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DOE OSTI2022

Statistical analysis on random quantum circuit sampling by Sycamore and Zuchongzhi quantum processors

Random quantum circuit sampling, a task to sample bit strings from a random quantum circuit, is considered a suitable benchmark task to demonstrate the outperformance of quantum computers even with noisy qubits. Recently, random quantum circuit sampling was performed on the Sycamore quantum processor with 53 qubits [Nature (London) 574, 505 (2019)] and on the Zuchongzhi quantum processor with 56 qubits [Phys. Rev. Lett. 127, 180501 (2021)]. Here, we analyze and compare the statistical properties of the outputs of the random quantum circuit sampling by the Sycamore and Zuchongzhi processors. Using the Marchenko-Pastur law of random matrices of bit strings and the Wasssertein distances between bit strings, we find that the statistical properties of Sycamore bit strings are quite different from those of Zuchongzhi bit strings, while both processors score similar values of linear cross-entropy fidelity for random circuit sampling. Some bit strings sampled by the Zuchongzhi processor pass the NIST random number tests while both Sycamore and Zuchongzhi processors show similar patterns in the heat maps of bit strings. Zuchongzhi bit strings are much closer to classical uniform random bits than those of Sycamore. It is shown that the statistical properties of bit strings of both random quantum circuits change little as the depth of the random quantum circuits increases. Our findings raise a question about the computational reliability of noisy quantum processors because two quantum processors with similar noise levels and similar qubit structures produced statistically different outputs for the same random quantum circuit sampling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗

DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

DOE OSTI2025

Dark Energy Survey Year 3 Results: Cosmological constraints from second- and third-order shear statistics

Here, we present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ξ ± with the mass aperture skewness statistic ⟨ M ap 3 ⟩ , which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ξ ± and ⟨ M ap 3 ⟩ measured from DES Y3 data with a Λ CDM model, we find S 8 = 0.780 ± 0.015 and Ω m = 0.26 6 - 0.040 + 0.039 , yielding 111% of figure-of-merit improvement in the Ω m - S 8 plane relative to ξ ± alone, consistent with expectations from simulated likelihood analyses. With a w CDM model, we find S 8 = 0.74 9 - 0.026 + 0.027 and w 0 = - 1.39 ± 0.31 , which gives an improvement of 22% on the joint S 8 - w 0 constraint. Our results are consistent with w 0 = - 1 . Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of ⟨ M ap 3 ⟩ the existing tension between the datasets is at the level of 2.3 σ . We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish ⟨ M ap 3 ⟩ as a practical observable for joint analyses in current and future surveys.

Gomes, R. C. H. [University of Pennsylvania] (ORCI↗

DOE OSTI2020

Convective Transition Statistics over Tropical Oceans for Climate Model Diagnostics: GCM Evaluation

To assess deep convective parameterizations in a variety of GCMs and examine the fast-time-scale convective transition, a set of statistics characterizing the pickup of precipitation as a function of column water vapor (CWV), PDFs and joint PDFs of CWV and precipitation, and the dependence of the moisture–precipitation relation on tropospheric temperature is evaluated using the hourly output of two versions of the GFDL Atmospheric Model, version 4 (AM4), NCAR CAM5 and superparameterized CAM (SPCAM). The 6-hourly output from the MJO Task Force (MJOTF)/GEWEX Atmospheric System Study (GASS) project is also analyzed. Contrasting statistics produced from individual models that primarily differ in representations of moist convection suggest that convective transition statistics can substantially distinguish differences in convective representation and its interaction with the large-scale flow, while models that differ only in spatial–temporal resolution, microphysics, or ocean–atmosphere coupling result in similar statistics. Most of the models simulate some version of the observed sharp increase in precipitation as CWV exceeds a critical value, as well as that convective onset occurs at higher CWV but at lower column RH as temperature increases. While some models quantitatively capture these observed features and associated probability distributions, considerable intermodel spread and departures from observations in various aspects of the precipitation–CWV relationship are noted. For instance, in many of the models, the transition from the low-CWV, nonprecipitating regime to the moist regime for CWV around and above critical is less abrupt than in observations. Additionally, some models overproduce drizzle at low CWV, and some require CWV higher than observed for strong precipitation. For many of the models, it is particularly challenging to simulate the probability distributions of CWV at high temperature.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Essential Statistical Concepts

Statistical methods are an essential element to making quality measurements, allowing the organization and interrogation of data in a structured way. This introductory chapter describes key concepts of measurement statistics that are used in many nondestructive assay (NDA) methods and is intended as a primer to the reading list provided in the reference section. (Croft and Burr 2016; Smith 1991; Smith 2013; Taylor 1997; Triola 2017). The textbooks by Triola on elementary statistics (Figure 1), Taylor, and Smith (2013) introduce uncertainty analysis in the physical sciences. Smith (1991) provides a rigorous introduction with examples to correlated variables. These texts collectively offer an excellent foundation for understanding essential statistical concepts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Validation of LOCA2 and STAR-ESDM Statistically Downscaled Products

The National Climate Assessment (NCA) is the preeminent national report examining current and future risks posed by climate change. Countless agencies, policymakers, stakeholders and other end-users rely upon guidance from the NCA to plan for an uncertain future. These groups all depend on modern curated data, provided alongside the NCA, to quantify the impact of climate change on metrics of relevance for their decision processes. In its fifth iteration (NCA5), two statistically downscaled ensemble products, each providing data at grid spacing of approximately 5km over the contiguous United States, were selected to accompany the report. These include LOCalized Analogs version 2 (LOCA2) and Seasonal Trends and Analysis of Residuals Empirical-Statistical Downscaling Model (STAR-ESDM). Both data products are produced through a process known as statistical downscaling, where relatively coarse Global Climate Model (GCM) data is refined to locally relevant scales through the application of scientifically-supported empirical and algorithmic relationships. In support of the NCA effort, this report provides an independent validation of these two products against historical observations, with a focus on precipitation and near-surface temperature variables. Based on the results of this validation, several recommendations are provided related to the use of these data products. The structure of this report is as follows: In section 2, we review three gridded observational products that are used as part of our intercomparison. In section 3, we describe the two statistical downscaling techniques and their corresponding datasets that are the focus of this study. In section 4, the methodology we employ for validation is described. Section 5 provides results of the validation, which in turn motivate our recommendations on the use of these data products. A brief summary is provided in section 6.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

(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↗

DOE OSTI2022

Toward Accurate Modeling of Galaxy Clustering on Small Scales: Constraining the Galaxy-halo Connection with Optimal Statistics

Applying halo models to analyze the small-scale clustering of galaxies is a proven method for characterizing the connection between galaxies and their host halos. Such works are often plagued by systematic errors or limited to clustering statistics that can be predicted analytically. In this work, we employ a numerical mock-based modeling procedure to examine the clustering of Sloan Digital Sky Survey DR7 galaxies. We apply a standard halo occupation distribution (HOD) model to dark matter only simulations with a ΛCDM cosmology. To constrain the theoreStical models, we utilize a combination of galaxy number density and selected scales of the projected correlation function, redshift-space correlation function, group multiplicity function, average group velocity dispersion, mark correlation function, and counts-in-cells statistics. We design an algorithm to choose an optimal combination of measurements that yields tight and accurate constraints on our model parameters. Compared to previous work using fewer clustering statistics, we find a significant improvement in the constraints on all parameters of our halo model for two different luminosity-threshold galaxy samples. Most interestingly, we obtain unprecedented high-precision constraints on the scatter in the relationship between galaxy luminosity and halo mass. However, our best-fit model results in significant tension (>4σ) for both samples, indicating the need to add second-order features to the standard HOD model. To guarantee the robustness of these results, we perform an extensive analysis of the systematic and statistical errors in our modeling procedure, including a first of its kind study of the sensitivity of our constraints to changes in the halo mass function due to baryonic physics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Utilizing Advanced Statistics to Determine Anomalistic Conditions in Pebble-Bed Reactors

Pebble-bed reactors (PBRs) utilize hundreds of thousands of fuel pebbles, which continuously circulate through the core, in lieu of traditional fuel assemblies to generate fissions and produce power. The use of unmarked fuel pebbles presents a challenge for international safeguards verification that nuclear material is not being diverted. To ensure pebble diversion is not taking place, new methods for accounting for and monitoring the pebbles should be examined to determine an appropriate methodology for performing bulk accountancy with pebbles. Here, this work examines the use of statistical methods for determining if the reactor is within a declared range of operation by examining the statistical distribution of pebble burnup as they are discharged from the core. Using this methodology, we created a model that detects diversion over 95% of the time, over multiple diversion pathways, if the reactor core maintains a constant power density during the diversion process and only falsely labels a diversion case nominal 2% of the time. For a diversion scenario where the reactor is maintained at a constant power, the statistical analysis can correctly identify if diversion is occurring over 80% of the time; however, nearly 20% of specific diversion pathways are mislabeled nominal. These results provide a basis and framework for exploring the further use of statistical methods to determine where these methods could be most useful and where additional methods, such as machine learning, could be used to capture if diversion is occurring in pebble-bed reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Persona of Transition Metal Ions in Solids: A Statistical Learning on Local Structures of Transition Metal Oxides

Abstract The local structure of a transition metal (TM) ion is a function of cation elements and valence states. More than that, in this work, by employing a trove of first‐principles data of TM oxides, the local structures of TM cations are statistically analyzed to extract detailed information about cation site preference, bond length, site structural distortion, and cation magnetization. It is found that cation radius alone poorly describes the local structure of a transition metal oxide, while the statistics of coordination number as well as the TMO bond length distribution, especially that of the 3d TMs, can provide comprehensive knowledge for understanding the behavior of TM elements. Based on these statistics, the interplay of site distortion due to the Jahn–Teller effect, cation site similarity, and a new set of ionic radii are all obtained to chart the “persona” of transition metal ions in solids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Statistical analysis of the performance and long-term stability of unquenched LSC standards ( 3 H, 14 C) used for radiochemical measurements

Multiple sets of toluene-based unquenched standards, procured over the last 3 decades, were analyzed to determine their stability over time. A statistical analysis was performed to provide insight into the variability for tSIE and counting efficiency measurements of 3 H and 14 C isotopes. Our data suggests that standards remain viable even 30 years after the manufacturer’s recommended expiration date. Overall, these standards have shown no statistically significant sign of performance degradation. We have proven through statistical analysis that these standards can provide comparable performance over time well past their manufactured expiration date.

LSC standards↗

DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Understanding the fusion yield dependencies in OMEGA DT-layered implosion experiments using a physics-based statistical mapping model

Improving the performance of inertial confinement fusion implosions requires physics models that can accurately predict the response to changes in the experimental inputs. Good predictive capability has been demonstrated for the fusion yield using a statistical mapping of simulated outcomes to experimental data [Gopalaswamy et al., Nature 565(771), 581–586 (2019)]. In this paper, a physics-based statistical mapping approach is used to extract and quantify all the major sources of degradation of fusion yield for direct-drive implosions on the OMEGA laser. Here, the yield is found to be dependent on the age of the deuterium tritium fill, the ℓ = 1 asymmetry in the implosion core, the laser beam-to-target size ratio, and parameters related to the hydrodynamic stability. A controlled set of experiments were carried out where only the target fill age was varied while keeping all other parameters constant. The measurements were found to be in excellent agreement with the fill age dependency inferred using the mapping model. In addition, a new implosion design was created, guided by the statistical mapping model by optimizing the trade-offs between increased laser energy coupling at larger target size and the degradations caused by the laser beam-to-target size ratio and hydrodynamic instabilities. When experimentally performed, an increased fusion yield was demonstrated in targets with larger diameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Quantification of spatial and seasonal trends in the atmosphere and construction of statistical models for infrasonic propagation

SUMMARY Infrasonic waves are influenced by variations in the density, pressure and temperature as well as the ambient winds. Modelling infrasonic propagation can be challenging due to the dynamic nature of the atmosphere as well as the sparseness of measurements which result in variability and notable uncertainty. A framework is presented to quantify spatial and seasonal trends in atmospheric structure via analysis of the effective sound speed profile and identification of temporal trends in the middle atmospheric waveguide produced by the circumpolar vortex winds. Seasonal definitions identifying typical atmospheric structures during the summer, winter and spring/fall transition periods are identified using atmospheric data from 2010 through 2020. Seasonal trend analysis is conducted for a number of locations across the contiguous United States to quantify spatial variations in atmospheric structure that impact infrasonic propagation. For each season and location, empirical orthogonal function analysis is used to reduce the historical archive of atmospheric data into a smaller representative set that can be analysed using numerical tools more efficiently. Infrasonic ray tracing and finite-frequency modal propagation analyses are applied to construct propagation path geometry and transmission loss statistics which are useful in localization and yield estimation for infrasonic sources, respectively. An example application is detailed in which transmission loss statistics are combined with an explosive source model and noise statistics to quantify the capability of a network to detect nearby sources.

58 GEOSCIENCES↗

DOE OSTI2021

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

In this paper, we report on a study of the spectral features associated with dipole resonances in medium mass nuclei (E ≤ 12 MeV), as revealed in the framework of the spd-interacting boson model. The effect of pairing correlations on the theory follows from solutions obtained through an application of the Bethe Ansatz Equation. In general, calculated spectra around the critical point of the vibrational to γ-soft transitions appears to approach that of a Gaussian Orthogonal Ensemble, while near the rotational and vibrational limits of the theory the spectra show more regular behavior. Specifically, the results reveal that the statistical features of the spectra are sensitive to the vector boson pairing strength, c p , in the transition region; that is, when c p is zero, or when the system approaches one of its dynamical symmetries limits the spectrum display regular features, while for stronger c p values, or when near to the critical phase transition region, the spectral feature show more chaotic behavior. Overall, our results indicate that the statistical features are governed by the interplay between dipole resonant energies, pairing correlations, and interactions between and among the single and vector bosons modes of the theory. As part of this work we also found out that chaoticity occurs when results were fit to a Berry-Robnik distribution. Throughout our analyses, we used experimentally known information about both positive and negative parity states. Our findings suggest that dipole resonances appear to be best-described by Poisson statistics for A ≈ 32-138 nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Statistical generic design of glass and optimization: Selective review on oxide glasses

Designing a single glass composition for a multidimensional property space is challenging, and the difficulty increases with the number of design criteria. Traditionally, the task is accomplished using multiple statistical models that describe the relationships between composition (C) and property (P) values, i.e., C-P models. Recently, the structure (S)-property (P) statistical modeling has emerged as a complementary approach. The S-P modeling approach has also been shown to be a preferred method for modeling glass properties, particularly when a small data set is available, such as in single-component studies, or when strong nonlinearities exist between composition and properties. The combined model package, C-S-P, implements the concept of generic glass design, i.e., designing glass for performance by first selecting a specific or optimized set of glass network structural groups using S-P models and then transferring the designed structures (genes) to a particular composition using C-S models. This article reviews a set of supporting cases from the previous C-S-P modeling studies of phosphate, silicate, and borosilicate glasses, which are relevant for many critical commercial applications. The methodology for developing the statistical C-S-P database is presented, enabling the application of P?S?C to achieve a generic glass design and optimization, targeting multiple design criteria for both performance and processing properties simultaneously.

Network structure↗

DOE OSTI2024

Rapid measurement of soluble xylo-oligomers using near-infrared spectroscopy (NIRS) and multivariate statistics: calibration model development and practical approaches to model optimization

Rapid monitoring of biomass conversion processes using techniques such as near-infrared (NIR) spectroscopy can be substantially quicker and less labor-, resource-, and energy-intensive than conventional measurement techniques such as gas or liquid chromatography (GC or LC) due to the lack of solvents and preparation methods, as well as removing the need to transfer samples to an external lab for analytical evaluation. The purpose of this study was to determine the feasibility of rapid monitoring of a biomass conversion process using NIR spectroscopy combined with multivariate statistical modeling, and to examine the impact of (1) subsetting the samples in the original dataset by process location and (2) reducing the spectral range used in the calibration model on model performance. We develop multivariate calibration models for the concentrations of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids at multiple points in a biomass conversion process which produces and then purifies XOS compounds from sugar cane bagasse. A single model using samples from multiple locations in the process stream showed acceptable performance as measured by standard statistical measures. However, compared to the single model, we show that separate models built by segregating the calibration samples according to process location show improved performance. We also show that combining an understanding of the sample spectra with simple multivariate analysis tools can result in a calibration model with a substantially smaller spectral range that provides essentially equal performance to the full-range model. We demonstrate that real-time monitoring of soluble xylo-oligosaccharides (XOS), monomeric xylose, and total solids concentration at multiple points in a process stream using NIR spectroscopy coupled with multivariate statistics is feasible. Segregation of sample populations by process location improves model performance. Models using a reduced spectral range containing the most relevant spectral signatures show very similar performance to the full-range model, reinforcing the importance of performing robust exploratory data analysis before beginning multivariate modeling.

09 BIOMASS FUELS↗