Optimality of Gaussian receivers for practical Gaussian distributed sensing
Not Available
Volkoff, T. J.↗
SEARCH · Engineering Papers
Results for “gaussian”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Sampling Functions from Gaussian Processes and Structured Covariance Gaussian Networks
When learning aerodynamic models from data, it is critical to incorporate estimates of model uncertainty. This motivates the design of probabilistic aerodynamic databases which can be sampled to generate physically and statistically plausible aerodynamic models. In this talk we discuss how to sample deterministic functions from two different kinds of probabilistic models and demonstrate their use. First, Gaussian Process Regressors (GPRs) are a widely used probabilistic kernel-based model which can be thought of as Gaussian distributions over functions. GPRs are generally trained by maximizing the marginal likelihood of seeing the training data over the kernel parameter space. Sample functions are easily generated by drawing points from the Gaussian distribution at desired input points. However, when the points are not known ahead of time, the classical sampling approach is not possible since successive function samples will generate different function realizations. We present an approach for sampling consistent function evaluations from a GPR over multiple samples. Second, we describe a neural network architecture which learns a conditional Gaussian distribution by maximizing the marginal likelihood at each point in the input space. We then discuss and compare several options for generating sample functions which match this distribution. Finally, we demonstrate the use of these probabilistic aerodynamic models in an atmospheric reentry simulation.
Gaussian process regression↗
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↗
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↗
Generation of controllable Ince – Gaussian modes in a passively Q-switched microchip laser under truncated decentred Gaussian beam pumping
We report a passively Q-switched (PQS) Nd : YAG/Cr{sup 4+}: YAG microchip laser pumped by a truncated decentred Gaussian beam for controllable Ince – Gaussian (IG) mode generation. IG{sup e}(n, n) modes (n = 0, …, 4) are obtained experimentally by choosing the appropriate truncation parameter, which is defined as a ratio of the radius of the aperture to the beam waist. The IG{sup e}(4, 4) mode is produced in the PQS Nd : YAG/Cr{sup 4+}: YAG microchip laser under decentred Gaussian beam pumping at a pump power of 2.6 W, the mode selection being achieved by reducing the truncation parameter. The threshold pump powers for different IG{sup e}(n, n) modes are theoretically calculated to illustrate the mode selection process. The pulsed IG{sup e}(n, n) (n ≥ 1) mode generation with a peak power exceeding 1 kW and a nanosecond pulse width is obtained in the PQS microchip laser, which is a potential laser source for forming flexible vortex arrays for optical tweezers. (control of laser radiation parameters)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
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↗
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↗
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↗
Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence
In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and highfidelity data using a parameterized GP with hyperparameters identified via optimization. Our approach reduces the cost of optimization for inferring hyperparameters by incorporating partial physical knowledge. We prove that the physical constraints in the form of deterministic linear operators are satisfied up to an error bound. Furthermore, we combine CoPhIK with a greedy active learning algorithm for guiding the selection of additional observation locations. The eciency and accuracy of CoPhIK are demonstrated for reconstructing the partially observed modified Branin function, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.
Yang, Xiu↗
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↗
A comparison between backscattering coefficients using Gaussian and non-Gaussian surface statistics
Backscattering coefficients computed using Gaussian and non-Gaussian surface statistics are compared. The computations are performed for a class of surface-height distributions and surface correlation functions. Results indicate that the coherent component of the scattering coefficient is strongly dependent upon the surface-height distribution. The noncoherent component also depends on the surface-height distribution and the surface root-mean-square (rms) slope when the rms surface height is large relative to the incident wavelength. On the other hand, when the surface rms height is moderate or small, the noncoherent component is sensitive mainly to the surface-height correlation function.
Eom, H. J.↗
Spin–phonon interactions in silicon carbide addressed by Gaussian acoustics [Probing spin-phonon interactions in silicon carbide with Gaussian acoustics]
Hybrid spin-mechanical systems provide a platform for integrating quantum registers and transducers. Efficient creation and control of such systems require a comprehensive understanding of the individual spin and mechanical components as well as their mutual interactions. Point defects in silicon carbide (SiC) offer long-lived, optically addressable spin registers in a wafer-scale material with low acoustic losses, making them natural candidates for integration with high quality factor mechanical resonators. Here, we show Gaussian focusing of a surface acoustic wave in SiC, characterized by a novel stroboscopic X-ray diffraction imaging technique, which delivers direct, strain amplitude information at nanoscale spatial resolution. Using ab initio calculations, we provide a more complete picture of spin-strain coupling for various defects in SiC with C 3v symmetry. This reveals the importance of shear for future device engineering and enhanced spin-mechanical coupling. We demonstrate all-optical detection of acoustic paramagnetic resonance without microwave magnetic fields, relevant to sensing applications. Lastly, we show mechanically driven Autler-Townes splittings and magnetically forbidden Rabi oscillations. These results offer a basis for full strain control of three-level spin systems.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗
Gaussian process regression as a surrogate model for the computation of dispersion relations
Not provided.
Engineering↗
Surrogate modeling of advanced computer simulations using deep Gaussian processes
Not provided.
Engineering↗
Gaussian fluctuation corrections to a mean-field theory of complex hidden order in URu 2 Si 2
Not Available
Shen, Pengtao↗