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At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Quantifying Microstructure Variability in Laser Powder Bed Fusion 316 L Stainless Steel Microstructures with Spatial Statistics

Here, we have explored data-driven methods for material microstructure quantification that improve sensitivity to microstructural changes compared to traditional approaches. The methods integrate multiple microstructural properties, including grain morphology, crystallographic orientation, and material phase information. The simpler method employs maps of the Euclidean distance transformation metric to evaluate the morphology of grain boundary networks. The more intensive approach employs generalized spherical harmonic mapping for crystallographic orientations, per-pixel phase information, and a variational auto-encoder for dimensionality reduction and results in a multidimensional clustering of by microstructure similarity. Applied to an experimental dataset of additively manufactured steel, both methods detected slight variations in samples produced under nominally identical processing conditions. Both methods were able to distinguish between samples from multiple (nominally identical) builds, while the generalized spherical harmonics-based method could additionally cluster data samples rotated at two orientations on the build plate. The improved sensitivity of the methods, demonstrated through comparison with traditional microstructure characterization techniques, offers advantages for microstructure quantification and comparisons in advanced manufacturing applications.

SS316L↗
DOE OSTI2021

Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

Since variational symplectic integrators for the guiding center was proposed, structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Unveiling mesoscopic structures in distorted lamellar phases through deep learning-based small angle neutron scattering analysis

Hypothesis: The formation of distorted lamellar phases, distinguished by their arrangement of crumpled, stacked layers, is frequently accompanied by the disruption of long-range order, leading to the formation of interconnected network structures commonly observed in the sponge phase. Nevertheless, traditional scattering functions grounded in deterministic modeling fall short of fully representing these intricate structural characteristics. Our hypothesis posits that a deep learning method, in conjunction with the generalized leveled wave approach used for describing structural features of distorted lamellar phases, can quantitatively unveil the inherent spatial correlations within these phases. Experiments and Simulations: This report outlines a novel strategy that integrates convolutional neural networks and variational autoencoders, supported by stochastically generated density fluctuations, into a regression analysis framework for extracting structural features of distorted lamellar phases from small angle neutron scattering data. To evaluate the efficacy of our proposed approach, we conducted computational accuracy assessments and applied it to the analysis of experimentally measured small angle neutron scattering spectra of AOT surfactant solutions, a frequently studied lamellar system. Findings: The findings unambiguously demonstrate that deep learning provides a dependable and quantitative approach for investigating the morphology of wide variations of distorted lamellar phases. It is adaptable for deciphering structures from the lamellar to sponge phase including intermediate structures exhibiting fused topological features. In conclusion, this research highlights the effectiveness of deep learning methods in tackling complex issues in the field of soft matter structural analysis and beyond.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Jensen–Shannon divergence based novel loss functions for Bayesian neural networks

Bayesian neural networks (BNNs) are state-of-the-art machine learning methods that can naturally regularize and systematically quantify uncertainties using their stochastic parameters. Kullback–Leibler (KL) divergence-based variational inference used in BNNs suffer from unstable optimization and challenges in approximating light-tailed posteriors due to the unbounded nature of the KL divergence. To resolve these issues, we formulate a novel loss function for BNNs based on a new modification to the generalized Jensen–Shannon (JS) divergence, which is bounded. In addition, we propose a Geometric JS divergence-based loss, which is computationally efficient since it can be evaluated analytically. We found that the JS divergence-based variational inference is intractable, and hence employed a constrained optimization framework to formulate these losses. Our theoretical analysis and empirical experiments on multiple regression and classification data sets suggest that the proposed losses perform better than the KL divergence-based loss, especially when the data sets are noisy or biased. Specifically, there are approximately 5% and 8% improvements in accuracy for a noise-added CIFAR-10 dataset and a regression dataset, respectively. There is about 13% reduction in false negative predictions of a biased histopathology dataset. Additionally, we quantify and compare the uncertainty metrics for the regression and classification tasks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An Ab initio based OH initiated oxidation kinetics of glycerol carbonate: A promising biofuel component

The global energy demand is steadily increasing because of the population explosion and economic growth. Fossil fuels supply around 85 % of global primary energy demand. On one hand, fulfilling the increasing energy demands is a big challenge for the next few decades. On the other hand, the continued burning of fossil fuels leads to higher CO2 emissions, severely impacting global warming. Therefore, the policymakers vow to shift from conventional fuels to renewable resources for economic, environmental, and future energy security reasons. In this context, biofuels from lignocellulosic biomass and/or carbon-neutral fuels produced in the sustainable carbon cycle can close the carbon cycle and reach net zero-carbon emission. Recently, glycerol carbonate has been proposed as a promising fuel or fuel additive for future sustainability. Therefore, we investigated the hydrogen abstraction reactions of glycerol carbonate (GC) by OH radicals using high-level ab initio and variational transition state theory calculations. We mapped out the potential energy surface using the CCSD(T)/cc-pV(D, T)Z//MP2/cc-pVTZ level of theory. Here we used the ab initio parameters to obtain the site-specific rate coefficients by employing the variational transition state theory. We observed that every hydrogen atom in GC displays a unique reactivity with OH radicals. We derived branching ratio of each channel that are difficult to access experimentally. The overall rate coefficients exhibit a strong non-Arrhenius behaviour, which can be represented as: $k^{CVT/SCT}_{ov}$ (T) = 3.39 x 10 -20 x T 2.659 x e$\frac{-750.0 Jmol^{-1}}{RT}$ $\frac{cm^{3}}{molecule s}$ This is the first reported rate data for the glycerol carbonate and OH radicals reaction.

09 BIOMASS FUELS↗
DOE OSTI2021

Annual Tropical‐Rainforest Productivity Through Two Decades: Complex Responses to Climatic Factors, [CO 2 ] and Storm Damage

Abstract Yearly changes in tropical carbon‐cycling have been a major biotic determinant of the interannual variation in the rise of atmospheric carbon dioxide ([CO 2 ]). The environmental responses underlying these changes remain poorly understood. A 21‐year field study (1997–2018) in a Costa Rican rainforest has produced the first multi‐decade record of landscape‐scale annual aboveground productivity for a tropical ecosystem. While none of the four production components (wood production; leaf‐, twig‐, and reproductive litterfall) increased over two decades, all significantly varied among years. Multi‐factor environmental models explained a large fraction of the inter‐year changes in two production components. Annual changes in three climatic factors and [CO 2 ] jointly accounted for 84% of the variation in annual wood production. While the strongest response of wood production was to decline in years of slightly warmer nights, it also significantly declined in years with more dry‐season hours hotter than 28°C. The yearly changes in reproductive litterfall were largely (52%) determined by the combined effects of increasing [CO 2 ] and declining annual radiation. Twig litterfall declined over the 21 years. Annual leaf litterfall, the largest component of field‐assessed aboveground production, showed no significant environmental responses. An extreme storm in the study's final year disrupted the environmental controls on production that prevailed through the prior 20 years. While important uncertainties are introduced by some of the field methods for assessing aboveground forest production, the findings of this first long‐term field study of annual landscape‐scale productivity raise deep concerns for the future of tropical forests as global warming proceeds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton’s equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Measurement accuracy and spatial resolution of a distributed temperature sensor based on a two-pulse differential coherent reflectometer

We present a model and numerical simulation of a distributed temperature sensor based on a two-pulse differential coherent optical time-domain reflectometer (COTDR). The differential phase measured using a phase-sensitive Rayleigh reflectometer is shown to have a regular component, which is a linear function of temperature, and a random component, which is related to a random distribution of scattering centres in the fibre and restricts the accuracy of measurements of variations in temperature. Measurement accuracy can be improved by reducing the relative contribution of the random component via a decrease in pulse duration and/or an increase in the time delay between pulses. The spatial resolution of a differential two-pulse phase-sensitive reflectometer is shown to be determined by the time delay between pulses and to vary little with pulse duration. At a typical pulse duration (200 ns) and delay time (300 ns), the accuracy in measurements of variations in temperature in the 0.1-K range is 2 % and the spatial resolution is about 30 m. (fibre-optic sensors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Quantum error mitigation by hidden inverses protocol in superconducting quantum devices

We present a method to improve the convergence of variational algorithms based on hidden inverses (HIs) to mitigate coherent errors. In the context of error mitigation, this means replacing the hardware implementation of certain Hermitian gates with their inverses. Doing so results in noise cancellation and a more resilient quantum circuit. This approach improves performance in a variety of two-qubit error models where the noise operator also inverts with the gate inversion. We apply the mitigation scheme on superconducting quantum processors running the variational quantum eigensolver (VQE) algorithm to find the H 2 ground-state energy. When implemented on superconducting hardware we find that the mitigation scheme effectively reduces the energy fluctuations in the parameter learning path in VQE, reducing the number of iterations for a converged value. We also provide a detailed numerical simulation of VQE performance under different noise models and explore how HIs and randomized compiling affect the underlying loss landscape of the learning problem. These simulations help explain our experimental hardware outcomes, helping to connect lower-level gate performance to application-specific behavior in contrast to metrics like fidelity which often do not provide an intuitive insight into observed high level performance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Aging Effect Analysis of PV Inverter Semiconductors for Ancillary Services Support

PV inverters can provide reactive power while generating active power. An ongoing microgrid implementation at Duke Energy actively engages non-utility PVs to generate/absorb reactive power in support of ancillary services to increase microgrid resiliency during extreme events. PV systems are requested to provide reactive power support: 1) in response to grid voltage variation to better regulate the local voltage; or 2) in response to utility incentives, such as following Transactive Energy System (TES) incentives. However, providing ancillary services might shorten the lifetime expectation of PV inverter semiconductors. This paper summarizes the potential impacts on a PV inverter semiconductor's lifetime when providing ancillary services. The analysis presented in this research work shows that providing reactive power support will increase the mean junction temperature and the junction temperature variation of the inverter diodes. This increased junction temperature will eventually lead to shorter diode lifetime. The lifetime estimation of semiconductors is briefly reviewed. The power losses of PV inverter semiconductors are derived as a support analysis to the junction temperature calculation. In addition, the impact of the filtering inductor on the semiconductor current distribution is discussed. The theoretical analysis presented in this research work is supported by simulation results.

14 SOLAR ENERGY↗
DOE OSTI2024

Spike-and-Slab Shrinkage Priors for Structurally Sparse Bayesian Neural Networks

Network complexity and computational efficiency have become increasingly significant aspects of deep learning. Sparse deep learning addresses these challenges by recovering a sparse representation of the underlying target function by reducing heavily overparameterized deep neural networks. Specifically, deep neural architectures compressed via structured sparsity (e.g., node sparsity) provide low-latency inference, higher data throughput, and reduced energy consumption. In this article, we explore two well-established shrinkage techniques, Lasso and Horseshoe, for model compression in Bayesian neural networks (BNNs). To this end, we propose structurally sparse BNNs, which systematically prune excessive nodes with the following: 1) spike-and-slab group Lasso (SS-GL) and 2) SS group Horseshoe (SS-GHS) priors, and develop computationally tractable variational inference, including continuous relaxation of Bernoulli variables. We establish the contraction rates of the variational posterior of our proposed models as a function of the network topology, layerwise node cardinalities, and bounds on the network weights. Furthermore, we empirically demonstrate the competitive performance of our models compared with the baseline models in prediction accuracy, model compression, and inference latency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Graphical Model for Fusing Diverse Microbiome Data

This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high-dimensional features, in this case, transcripts, collected from different treatments. In such datasets, there are no explicit correspondences between the communities and each corresponds to different factors, making data fusion challenging. We introduce a flexible multinomial-Gaussian generative model for jointly modeling such count data. This latent variable model jointly characterizes the observed data through a common multivariate Gaussian latent space that parameterizes the set of multinomial probabilities of the transcriptome counts. The covariance matrix of the latent variables induces a covariance matrix of co-dependencies between all the transcripts, effectively fusing multiple data sources. We present a computationally scalable variational Expectation-Maximization (EM) algorithm for inferring the latent variables and the parameters of the model. Here, the inferred latent variables provide a common dimensionality reduction for visualizing the data and the inferred parameters provide a predictive posterior distribution. In addition to simulation studies that demonstrate the variational EM procedure, we apply our model to a bacterial microbiome dataset.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Genetic Basis of Non–Photochemical Quenching and Photosystem II Efficiency Responses to Chilling in the Biomass Crop Miscanthus

Miscanthus holds a promise as a biocrop due to its high yield, perenniality and ability to grow on infertile soils. However, the current commercial biomass production of Miscanthus is mostly limited to a single sterile triploid clone of M. × giganteus. Nevertheless, parental species of M. × giganteus, Miscanthus sacchariflorus and Miscanthus sinensis contain vast genetic diversity for crop improvement. With M. sacchariflorus having a natural geographic distribution in cold-temperate northeast China and eastern Russia, we hypothesised that it has substantial variation in physiological response to chilling. Using a semi-high-throughput method, we phenotyped 209 M. sacchariflorus genotypes belonging to six genetic groups for non-photochemical quenching (NPQ) and photosystem II efficiency (ΦPSII) kinetics under warm and chilling treatments in three growing seasons. In response to the chilling treatment, all genetic groups exhibited an increase in NPQ induction rate indicating faster activation of NPQ in light. Notably, under chilling, the Korea/NE China/Russia 2x and N China 2x groups stood out for the highest NPQ rate in light and the highest steady-state NPQ in light. This NPQ phenotype may contribute adaptation to chilling during bright, cold mornings of spring and early autumn in temperate climates, when faster NPQ would better protect from oxidative stress. Such enhanced adaptation could expand the growing season and thus productivity at a given location or expand the range of economically viable growing locations to higher latitudes and altitudes. A genome-wide association study identified 126 unique SNPs associated with NPQ and ΦPSII traits. Among the identified candidate genes were enzymes involved in the ascorbate recycle and shikimate pathway, gamma-aminobutyric acid and cation efflux transporters. Identifying natural variation and genes involved in NPQ and ΦPSII kinetics considerably enlarges the toolbox for breeding and/or engineering Miscanthus with optimised photosynthesis under warm and chilling conditions for sustainable feedstock production for bioenergy.

09 BIOMASS FUELS↗
DOE OSTI2020

Spatial and temporal patterns in age structure of Golden Eagles wintering in eastern North America

The behavior of wildlife varies seasonally, and that variation can have substantial demographic consequences. This is especially true for long-distance migrants where the use of landscapes varies by season and, sometimes, age cohort. In this study, we tested the hypothesis that distributional patterns of Golden Eagles (Aquila chrysaetos) wintering in eastern North America are age-structured (i.e., birds of similar ages winter together) through the analysis of 370,307 images collected by motion-sensitive trail cameras set over bait during the winters of 2012–2013 and 2013–2014. At nine sites with sufficient data for analysis, we documented 145 eagle visits in 2012–2013 and 146 in 2013–2014. We found significant between-year variation in age structure of wintering eastern Golden Eagles, driven largely by annual differences in the proportion of first-winter birds. However, although many other species show spatial structure in wintering behavior, our analysis revealed no latitudinal organization among age cohorts of wintering eastern Golden Eagles. The lack of age-related latitudinal segregation in wintering behavior does not exclude the possibility that these eagles have sex-based or other types of dominance hierarchies that could result in spatial or temporal segregation. Alternatively, other mechanisms such as food availability or habitat structure may determine the distribution and abundance of Golden Eagles in winter.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Approaches to investigate crop responses to ozone pollution: from O 3 -FACE to satellite-enabled modeling

Ozone (O 3 ) is a damaging air pollutant to crops. As one of the most reactive oxidants known, O 3 rapidly forms other reactive oxygen species (ROS) once it enters leaves through stomata. Those ROS in turn can cause oxidative stress, reduce photosynthesis, accelerate senescence, and decrease crop yield. To improve and adapt our feed, fuel, and food supply to rising O 3 pollution, a number of Free Air Concentration Enrichment (O 3 -FACE) facilities have been developed around the world and have studied key staple crops. In this review, we provide an overview of the FACE facilities and highlight some of the lessons learned from the last two decades of research. We discuss the differences between C 3 and C 4 crop responses to elevated O 3 , the possible trade-off between productivity and protection, genetic variation in O 3 response within and across species, and how we might leverage this observed variation for crop improvement. We also highlight the need to improve understanding of the interaction between rising O 3 pollution and other aspects of climate change, notably drought. Finally, we propose the use of globally modeled O 3 data that are available at increasing spatial and temporal resolutions to expand upon the research conducted at the limited number of global O 3 -FACE facilities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A Nonlocal Feature-Driven Exemplar-Based Approach for Image Inpainting

Here, we present a nonlocal variational image completion technique which admits simultaneous inpainting of multiple structures and textures in a unified framework. The recovery of geometric structures is achieved by using general convolution operators as a measure of behavior within an image. These are combined with a nonlocal exemplar-based approach to exploit the self-similarity of an image in the selected feature domains and to ensure the inpainting of textures. We also introduce an anisotropic patch distance metric to allow for better control of the feature selection within an image and present a nonlocal energy functional based on this metric. Finally, we derive an optimization algorithm for the proposed variational model and examine its validity experimentally with various test images.

97 MATHEMATICS AND COMPUTING↗