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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 OSTI2021

A Nonstationary and Non-Gaussian Moving Average Model for Solar Irradiance

Historically, power has flowed from large power plants to customers. Increasing penetration of distributed energy resources such as solar power from rooftop photovoltaic has made the distribution network a two-way-street with power being generated at the customer level. The incorporation of renewables introduces additional uncertainty and variability into the power grid. Distribution network operation studies are being adapted to include renewables; however, such studies require high quality solar irradiance data that adequately reflect realistic meteorological variability. Data from satellite-based products are spatially complete, but temporally coarse, whereas solar irradiances exhibit high frequency variation at very fine timescales. We propose a new stochastic method for temporally downscaling global horizontal irradiance (GHI) to 1 min resolution, but we do not consider the spatial aspect due to limited availability of the in situ irradiance measurements. Solar irradiance's first and second-order structures vary diurnally and seasonally, and our model adapts to such nonstationarity. Empirical irradiance data exhibits highly non-Gaussian behavior; we develop a nonstationary and non-Gaussian moving average model that is shown to capture realistic solar variability at multiple timescales. We also propose a new estimation scheme based on Cholesky factors of empirical autocovariance matrices, bypassing difficult and inaccessible likelihood-based approaches. The model is demonstrated for a case study of three locations that are located in diverse climates through the United States. The model is compared against competitors from the literature and is shown to provide better uncertainty and variability quantification on testing data.

Cholesky factor↗
DOE OSTI2020

Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Absorptive Weak Plume Detection on Gaussian and Non-Gaussian Background Clutter

For additive signals on Gaussian clutter, the optimal detector is a linear matched filter that is adapted to the known signal and the covariance of the background. This adaptive matched filter is widely used for gas-phase plume detection, even though the effect of the plume on the background is not strictly additive. Here, a derivation of the matched filter for a strictly absorptive plume produces, in the weak plume limit, a quadratic filter. This quadratic matched filter is extended in two ways: an elliptically-contoured multivariate t distribution is used to generalize the Gaussian background clutter, and a generalized likelihood ratio test detector is derived to extend applicability to stronger plumes. In addition to detectors whose purpose is to identify presence versus absence of a plume, expressions are also derived for estimating plume strength. The performance of these various detectors is evaluated by implanting simulated plume into background images that are either real hyperspectral images or simulated images based on different (Gaussian, multivariate t, and lognormal) clutter distributions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Gaussian FLOWERS: Wind-rose-based analytical integration of Gaussian wake model for extremely fast AEP estimation

A major cost in the study of wind farm layout optimization is the repeated evaluation of the annual energy production (AEP). The current approach to estimating AEP requires a large set of flow simulations to be performed that cover each discrete wind speed and direction combination contained within the wind rose, followed by a probability-weighted sum of the power production resulting from each simulation. Even with inexpensive engineering wake models, this numerical integration scheme can lead to high computational costs. In this paper, we derive an analytical formulation for estimating farm AEP across every wind direction, based on a Gaussian wake velocity model, which reduces the number of wind farm simulations to a single function evaluation. As a result, we find that the Gaussian-FLOWERS approach reduces the time for AEP calculations by more than two orders of magnitude with a small trade-off in accuracy when compared to a conventional approach. This massive reduction in computation cost is useful to reduce overall costs in wind farm layout optimization studies.

17 WIND ENERGY↗
DOE OSTI2024

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗
DOE OSTI2021

Reducing Ground-based Astrometric Errors with Gaia and Gaussian Processes

Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2D distortion field is curl-free. Applied to several hundred 90 s exposures from the Dark Energy Survey as a test bed, we find that the GPR correction reduces the variance of the turbulent astrometric distortions ≈12× , on average, with better performance in denser regions of the Gaia catalog. The rms per-coordinate distortion in the riz bands is typically ≈7 mas before any correction and ≈2 mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas rms, the residuals to an orbit fit to riz-band observations over 5 yr of the r = 18.5 trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5D stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Enhanced Data Efficiency Using Deep Neural Networks and Gaussian Processes for Aerodynamic Design Optimization

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models. Our methodology finds applications in the early stages of aerospace design. (C) 2021 Published by Elsevier Masson SAS.

Renganathan, S. Ashwin↗
DOE OSTI2025

Decoherence dynamics in molecular qubits: Exponential, Gaussian and beyond

In this article, we examine how the structure of system–bath interactions can determine commonly encountered temporal decoherence patterns, such as Gaussian and exponential decay, in molecular and other qubits coupled to a thermal bosonic bath. The analysis, based on a pure dephasing picture that admits analytical treatment, shows that decoherence, in general, is neither purely Gaussian nor exponential but rather the exponential of oscillatory functions, with periods determined by the bath’s frequencies. For initially unentangled qubit-bath states, Gaussian decay is always present at early times. It becomes increasingly dominant with increasing temperature, qubit–bath interaction strength, and bath correlation time. Initial system–bath entanglement that arises due to displacement in the position of the bath states preserves the Gaussian decay. By contrast, strict exponential decay arises only in very specific models that we isolate. However, it becomes dominant for times longer than the bath correlation time or for early times when there is initial entanglement due to momentum displacement of the bath states. For molecular electronic decoherence, the long-time exponential regime plays a limited role as it emerges after most coherence is lost. Thus, the Gaussian decay provides a more suitable (albeit imperfect) model of such decoherence. Furthermore, we discuss the connection between electronic decoherence dynamics and electronic spectroscopic line shape theory, where Gaussian spectral peaks correspond to Gaussian coherence decay and Lorentzian peaks correspond to exponential coherence decay. We find that Gaussian spectral peaks, usually associated with inhomogeneous broadening, can emerge from the entangling unitary system–bath dynamics even when there is no inhomogeneity in the initial conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Dynamical Complexity of Non-Gaussian Many-Body Systems with Dissipation

We characterize the dynamical state of many-body bosonic and fermionic many-body models with intersite Gaussian couplings, on-site non-Gaussian interactions, and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian intersite couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the intersite couplings.

Computational complexity↗
DOE OSTI2022

Non-Gaussianities in collider energy flux

The microscopic dynamics of particle collisions is imprinted into the statistical properties of asymptotic energy flux, much like the dynamics of inflation is imprinted into the cosmic microwave background. This energy flux is characterized by correlation functions < E(n → 1 )…E(n → k ) > of energy flow operators E(n → ). There has been significant recent progress in studying energy flux, including the calculation of multi-point correlation functions and their direct measurement inside high-energy jets at the Large Hadron Collider (LHC). In this paper, we build on these advances by defining a notion of “celestial non-gaussianity” as a ratio of the three-point function to a product of two-point functions. We show that this celestial non-gaussianity is under perturbative control within jets at the LHC, allowing us to cleanly access the non-gaussian interactions of quarks and gluons. We find good agreement between perturbative calculations of the non-gaussianity and a charged-particle-based analysis using CMS Open Data, and we observe a strong non-gaussianity peaked in the “flattened triangle” regime. The ability to robustly study three-point correlations is a significant step in advancing our understanding of jet substructure at the LHC. We anticipate that the celestial non-gaussianity, and its generalizations, will play an important role in the development of higher-order parton showers simulations and in the hunt for ever more subtle signals of potential new physics within jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Evaluating generative networks using Gaussian mixtures of image features

We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fréchet Inception Distance (FID). However, FID assumes that images featurized using the penultimate layer of Inception follow a Gaussian distribution. This assumption allows FID to be easily computed, since FID uses the 2-Wasserstein distance of two Gaussian distributions fitted to the featurized images. However, we show that Inception features of the ImageNet dataset are not Gaussian; in particular, each marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using inception (or another classifier) to featurize the images, estimate two GMMs, and use the restricted 2-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to image perturbations. By modelling the non-Gaussian features obtained from inception as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.

machine learning, genrative adversarial networks↗
DOE OSTI2022

Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

FORSE+: Simulating non-Gaussian CMB foregrounds at 3 arcmin in a stochastic way based on a generative adversarial network

We present FORSE+, a Python package that produces non-Gaussian diffuse Galactic thermal dust emission maps at arcminute angular scales and that has the capacity to generate random realizations of small scales. This represents an extension of the FORSE (Foreground Scale Extender) package, which was recently proposed to simulate non-Gaussian small scales of thermal dust emission using generative adversarial networks (GANs). With the input of the large-scale polarization maps from observations, FORSE+ has been trained to produce realistic polarized small scales at 3′ following the statistical properties, mainly the non-Gaussianity, of observed intensity small scales, which are evaluated through Minkowski functionals. Furthermore, by adding different realizations of random components to the large-scale foregrounds, we show that FORSE+ is able to generate small scales in a stochastic way. In both cases, the output small scales have a similar level of non-Gaussianity compared with real observations and correct amplitude scaling as a power law. These realistic new maps will be useful, in the future, to understand the impact of non-Gaussian foregrounds on the measurements of the cosmic microwave background (CMB) signal, particularly on the lensing reconstruction, de-lensing, and the detection of cosmological gravitational waves in CMB polarizationB-modes.

Astronomy & Astrophysics↗