Search NASA⌕ Search

SEARCH · Search NASA

Results for “Gaussian process”

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.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

K-means-driven Gaussian Process data collection for angle-resolved photoemission spectroscopy

Abstract We propose the combination of k-means clustering with Gaussian Process (GP) regression in the analysis and exploration of 4D angle-resolved photoemission spectroscopy (ARPES) data. Using cluster labels as the driving metric on which the GP is trained, this method allows us to reconstruct the experimental phase diagram from as low as 12% of the original dataset size. In addition to the phase diagram, the GP is able to reconstruct spectra in energy-momentum space from this minimal set of data points. These findings suggest that this methodology can be used to improve the efficiency of ARPES data collection strategies for unknown samples. The practical feasibility of implementing this technology at a synchrotron beamline and the overall efficiency implications of this method are discussed with a view on enabling the collection of more samples or rapid identification of regions of interest.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Star–Galaxy Image Separation with Computationally Efficient Gaussian Process Classification

Abstract We introduce a novel method for discerning optical telescope images of stars from those of galaxies using Gaussian processes (GPs). Although applications of GPs often struggle in high-dimensional data modalities such as optical image classification, we show that a low-dimensional embedding of images into a metric space defined by the principal components of the data suffices to produce high-quality predictions from real large-scale survey data. We develop a novel method of GP classification hyperparameter training that scales approximately linearly in the number of image observations, which allows for application of GP models to large-size Hyper Suprime-Cam Subaru Strategic Program data. In our experiments, we evaluate the performance of a principal component analysis embedded GP predictive model against other machine-learning algorithms, including a convolutional neural network and an image photometric morphology discriminator. Our analysis shows that our methods compare favorably with current methods in optical image classification while producing posterior distributions from the GP regression that can be used to quantify object classification uncertainty. We further describe how classification uncertainty can be used to efficiently parse large-scale survey imaging data to produce high-confidence object catalogs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Global Sensitivity Analysis of Large Distribution System with PVs using Deep Gaussian Process

Global sensitivity analysis (GSA) of the voltage to uncertain power injection variations plays an important role for appropriate Volt-VAR optimization. This paper proposes a data-driven GSA method for large-scale distribution systems with a large number of uncertain sources. Specifically, the deep Gaussian process is used to identify the mapping relationship between uncertain power injections and voltages. This allows us to resort to the analysis of variance framework to calculate the Sobol indices for GSA. Unlike the existing polynomial chaos expansion and Gaussian process-based approaches, our proposed method has much better scalability. Test results on the EPRI 1747-node K1 circuit with a different number and different probability distributions of uncertain sources demonstrate that the proposed method can achieve accurate GSA under various conditions.

14 SOLAR ENERGY↗
DOE OSTI2023

Parallel Implementation of Nonadditive Gaussian Process Potentials for Monte Carlo Simulations

A strategy is presented to implement Gaussian process potentials in molecular simulations through parallel programming. Attention is focused on the three-body nonadditive energy, though all algorithms extend straightforwardly to the additive energy. The method to distribute pairs and triplets between processes is general to all potentials. Results are presented for a simulation box of argon, including full box and atom displacement calculations, which are relevant to Monte Carlo simulation. Data on speed-up are presented for up to 120 processes across four nodes. A 4-fold speed-up is observed over five processes, extending to 20-fold over 40 processes and 30-fold over 120 processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Learning-Based Demand Response in Grid Interactive Buildings via Gaussian Processes

This paper presents a predictive controller for a grid-interactive multi-zone building where the temperature dynamics are learned via Gaussian Process (GP) regression. We investigate the development of a learning-based predictive control with two main objectives: (i) continuously learn the temperature dynamics of the building based on data; and, (ii) use the learned dynamics to solve a multi-objective predictive control problem to guarantee occupants' comfort and energy efficiency during normal conditions and demand response events. We leverage the probabilistic non-parametric properties of GPs to estimate the (unknown) non-linear temperature dynamics of the building and to incorporate the uncertainty of those predictions in a multi-objective optimization problem. The GP-based predictive control is solved via a zero-order primal-dual projected-gradient algorithm. We evaluate numerically the performance of the proposed controller using a five-zone commercial building.

demand response↗
DOE OSTI2024

Analytic Neural Network Gaussian Process Enabled Chance-Constrained Voltage Regulation for Active Distribution Systems with PVs, Batteries and EVs

This paper proposes an analytic neural network Gaussian process (NNGP)-based chance-constrained real-time voltage regulation method for active distribution systems with photovoltaics (PVs), batteries, and electric vehicles (EVs). NNGP can utilize historical measurement data to achieve real-time probabilistic node voltage estimation through Bayesian inference. Then, NNGP is fully analytically embedded into the optimal power flow model to perform voltage regulation and adapt to various topological changes. The uncertainties of voltage estimations are easily considered via the chance constraint, and it has been shown that the adoption of this chance constraint can significantly improve the reliability of voltage regulation under various scenarios. The comparison results with other methods, carried out on a real 759-node distribution system located in western Colorado, U.S., show that the proposed method can achieve accurate voltage estimation across different topologies and reliably perform voltage regulation considering PVs, batteries, and EVs.

active distribution systems↗
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 OSTI2025

Applying Gaussian Process Machine Learning and Modern Probabilistic Programming to Satellite Data to Infer CO 2 Emissions

Satellite data provides essential insights into the spatiotemporal distribution of CO 2 concentrations. However, many atmospheric inverse models fail to adequately incorporate the spatial and temporal correlations inherent in satellite observations and often lack rigorous methods for estimating parameters like spatial length scales. We introduce an inference model that processes the spatiotemporal covariance in satellite data and estimates hyperparameters such as covariance length scales. Our approach uses the Gaussian process (GP) machine learning (ML) and modern probabilistic programming languages (PPLs) to perform atmospheric inversions of emissions from satellite data. We develop a GP ML inversion system based on modern PPLs and the GEOS-Chem chemical transport model, simulating atmospheric CO 2 concentrations corresponding to the Orbiting Carbon Observatory-2/3 (OCO-2/3) data for July 2020. In our supervised learning framework, we treat the GEOS-Chem simulated data set as the target, with predictors derived by scaling the target with sector-specific factors hidden from the GP machine. Our results show that the GP model, combined with GPU-enabled PPLs, effectively retrieves true emission scaling factors and infers noise levels concealed within the data. This suggests that our method could be applied over larger areas with more complex covariance structures, enabling comprehensive analysis of the spatiotemporal patterns observed in OCO-2/3 and similar satellite data sets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Recursive Gaussian Process over graphs for Integrating Multi-timescale Measurements in Low-Observable Distribution Systems

The transition to a smarter grid is empowered by enhanced sensor deployments and smart metering infrastructure in the distribution system. Measurements from these sensors and meters can be used for many applications, including distribution system state estimation (DSSE). However, these measurements are typically sampled at different rates and could be intermittent due to losses during the aggregation process. These multi timescale measurements should be reconciled in real-time to perform accurate grid monitoring. This paper tackles this problem by formulating a recursive multi-task Gaussian process (RGP-G) approach that sequentially aggregates sensor measurements. Specifically, we formulate a recursive multi-task GP with and without network connectivity information to reconcile the multi time-scale measurements in distribution systems. Here, the proposed framework is capable of aggregating the multi-time scale measurements batch-wise or in real-time. Following the aggregation of the multi time-scale measurements, the spatial states of the consistent time-series are estimated using matrix completion based DSSE approach. Simulation results on IEEE 37 and IEEE 123 bus test systems illustrate the efficiency of the proposed methods from the standpoint of both multi time-scale data aggregation and DSSE.

42 ENGINEERING↗
DOE OSTI2023

Exact Gaussian processes for massive datasets via non-stationary sparsity-discovering kernels

Abstract A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. Its success is largely attributed to the GP’s analytical tractability, robustness, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $$O(N^3)$$ O ( N 3 ) in computation and $$O(N^2)$$ O ( N 2 ) in storage. All existing methods addressing this issue utilize some form of approximation—usually considering subsets of the full dataset or finding representative pseudo-points that render the covariance matrix well-structured and sparse. These approximate methods can lead to inaccuracies in function approximations and often limit the user’s flexibility in designing expressive kernels. Instead of inducing sparsity via data-point geometry and structure, we propose to take advantage of naturally-occurring sparsity by allowing the kernel to discover—instead of induce—sparse structure. The premise of this paper is that the data sets and physical processes modeled by GPs often exhibit natural or implicit sparsities, but commonly-used kernels do not allow us to exploit such sparsity. The core concept of exact, and at the same time sparse GPs relies on kernel definitions that provide enough flexibility to learn and encode not only non-zero but also zero covariances. This principle of ultra-flexible, compactly-supported, and non-stationary kernels, combined with HPC and constrained optimization, lets us scale exact GPs well beyond 5 million data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A crystal-plasticity-informed Gaussian Process Regression model to capture anisotropy in single crystal shape memory alloys

This work presents a machine learning (ML) framework that model the anisotropic actuation responses in a shape memory alloy. A Gaussian Process Regression (GPR) based ML model is trained on a set of different crystal orientations subjected to different actuation conditions. The training employed thermo-mechanical responses from a crystal-plasticity model that captures phase-transformation, stress-induced plasticity, and transformation-induced plasticity. Further, on training the GPR-ML model at fixed stress level for different orientations, it captured the thermo-mechanical responses accounting for the anisotropy, and predicted responses for new orientations with good accuracy. The GPR-ML model is able to capture the transformation temperature variations even when trained using multiple stress levels, and the transformation strain showed significant deviations. The developed GPR-ML model gave reasonable predictions for an unexplored sample set of orientations and loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Cleaning Images with Gaussian Process Regression

Many approaches to astronomical data reduction and analysis cannot tolerate missing data: corrupted pixels must first have their values imputed. This paper presents astrofix, a robust and flexible image imputation algorithm based on Gaussian process regression. Through an optimization process, astrofix chooses and applies a different interpolation kernel to each image, using a training set extracted automatically from that image. It naturally handles clusters of bad pixels and image edges and adapts to various instruments and image types. For bright pixels, the mean absolute error of astrofix is several times smaller than that of median replacement and interpolation by a Gaussian kernel. We demonstrate good performance on both imaging and spectroscopic data, including the SBIG 6303 0.4 m telescope and the FLOYDS spectrograph of Las Cumbres Observatory and the CHARIS integral-field spectrograph on the Subaru Telescope.

42 ENGINEERING↗
DOE OSTI2021

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

Abstract We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student- t observations; (ii) Student- t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes

Uncertainty propagation in complex engineering systems often poses significant computational challenges related to modeling and quantifying probability distributions of model outputs, as those emerge as the result of various sources of uncertainty that are inherent in the system under investigation. Gaussian Processes regression (GPs) is a robust meta-modeling technique that allows for fast model prediction and exploration of response surfaces. Multi-fidelity variations of GPs further leverage information from cheap and low fidelity model simulations in order to improve their predictive performance on the high fidelity model. In order to cope with the high volume of data required to train GPs in high dimensional design spaces, a common practice is to introduce latent design variables that are typically projections of the original input space to a lower dimensional subspace, and therefore substitute the problem of learning the initial high dimensional mapping, with that of training a GP on a low dimensional space. Here in this paper, we present a Bayesian approach to identify optimal transformations that map the input points to low dimensional latent variables. The \projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to be inferred jointly with the GP parameters, conditioned on the available training data. The proposed Bayesian inference scheme relies on a two-step iterative algorithm that samples from the marginal posteriors of the GP parameters and the projection matrix respectively, both using Markov Chain Monte Carlo (MCMC) sampling. In order to take into account the orthogonality constraints imposed on the orthonormal projection matrix, a Geodesic Monte Carlo sampling algorithm is employed, that is suitable for exploiting probability measures on manifolds. We extend the proposed framework to multi-fidelity models using GPs including the scenarios of training multiple outputs together. We validate our framework on three synthetic problems with a known lower-dimensional subspace. The benefits of our proposed framework, are illustrated on the computationally challenging aerodynamic optimization of a last-stage blade for an industrial gas turbine, where we study the effect of an 85-dimensional shape parameterization of a three-dimensional airfoil on two output quantities of interest, specifically on the aerodynamic efficiency and the degree of reaction

42 ENGINEERING↗
DOE OSTI2021

Conditioned Simulation of Ground-Motion Time Series at Uninstrumented Sites Using Gaussian Process Regression

Ground-motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free-field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground-motion recording instrumentation. In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics-based simulated ground motions of the 1906 Mw 7.9 San Francisco earthquake and Mw 7.0 Hayward fault scenario earthquake in northern California. Additionally, the method’s performance is further evaluated using the 2019 Mw 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground-motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long-period content of the ground motions as well as directivity pulses.

58 GEOSCIENCES↗
DOE OSTI2020

Storage ring nonlinear dynamics optimization with multi-objective multi-generation Gaussian process optimizer

Nonlinear beam dynamics optimization is essential in a low emittance storage ring design. Multi-objective optimization algorithms are needed in order to simultaneously optimize the dynamic aperture and the momentum aperture. In this study we demonstrate the application of a highly efficient stochastic optimization algorithm, the multi-generation Gaussian process optimizer (MG-GPO), to storage ring nonlinear dynamics optimization by successfully applying the method to the SPEAR3 upgrade lattice. It is shown that the new method, owing to its capability of selecting high rank candidates from a large number of trial solutions, converges significantly faster than the commonly used traditional algorithms, multi-objective genetic algorithms (MOGA) and particle swarm optimization (PSO).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

A Gaussian process guide for signal regression in magnetic fusion

Extracting reliable information from diagnostic data in tokamaks is critical for understanding, analyzing, and controlling the behavior of fusion plasmas and validating models describing that behavior. Recent interest within the fusion community has focused on the use of principled statistical methods, such as Gaussian process regression (GPR), to attempt to develop sharper, more reliable, and more rigorous tools for examining the complex observed behavior in these systems. While GPR is an enormously powerful tool, there is also the danger of drawing fragile, or inconsistent conclusions from naive GPR fits that are not driven by principled treatments. Here we review the fundamental concepts underlying GPR in a way that may be useful for broad-ranging applications in fusion science. We also revisit how GPR is developed for profile fitting in tokamaks. We examine various extensions and targeted modifications applicable to experimental observations in the edge of the DIII-D tokamak. Finally, we discuss best practices for applying GPR to fusion data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗