon (SOC) stock estimates across the State of Alaska, USA. Standard deviations in existing SOC samples indicated that 657, 870, and 906 randomly distributed pedons would be required to quantify the average SOC stocks for 0–1 m, 0–2 m, and whole‐profile depths, respectively, at a confidence interval of 5 kg C m −2 . Using the spatial correlation range of existing SOC samples, we identified that 309, 446, and 484 new observation sites are needed to estimate current SOC stocks to 1 m, 2 m, and whole‐profile depths, respectively. We also investigated whether the identified sites might change under future climate by using eight decadal (2020–2099) projections of precipitation, temperature, and length of growing season for three representative concentration pathway (RCP 4.5, 6.0, and 8.5) scenarios of the Intergovernmental Panel on Climate Change. These analyses determined that 12 to 41 additional sites (906 + 12 to 41; depending upon the emission scenarios) would be needed to capture the impact of future climate on Alaskan whole‐profile SOC stocks by 2100. The identified observation sites represent spatially distributed locations across Alaska that captures the multivariate heterogeneity of soil‐forming factors under current and future climatic conditions. This information is needed for designing monitoring networks and benchmarking of Earth system model results.

54 ENVIRONMENTAL SCIENCES↗

Improving the accuracy of freight mode choice models: A case study using the 2017 CFS PUF data set and ensemble learning techniques

Here, the US Census Bureau has collected two rounds of experimental data from the Commodity Flow Survey, providing shipment-level characteristics of nationwide commodity movements, published in 2012 (i.e., Public Use Microdata) and in 2017 (i.e., Public Use File). With this information, data-driven methods have become increasingly valuable for understanding detailed patterns in freight logistics. In this study, we used the 2017 Commodity Flow Survey Public Use File data set to explore building a high-performance freight mode choice model, considering three main improvements: (1) constructing local models for each separate commodity/industry category; (2) extracting useful geographical features, particularly the derived distance of each freight mode between origin/destination zones; and (3) applying additional ensemble learning methods such as stacking or voting to combine results from local and unified models for improved performance. The proposed method achieved over 92% accuracy without incorporating external information, an over 19% increase compared to directly fitting Random Forests models over 10,000 samples. Furthermore, SHAP (Shapely Additive Explanations) values were computed to explain the outputs and major patterns obtained from the proposed model. The model framework could enhance the performance and interpretability of existing freight mode choice models.

42 ENGINEERING↗

Understanding the bias introduced in quantum dot blinking using change point analysis

Quantum dots are semiconductor crystals that are less than 100 nanometers in size; that is, between 1 billionth and 100 billionths of a meter. They can be composed of one semiconductor material or a core of one semiconductor surrounded by a shell of another. The quantum dots studied in this work consisted of a cadmium selenide core surrounded by a cadmium sulfide shell. When a quantum dot is illuminated with light, some of it can be absorbed and excites the quantum dot to a higher energy state. To relax back down to its resting state, light can be emitted in the form of fluorescence. The nature of the fluorescence that is emitted from a single quantum dot differs from that which is emitted from a bulk sample (usually a solid film or a solution of quantum dots). While in bulk samples the fluorescence over time fluctuates randomly about some average, maintaining a continuous average intensity, single quantum dot fluorescence switches between two or more intensities. This phenomenon is referred to as quantum dot blinking, and its origin is of significant relevance to solar cell, light emitting diode and biological tracking applications. Quantum dot blinking can be studied by exciting an isolated quantum dot with light and recording the ensuing fluorescence using sensitive detectors. This is done over many minutes, resulting in a fluorescence intensity (in counts per second) versus time trajectory. These trajectories must be further analyzed in order to understand the nature of the blinking behavior. Conventionally, a bin and threshold analysis is used, whereby the arrival times of fluorescent photons are binned to reduce the signal noise, and a threshold is used to separate the trajectory into periods of high and low fluorescence. In this study, the effects of bin size and threshold on the blinking kinetics were investigated, and the assumption that there is only one bright and one dark state was tested. To do so, a statistically rigorous method called change point analysis was needed which does not require binning and which can determine the number of intensity levels present. Blinking in 17 quantum dots was studied using both analysis methods. The primary parameter that was compared between the two methods is called a truncation time. Increasing the bin size was found to generally lead to a larger truncation time while increasing the threshold always decreased the truncation time. Using the change point analysis method, 12 out of 17 quantum dots were found to exhibit more than two intensity levels. Lastly, the assumption that only two intensity levels exist was found to significantly affect the blinking statistics: when individual levels were combined into one bright level, the truncation time would increase. The change point analysis method was found to be more suitable for studying multilevel blinking in quantum dots than the conventional bin and threshold method, since the effects of binning and thresholding can be alleviated and the two-level assumption relaxed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum algorithm to simulate Lindblad master equations

We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest. Published by the American Physical Society 2025

Borras, Evan (ORCID:000900017709037X)↗

Uncertainty Quantification in Scientific ML

The intricate interactions between data sampling, model selection and the inherent randomness in complex systems strongly emphasize the need for a rigorous characterization of ML algorithms. In conventional statistics, uncertainty quantification (UQ) provides this characterization by measuring how accurately a model reflects the physical reality and by studying the impact of different error sources on the prediction.

97 MATHEMATICS AND COMPUTING↗

(U) Correlated Sampling Using Batch Statistics to Reduce the Uncertainty of Combinations of KSEN Outputs with MCNP6

The relative sensitivity of k eff to the densities of nuclides in a material are combined to compute relative sensitivities to other inputs. When computed in a single Monte Carlo run, the nuclide density sensitivities are correlated, and the statistical uncertainties propagated to other inputs will be incorrect unless those correlations are accounted for. Equations are presented to apply correlated sampling using batch statistics for the sum of an arbitrary number of random tallies and the difference of two random tallies when each is multiplied by a different constant. When correlated sampling is used on a recent benchmark evaluation, the correct statistical uncertainties for certain combinations of sensitivities are dramatically smaller than the incorrect uncertainties. A user-controlled, regular output of MCNP6’s KSEN sensitivities that allows batch statistics to be applied to combinations would be extremely valuable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Preliminary stratigraphy of the Apollo 15 drill core

The crew of Apollo 15 collected a 242-cm-long core of the regolith developed on the surface of Palus Putredinus (3 deg 39 min 20 sec E, 26 deg 26 min 00 sec N). This core consists of 42 major textural units, which range from a few millimeters to 13 cm thick. The regolith at this site was deposited layer by layer, each layer having been reworked, to some degree, by micrometeorite bombardment. The particle composition of six layers for which samples were obtained varies in a random fashion, thus supporting the heterogeneous, layered model of the regolith. The ratio of lithic fragments derived from the Apennine Front to that derived from the mare surface is about 1:1. This lithic ratio, in a regolith section 3.75 km from the base of the front, is an indication of the efficiency of lateral transport of soil by impact processes and mass wasting.

Heiken, G.↗