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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A generalized approximate control variate framework for multifidelity uncertainty quantification

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost models — which are typically lower fidelity with unknown statistics — are used to reduce the variance in statistical estimators relative to a MC estimator with equivalent cost. We derive the conditions under which our proposed approximate control variate framework recovers existing multifidelity variance reduction schemes as special cases. We demonstrate that existing recursive/nested strategies are suboptimal because they use the additional low-fidelity models only to efficiently estimate the unknown mean of the first low-fidelity model. As a result, they cannot achieve variance reduction beyond that of a control variate estimator that uses a single low-fidelity model with known mean. However, there often exists about an order-of-magnitude gap between the maximum achievable variance reduction using all low-fidelity models and that achieved by a single low-fidelity model with known mean. We show that our proposed approach can exploit this gap to achieve greater variance reduction by using non-recursive sampling schemes. The proposed strategy reduces the total cost of accurately estimating statistics, especially in cases where only low-fidelity simulation models are accessible for additional evaluations. Several analytic examples and an example with a hyperbolic PDE describing elastic wave propagation in heterogeneous media are used to illustrate the main features of the methodology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Analysis of the Challenges in Developing Sample-Based Multi-fidelity Estimators for Non-deterministic Models

Multifidelity (MF) uncertainty quantification (UQ) seeks to leverage and fuse information from a collection of models to achieve greater statistical accuracy with respect to a single-fidelity counterpart, while maintaining an efficient use of computational resources. Despite many recent advancements in MF UQ, several challenges remain and these often limit its practical impact in certain application areas. In this manuscript, we focus on the challenges introduced by nondeterministic models to sampling MF UQ estimators. Nondeterministic models produce different responses for the same inputs, which means their outputs are effectively noisy. MF UQ is complicated by this noise since many state-of-the-art approaches rely on statistics, e.g., the correlation among models, to optimally fuse information and allocate computational resources. Here, we demonstrate how the statistics of the quantities of interest, which impact the design, effectiveness, and use of existing MF UQ techniques, change as functions of the noise. With this in hand, we extend the unifying approximate control variate framework to account for nondeterminism, providing for the first time a rigorous means of comparing the effect of nondeterminism on different multifidelity estimators and analyzing their performance with respect to one another. Numerical examples are presented throughout the manuscript to illustrate and discuss the consequences of the presented theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control

Herein, we present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional sub-spaces whose basis functions are realizations of a sequence of neural networks. Here, the finite-dimensional subspaces are then used to define a standard Galerkin approximation of the variational equation. This approach enjoys a number of advantages, including: the sequential nature of the algorithm offers a systematic approach to enhancing the accuracy of a given approximation; the sequential enhancements provide a useful indicator for the error that can be used as a criterion for terminating the sequential updates; the basic approach is largely oblivious to the nature of the partial differential equation under consideration; and, some basic theoretical results are presented regarding the convergence (or otherwise) of the method which are used to formulate basic guidelines for applying the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control

We present extended Galerkin neural networks, a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs, and (2) an “extended” feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Furthermore, numerical results are presented for several problems, including steady Stokes flow around reentrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method.

a posteriori error estimate↗
DOE OSTI2026

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗
DOE OSTI2019

Analysis of the Zero Relaxation Limit of Hyperbolic Balance Laws with Random Initial Data

We show the convergence of the zero relaxation limit of $2 \times 2$ systems of hyperbolic balance laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation time tends to zero. The initial data are assumed to depend on finitely many random variables, and the convergence is then proved via the appropriate analogues of the compensated compactness methods used in treating the deterministic case. We also demonstrate the validity of this limit in the case of the semilinear $p$-system; the well-posedness of both the system and its equilibrium approximation is proved, and the convergence is shown with no a priori conditions on solutions. Here, this model serves as a prototype for understanding how asymptotic approximations can be used as control variates for hyperbolic balance laws with uncertainty.

$p$-system↗
DOE OSTI2022

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Fully discrete schemes for monotone optimal control problems

In this article, we study an infinite horizon optimal control problem with monotone controls. We analyze the associated Hamilton–Jacobi–Bellman (HJB) variational inequality which characterizes the value function and consider the totally discretized problem using Lagrange elements to approximate the state space Ω. The convergence orders of these approximations are proved, which are in general (h+(k/(√h))){sup γ} where γ is the Hölder constant of the value function u, h and k are the time and space discretization parameters, respectively. A special election of the relations between h and k allows to obtain a convergence of order k{sup (2/3)γ}, which is valid without semiconcavity hypotheses over the problem’s data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improving the nonlinear control performance of the supply fan at air handling units using a gain scheduling control strategy

Due to its nonlinear nature, the supply fan at air handling units with the controller tuned at the design condition tends to be aggressive and oscillate under partial load conditions. Here, the objective of this paper is to develop and validate a gain scheduling control strategy to improve its nonlinear control performance. First, a control-oriented model, which does not require numerous physical parameters and extensive test data, is developed to study the nonlinearity of the fan system. Based on the theoretical model and experimental verifications, the issue of an aggressive response with a conventional fixed-gain controller is caused by the fact that the system gain is proportional to the ratio of the duct static pressure to the fan speed. To address the issue, a scheduling function of the measurable duct static pressure and fan speed is proposed to be included in the conventional fixed-gain controller to compensate for the fan system gain variation. The gain scheduling control strategy is found to approximately maintain the identical control performance under all operation conditions. Most importantly, the gain scheduling control strategy can be readily implemented without intensive computation and additional measurements, showing a promising potential in industrial applications.

42 ENGINEERING↗
DOE OSTI2023

Long-term warming modulates diversity, vertical structuring of microbial communities, and sulfate reduction in coastal Baltic Sea sediments

Coastal waters such as those found in the Baltic Sea already suffer from anthropogenic related problems including increased algal blooming and hypoxia while ongoing and future climate change will likely worsen these effects. Microbial communities in sediments play a crucial role in the marine energy- and nutrient cycling, and how they are affected by climate change and shape the environment in the future is of great interest. The aims of this study were to investigate potential effects of prolonged warming on microbial community composition and nutrient cycling including sulfate reduction in surface (∼0.5 cm) to deeper sediments (∼ 24 cm). To investigate this, 16S rRNA gene amplicon sequencing was performed, and sulfate concentrations were measured and compared between sediments in a heated bay (which has been used as a cooling water outlet from a nearby nuclear power plant for approximately 50 years) and a nearby but unaffected control bay. The results showed variation in overall microbial diversity according to sediment depth and higher sulfate flux in the heated bay compared to the control bay. A difference in vertical community structure reflected increased relative abundances of sulfur oxidizing- and sulfate reducing bacteria along with a higher proportion of archaea, such as Bathyarchaeota, in the heated compared to the control bay. This was particularly evident closer to the sediment surface, indicating a compression of geochemical zones in the heated bay. These results corroborate findings in previous studies and additionally point to an amplified effect of prolonged warming deeper in the sediment, which could result in elevated concentrations of toxic compounds and greenhouse gases closer to the sediment surface.

16S rRNA gene amplicon↗
DOE OSTI2025

Breakdown of the Static Dielectric Screening Approximation of Coulomb Interactions in Atomically Thin Semiconductors

Coulomb interactions in atomically thin materials are remarkably sensitive to variations in the dielectric screening of the environment, which can be used to control exotic quantum many-body phases and engineer exciton potential landscapes. For decades, static or frequency-independent approximations of the dielectric response, where increased dielectric screening is predicted to cause an energy redshift of the exciton resonance, have been sufficient. These approximations were first applied to quantum wells and were more recently extended with initial success to layered transition metal dichalcogenides (TMDs). Here, we use charge-tunable exciton resonances to investigate screening effects in TMD monolayers embedded in materials with low-frequency dielectric constants ranging from 4 to more than 1000, a range of 2 orders of magnitude larger than in previous studies. In contrast to the redshift predicted by static models, we observe a blueshift of the exciton resonance exceeding 30 meV in higher dielectric constant environments. We explain our observations by introducing a dynamical screening model based on a solution to the Bethe-Salpeter equation (BSE). When dynamical effects are strong, we find that the exciton binding energy remains mostly controlled by the low-frequency dielectric response, while the exciton self-energy is dominated by the high-frequency one. Our results supplant the understanding of screening in layered materials and their heterostructures, introduce a knob to tune selected many-body effects, and reshape the framework for detecting and controlling correlated quantum many-body states and designing optoelectronic and quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological N-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

PNNL-CompBio/bayesian-inference

Bayesian Metabolic Inference is a platform to integrate genome-scale multi-omics data into an iterative method to obtain optimized recommendations for optimal target compound production. This method uses a variational inference approach to approximate new posterior data to analyze in order to obtain useful correlations and control coefficients.

Kumar, Neeraj↗
DOE OSTI2024

Production of chitosan-based composite film reinforced with lignin-rich lignocellulose nanofibers from rice husk

Lignocellulosic nanofibers (LCNFs), implying lignin-containing cellulose fibers, maintain the properties of both lignin and cellulose, which are hydrophobic and hydrophilic, respectively. The presence of hydrophobic lignin in LCNFs is expected to be an economical and attractive option that can improve the thermal and mechanical properties of polymers. Thus, this study was conducted to produce lignin-rich LCNFs from sugar-rich waste obtained from rice husks after acidic pretreatment. The LCNFs were produced from the lignin-rich solid fractions obtained after pretreatment and enzymatic hydrolysis, which were then incorporated as an additive into a chitosan-based film. The variations in lignin content in the range of approximately 50.6%-66.8% in differently obtained LCNFs gave significantly different optical strengths and mechanical properties. These controllable processes may allow for customized film formation. Additionally, the glucose-rich liquid fractions obtained after pretreatment and enzymatic hydrolysis were used as a substrate for ethanol fermentation to achieve total utilization of rice husk biomass waste. In conclusion, the lignin-rich biomass fraction holds promise as a suitable material for chitosan-LCNF film and has the potential to increase the economic feasibility of the biomaterial industry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Climatic controls of decomposition drive the global biogeography of forest-tree symbioses

The identity of the dominant microbial symbionts in a forest determines the ability of trees to access limiting nutrients from atmospheric or soil pools, sequester carbon and withstand the impacts of climate change. Characterizing the global distribution of symbioses, and identifying the factors that control it, are thus integral to understanding present and future forest ecosystem functioning. In this work we generate the first spatially explicit global map of forest symbiotic status using a database of over 1.1 million forest inventory plots with over 28,000 tree species. Our analyses indicate that climatic variables, and in particular climatically-controlled variation in decomposition rate, are the primary drivers of the global distribution of major symbioses. We estimate that ectomycorrhizal (EM) trees, which represent only 2% of all plant species, constitute approximately 60% of tree stems on Earth. EM symbiosis dominates forests where seasonally cold and dry climates inhibit decomposition, and are the predominant symbiosis at high latitudes and elevation. On the other hand, arbuscular mycorrhizal (AM) trees dominate aseasonally warm tropical forests and occur with EM trees in temperate biomes where seasonally warm-and-wet climates enhance decomposition. Continental transitions between AM and EM dominated forests occur relatively abruptly along climate driven decomposition gradients, which is likely caused by positive plant-microbe feedbacks. Symbiotic N-fixers, which are insensitive to climatic controls on decomposition compared with mycorrhizal fungi, are most abundant in arid biomes with alkaline soils and high maximum temperatures. The climatically driven global symbiosis gradient we document represents the first spatially-explicit, quantitative understanding of microbial symbioses at the global scale and demonstrates the critical role of microbial mutualisms in shaping the distribution of plant species.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this paper, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.

Chemical calculations↗