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DOE OSTI2021

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Abstract Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics‐based justification and have achieved promising performance. Two versions use LVs in Cartesian (LV‐Car) space and hyperspherical (LV‐sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed‐variable GP models, from which we conclude that the LV‐sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank‐based perspective like in the theorem, we propose a new alternative model named LV‐mix that combines the LV‐based correlation structures from both LV‐Car and LV‐sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV‐mix achieves higher average accuracy compared with the existing two.

Tao, Siyu↗

DOE OSTI2024

e RPCA : Robust Principal Component Analysis for Exponential Family Distributions

Abstract Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient decomposition, under either its natural or canonical parametrization. The effectiveness of is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area.

Zheng, Xiaojun↗

DOE OSTI2025

Gaussian integral method for void fraction

Here, a novel method, the Gaussian Integral Method (GIM), is presented for calculating void fractions in Computational Fluid Dynamics–Discrete Element Method (CFD-DEM) simulations. GIM is versatile and applicable to various grid types, including structured and unstructured polyhedral meshes, without requiring special boundary treatments. An optimization technique is introduced to make GIM independent of grid resolution and type. The method is validated against experimental data from a fluidized bed, demonstrating that GIM produces realistic simulations closely resembling experimental observations. Additionally, unstructured polyhedral grids using GIM outperform structured grids of equivalent resolution, yielding results more aligned with experimental data. The gradient of the void fraction is computed in the CFD solver and utilized in the DEM solver for precise estimation at particle locations. Overall, GIM provides an effective solution for void fraction calculations in particulate media simulations with complex geometries, enhancing the accuracy and applicability of CFD-DEM simulations for industrial processes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

On‐site surrogates for large‐scale calibration

Abstract Motivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on‐site design and surrogate modeling for a computer simulator acting on a high‐dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data‐faithful modeling and computational tractability in a calibration framework—tailoring the computer model to a limited field experiment. Situating our on‐site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example.

Huang, Jiangeng↗

DOE OSTI2016

Oxide-cladding aluminum nitride photonic crystal slab: Design and investigation of material dispersion and fabrication induced disorder

Photonic crystal slabs with a lower-index material surrounding the core layer are an attractive choice to circumvent the drawbacks in the fabrication of membranes suspended in air. In this work we propose a photonic crystal (PhC) slab structure composed of a triangular pattern of air holes in a multilayer thin film of aluminum nitride embedded in silicon dioxide layers designed for operating around 450 nm wavelengths. We show the design of an ideal structure and analyze the effects of material dispersion based on a first-order correction perturbation theory approach using dielectric functions obtained by experimental measurements of the thin film materials. Numerical methods were used to investigate the effects of fabrication induced disorder of typical nanofabrication processes on the bandgap size and spectral response of the proposed device. Deviation in holes radii and positions were introduced in the proposed PhC slab model with a Gaussian distribution profile. Impacts of slope in holes sidewalls that might result from the dry etching of AlN were also evaluated. The results show that for operation at the midgap frequency, slope in holes sidewalls is more critical than displacements in holes sizes and positions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Automated single-ion peak fitting as an efficient approach for analyzing complex chromatographic data

Chromatography provides important detail on the composition of environmental samples and their chemical processing. However, the complexity of these samples and their tendency to contain many structurally and chemically similar compounds frequently results in convoluted or poorly resolved data. Data reduction from raw chromatograms of complex environmental data into integrated peak areas consequently often requires substantial operator interaction. This difficulty has led to a bottleneck in analysis that increases analysis time, decreases data quality, and will worsen as advances in field-based instrumentation multiply the quantity and informational density of data produced. In this work, we develop and validate an automated approach to fitting chromatographic data within a target retention time window with a combination of multiple idealized peaks (Gaussian peaks either with or without an exponential decay component). Herein we compare this single-ion peak fitting approach to drawn baseline integration methods of more than 70,000 peaks collected by field-based chromatographs spanning across a wide range of volatilities and functionalities. Accuracy of peak fitting under real-world conditions is found to be within 10%. The quantitative parameters describing the fit (e.g. coefficients, fit residuals, etc.) are found to provide valuable information to increase the efficiency of quality control and provide constraints to accurately integrate peaks that are significantly convoluted with neighboring peaks. Implementation of the peak fitting method is shown to yield accurate integration of peaks otherwise too poorly resolved to separate into individual compounds and improved quantitative metrics to determine the fidelity of the data reduction process, while substantially decreasing the time spent by operators on data reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Automated Bayesian high-throughput estimation of plasma temperature and density from emission spectroscopy

Here, this paper introduces a novel approach for automated high-throughput estimation of plasma temperature and density using atomic emission spectroscopy, integrating Bayesian inference with sophisticated physical models. We provide an in-depth examination of Bayesian methods applied to the complexities of plasma diagnostics, supported by a robust framework of physical and measurement models. Our methodology is demonstrated using experimental observations in the field of magneto-inertial fusion, focusing on individual and sequential shot analyses of the Plasma Liner Experiment at LANL. The results demonstrate the effectiveness of our approach in enhancing the accuracy and reliability of plasma parameter estimation and in using the analysis to reveal the deep hidden structure in the data. This study not only offers a new perspective of plasma analysis but also paves the way for further research and applications in nuclear instrumentation and related domains.

Bayesian inference↗

DOE OSTI2023

Improving resolution and resolvability of single-particle cryoEM structures using Gaussian mixture models

Cryogenic electron microscopy is widely used in structural biology, but its resolution is often limited by the dynamics of the macromolecule. Here, we developed a refinement protocol based on Gaussian mixture models that integrates particle orientation and conformation estimation, and improves the alignment for flexible domains of protein structures. We demonstrated this protocol on multiple datasets, resulting in improved resolution and resolvability, locally and globally, by visual and quantitative measures.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A Reanalysis of Public Galactic Bulge Gravitational Microlensing Events from OGLE-III and -IV

Abstract Modern surveys of gravitational microlensing events have progressed to detecting thousands per year, and surveys are capable of probing Galactic structure, stellar evolution, lens populations, black hole physics, and the nature of dark matter. One of the key avenues for doing this is the microlensing Einstein radius crossing time (t E) distribution. However, systematics in individual light curves as well as oversimplistic modeling can lead to biased results. To address this, we developed a model to simultaneously handle the microlensing parallax due to Earth's motion, systematic instrumental effects, and unlensed stellar variability with a Gaussian process model. We used light curves for nearly 10,000 OGLE-III and -IV Milky Way bulge microlensing events and fit each with our model. We also developed a forward model approach to infer the t E distribution by forward modeling from the data rather than using point estimates from individual events. We find that modeling the variability in the baseline removes a source of significant bias in individual events, and the previous analyses overestimated the number of t E > 100 day events due to their oversimplistic model ignoring parallax effects. We use our fits to identify the hundreds filling a regime in the microlensing parameter space that are 50% pure of black holes. Finally, we have released the largest-ever catalog of Markov Chain Monte Carlo parameter estimates for microlensing events.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Development and Modeling of a Novel Self-Assembly Process for Polymer and Polymeric Composite Nanoparticles

Extensive computational simulations and experiments have been used to investigate the structure, dynamics and resulting photophysical properties of a number para-phenylenevinylene (PPV) based polymers and oligomers. These studies have shown how the morphology and structure are controlled to a large extent by the nature of the solute-solvent interactions in the initial solution phase preparation. A good solvent such as dichloromethane generates non-compact structures with more of a defect-extended chain like morphology while a bad solvent such as toluene leads to compact organized and folded structures with rod-like morphologies. Secondary structural organization is induced by using the solution phase structures to generate solvent-free single molecule nanoparticles. These nanoparticles are very compact and rod shaped, consisting of near-cofacial ordering of the conjugated PPV chain backbones between folds located at tetrahedral defects (sp3 C-C bonds). The resulting photophysical properties exhibit a significant enhancement in the photoluminescence quantum yield, lifetime, and stability. In addition, the single molecule nanoparticles have Gaussian-like emission spectra with discrete center frequencies that are correlated to a conjugation length, allowing the design of nanoparticles which luminesces at a particular frequency. We followed a similar approach and applied a comparable methodology in our recent work on polythiophenes in order to study the effect of polymer architecture on nanoscale assembly. Unlike linear chains of comparable size, we observed aggregation of the bottlebrush architecture of poly(norbornene)-g-poly(3-hexylthiophene) (PNB-g-P3HT) after the freeze-drying and dissolution processes. The behavior can be attributed to a significant enhancement in the number of π-π interactions between grafted P3HT side chains.

Sumpter, Bobby G.↗

DOE OSTI2024

Understanding Process–Structure Relationships during Lamination of Halide Perovskite Interfaces

Fabrication of halide perovskite (HP) solar cells typically involves the sequential deposition of multiple layers to create a device stack, which is limited by the thermal and chemical incompatibility of top contact layers with the underlying HP semiconductor. One emerging strategy to overcome these restrictions on material selection and processing conditions is lamination, where two half-stacks are independently processed and then diffusion bonded to complete the device. Lamination reduces the processing constraints on the top side of the solar cell to allow new device designs, expanded use of deposition methods, and self-encapsulation of devices. While laminated perovskite solar cells with high efficiencies and novel interlayer combinations have been demonstrated, there is a limited understanding of how the lamination process parameters affect the diffusion-bond quality and material properties of the resulting HP layer. In this study, we systematically vary temperature, pressure, and time during lamination and quantify the resulting impacts on bonded area, grain domain size, and photoluminescence. A design of experiments is performed, and statistical analysis of the experimental results is used to quantitatively evaluate the resulting process–structure–property relationships. The lamination temperature is found to be the key parameter controlling these properties. Furthermore, a temperature of 150 °C enables successful bonding over 95% of the substrate area and also results in increases in apparent grain domain size and photoluminescence intensity. Based on these insights, the lamination temperature of functional perovskite solar cell devices is varied, demonstrating the importance of the resulting bond quality on device performance metrics.

14 SOLAR ENERGY↗

DOE OSTI2016

Multi-fidelity machine learning models for accurate bandgap predictions of solids

Here, we present a multi-fidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. Additionally, the adopted Gaussian process regression formulation allows us to predict the underlying uncertainties as a measure of our confidence in the predictions. In using a set of 600 elpasolite compounds as an example dataset and using semi-local and hybrid exchange correlation functionals within density functional theory as two levels of fidelities, we demonstrate the excellent learning performance of the method against actual high fidelity quantum mechanical calculations of the bandgaps. The presented statistical learning method is not restricted to bandgaps or electronic structure methods and extends the utility of high throughput property predictions in a significant way.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Flow Redirection and Induction in Steady State (FLORIS) Wind Plant Power Production Data Sets

This dataset contains turbine- and plant-level power outputs for 252,500 cases of diverse wind plant layouts operating under a wide range of yawing and atmospheric conditions. The power outputs were computed using the Gaussian wake model in NREL's FLOw Redirection and Induction in Steady State (FLORIS) model, version 2.3.0. The 252,500 cases include 500 unique wind plants generated randomly by a specialized Plant Layout Generator (PLayGen) that samples randomized realizations of wind plant layouts from one of four canonical configurations: (i) cluster, (ii) single string, (iii) multiple string, (iv) parallel string. Other wind plant layout parameters were also randomly sampled, including the number of turbines (25-200) and the mean turbine spacing (3D-10D, where D denotes the turbine rotor diameter). For each layout, 500 different sets of atmospheric conditions were randomly sampled. These include wind speed in 0-25 m/s, wind direction in 0 deg.-360 deg., and turbulence intensity chosen from low (6%), medium (8%), and high (10%). For each atmospheric inflow scenario, the individual turbine yaw angles were randomly sampled from a one-sided truncated Gaussian on the interval 0 deg.-30 deg. oriented relative to wind inflow direction. This random data is supplemented with a collection of yaw-optimized samples where FLORIS was used to determine turbine yaw angles that maximize power production for the entire plant. To generate this data, a subset of cases were selected (50 atmospheric conditions from 50 layouts each for a total of additional 2,500 cases) for which FLORIS was re-run with wake steering control optimization. The IEA onshore reference turbine, which has a 130 m rotor diameter, a 110 m hub height, and a rated power capacity of 3.4 MW was used as the turbine for all simulations. The simulations were performed using NREL's Eagle high performance computing system in February 2021 as part of the Spatial Analysis for Wind Technology Development project funded by the U.S. Department of Energy Wind Energy Technologies Office. The data was collected, reformatted, and preprocessed for this OEDI submission in May 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub repository under explore_wind_plant_data_h5.ipynb.

AI↗

DOE OSTI2022

Fully self-consistent finite-temperature $GW$ in Gaussian Bloch orbitals for solids

In this work, we present algorithmic and implementation details for the fully self-consistent finite-temperature $GW$ method in Gaussian Bloch orbitals for solids. Our implementation is based on the finite-temperature Green's function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of the self-energy are explicitly evaluated. The method is tested by evaluating the band gaps of selected semiconductors and insulators. We show agreement with other, differently formulated, finite-temperature sc ⁢$GW$ implementations when finite-size corrections and basis-set errors are taken into account. By migrating computationally intensive calculations to graphics processing units, we obtain scalable results on large supercomputers with nearly optimal performance. Our work demonstrates the applicability of Gaussian orbital based sc⁢ $GW$ for ab initio correlated material simulations and provides a sound starting point for embedding methods built on top of $GW$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Triphenylamine based organic dyes for dye sensitized solar cells: A theoretical approach

The geometry, electronic structure and absorption spectra for newly designed triphenylamine based organic dyes were investigated by density functional theory (DFT) and time dependent density functional theory (TD-DFT) with the Becke 3-Parameter-Lee-Yang-parr(B3LYP) functional, where the 6-31G(d,p) basis set was employed. All calculations were performed using the Gaussian 09 software package. The calculated HOMO and LUMO energies show that charge transfer occurs in the molecule. Ultraviolet–visible (UV–vis) spectrum was simulated by TD-DFT in gas phase. The calculation shows that all of the dyes can potentially be good sensitizers for DSSC. The LUMOs are just above the conduction band of TiO{sub 2} and their HOMOs are under the reduction potential energy of the electrolytes (I{sup −}/I{sub 3}{sup −}) which can facilitate electron transfer from the excited dye to TiO{sub 2} and charge regeneration process after photo oxidation respectively. The simulated absorption spectrum of dyes match with solar spectrum. Frontier molecular orbital results show that among all the three dyes, the “dye 3” can be used as potential sensitizer for DSSC.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

The impact of resolution upon entropy and information in coarse-grained models

By eliminating unnecessary degrees of freedom, coarse-grained (CG) models tremendously facilitate numerical calculations and theoretical analyses of complex phenomena. However, their success critically depends upon the representation of the system and the effective potential that governs the CG degrees of freedom. This work investigates the relationship between the CG representation and the many-body potential of mean force (PMF), W, which is the appropriate effective potential for a CG model that exactly preserves the structural and thermodynamic properties of a given high resolution model. In particular, we investigate the entropic component of the PMF and its dependence upon the CG resolution. This entropic component, S{sub W}, is a configuration-dependent relative entropy that determines the temperature dependence of W. As a direct consequence of eliminating high resolution details from the CG model, the coarsening process transfers configurational entropy and information from the configuration space into S{sub W}. In order to further investigate these general results, we consider the popular Gaussian Network Model (GNM) for protein conformational fluctuations. We analytically derive the exact PMF for the GNM as a function of the CG representation. In the case of the GNM, −TS{sub W} is a positive, configuration-independent term that depends upon the temperature, the complexity of the protein interaction network, and the details of the CG representation. This entropic term demonstrates similar behavior for seven model proteins and also suggests, in each case, that certain resolutions provide a more efficient description of protein fluctuations. These results may provide general insight into the role of resolution for determining the information content, thermodynamic properties, and transferability of CG models. Ultimately, they may lead to a rigorous and systematic framework for optimizing the representation of CG models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Relative permeability as a stationary process: Energy fluctuations in immiscible displacement

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number ([Formula: see text]), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗