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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2021

A Gaussian Process Regression Reveals No Evidence for Planets Orbiting Kapteyn’s Star

Radial–velocity (RV) planet searches are often polluted by signals caused by gas motion at the star’s surface. Stellar activity can mimic or mask changes in the RVs caused by orbiting planets, resulting in false positives or missed detections. Here we use Gaussian process regression to disentangle the contradictory reports of planets versus rotation artifacts from Kapteyn’s star. To model rotation, we use joint quasiperiodic kernels for the RV and Hα signals, requiring that their periods and correlation timescales be the same. We find that the rotation period of Kapteyn’s star is 125 days, while the characteristic active-region lifetime is 694 days. Adding a planet to the RV model produces a best-fit orbital period of 100 yr, or 10 times the observing time baseline, indicating that the observed RVs are best explained by star rotation only. We also find no significant periodic signals in residual RV data sets constructed by subtracting off realizations of the best-fit rotation model and conclude that both previously reported “planets” are artifacts of the star’s rotation and activity. Our results highlight the pitfalls of using sinusoids to model quasiperiodic rotation signals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Efficient Active Learning for Gaussian Process Classification by Error Reduction

Active learning sequentially selects the best instance for labeling by optimizing an acquisition function to enhance data/label efficiency. The selection can be either from a discrete instance set (pool-based scenario) or a continuous instance space (query synthesis scenario). In this work, we study both active learning scenarios for Gaussian Process Classification (GPC). The existing active learning strategies that maximize the Estimated Error Reduction (EER) aim at reducing the classification error after training with the new acquired instance in a onestep-look-ahead manner. The computation of EER-based acquisition functions is typically prohibitive as it requires retraining the GPC with every new query. Moreover, as the EER is not smooth, it can not be combined with gradient-based optimization techniques to efficiently explore the continuous instance space for query synthesis. To overcome these critical limitations, we develop computationally efficient algorithms for EER-based active learning with GPC. Further, we derive the joint predictive distribution of label pairs as a one-dimensional integral, as a result of which the computation of the acquisition function avoids retraining the GPC for each query, remarkably reducing the computational overhead. We also derive the gradient chain rule to efficiently calculate the gradient of the acquisition function, which leads to the first query synthesis active learning algorithm implementing EER-based strategies. Our experiments clearly demonstrate the computational efficiency of the proposed algorithms. We also benchmark our algorithms on both synthetic and real-world datasets, which show superior performance in terms of sampling efficiency compared to the existing state-of-the-art algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussian process classification on Riemannian manifolds to efficiently determine the regions in the atria where arrhythmias are inducible. We build a probabilistic classifier that operates directly on the atrial surface. We take advantage of lower resolution models to explore the atrial surface and combine seamlessly with high-resolution models to identify regions of inducibility. We test our methodology in 9 different cases, with different levels of fibrosis and ablation treatments, totalling 1,800 high resolution and 900 low resolution simulations of atrial fibrillation. When trained with 40 samples, our multi-fidelity classifier that combines low and high resolution models, shows a balanced accuracy that is, on average, 5.7% higher than a nearest neighbor classifier. We hope that this new technique will allow faster and more precise clinical applications of computational models for atrial fibrillation. All data and code accompanying this manuscript will be made publicly available at: https://github.com/fsahli/AtrialMFclass.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Gaussian Process Modeling For Experimental Procedure Uncertainty

Many laboratory experiments generate data that are characterized by a form of uncertainty that differs from noise: experimental procedure uncertainty. The origin of this type of uncertainty is the difficulty in controlling a subset of experimental conditions in such a way that the experiment is perfectly reproducible within noise. In this report, we describe a Gaussian Process modeling-based method that accounts for experimental procedure uncertainty. The method accounts for variations in conditions from experiment to experiment that are independent between experiments, but correlated within each experiment, and incorporates the resulting uncertainty into predictions at future experimental settings. The method is discussed in the context of a specific chemistry application in which Raman scattering spectra are measured from three-component mixtures.

42 ENGINEERING↗
DOE OSTI2023

O’Hare Airport Short-Term Ground Transportation Modal Demand Forecast Using Gaussian Processes

Here, the principal objective of this study is to analyze the spatial and temporal variation of ground transportation airport demand and provide demand forecast to inform planning capability and explore alternatives for investments to accommodate airport growth. Because of its good adaptability and strong generalization ability for dealing with high-dimensional input, small-sample, and nonlinear spatial data, Gaussian process (GP) regression is used to provide forecast estimates using data from transportation network company (TNC) trips and urban rail passengers at Chicago's O'Hare International Airport. TNC airport trips differ significantly, with three times more distance, more than twice the travel time, and half of the share requests compared with nonairport trips. This highlights the need for separate demand models. Hourly analysis of the rail service indicates that this is likely heavily used by airport workers, whereas TNC services focus on travelers because of variations in the peak demand hours. Heteroscedastic GP regression is implemented because of differences in trip variance between night and day hours. Estimates are given for weekdays and weekend trips, and the 95% confidence intervals are calculated. The introduction of flight schedule information into the models shows marginal improvements in their performance. However, fitting a GP regression becomes computationally expensive with increased sample size and the introduction of spatial components. Transportation planners and policymakers can use the results and methods implemented in this study to optimize transportation assets and provide long-range simulations of the current and future conditions in the area.

42 ENGINEERING↗
DOE OSTI2022

Scalable Gaussian Processes, GPyTorch Application Benchmarking, and Targeted Adaptive Design (TAD) on ThetaGPU

We aim at showcasing the scalability of Gaussian Process (GP). The naive GP implementation scales cubically with data size, which can be prohibitive, so GP has not heretofore been considered suitable for very large-scale problem settings. We take advantage of GPyTorch, a library for scalable GPs built on top of PyTorch that incorporates GPU acceleration. With GPyTorch, one can achieve nearly linear scaling with structured kernel interpolation (SKI) and constant-time predictive covariances computation with LanczOs Variance Estimates (LOVE) while preserving accuracy. We also take advantage of the computational power of ThetaGPU, a supercomputer of Argonne Leadership Computing Facility (ALCF). In addition, we implement a scalable, GPU-ready version of Targeted Adaptive Design (TAD), a GP-based data-driven algorithm that efficiently searches the control space of an advanced manufacturing experiment for settings capable of producing a required design within a specified tolerance, despite the poorly known mapping from control settings to design. We finally show our benchmarking for GPyTorch and TAD performance on CPU vs. ThetaGPU and discuss the results and implications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar Radial Velocities

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m s{sup −1}. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass (∼0.5 m s{sup −1}) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus (∼0.1 m s{sup −1}) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

O'Hare Airport roadway traffic prediction via data fusion and Gaussian process regression

This study proposes an approach of leveraging information gathered from multiple traffic data sources at different resolutions to obtain approximate inference on the traffic distribution of Chicago's O'Hare Airport area. Specifically, it proposes the ingestion of traffic datasets at different resolutions to build spatiotemporal models for predicting the distribution of traffic volume on the road network. Due to its good adaptability and flexibility for spatiotemporal data, the Gaussian process (GP) regression was employed to provide short-term forecasts using data collected by loop detectors (sensors) and supplemented by telematics data. The GP regression is used to make predictions of the distribution of the proportion of sensor data traffic volume represented by the telematics data for each location of the sensors. Consequently, the fitted GP model can be used to determine the approximate traffic distribution for a testing location outside of the training points. Policymakers in the transportation sector can find the results of this work helpful for making informed decisions relating to current and future transportation conditions in the area.

42 ENGINEERING↗
DOE OSTI2020

Dynamical Mass Estimates of the β Pictoris Planetary System through Gaussian Process Stellar Activity Modeling

Nearly 15 yr of radial velocity (RV) monitoring and direct imaging enabled the detection of two giant planets orbiting the young, nearby star β Pictoris. The δ Scuti pulsations of the star, which overwhelm planetary signals, need to be carefully suppressed. In this work, we independently revisit the analysis of the RV data following a different approach than available in the literature to model the activity of the star. We show that a Gaussian process (GP) with a stochastically driven damped harmonic oscillator kernel can model the δ Scuti pulsations. It provides similar results to parametric models but with a simpler framework, using only three hyperparameters. It also enables us to model poorly sampled RV data that were excluded from previous analyses, hence extending the RV baseline by nearly five years. Altogether, the orbit and mass of both planets can be constrained from RV only, which was not possible with the parametric modeling. To characterize the system more accurately, we also perform a joint fit of all available relative astrometry and RV data. Our orbital solutions for β Pic b favor a low eccentricity of 0.029$_{−0.024}^{+0.061}$ and a relatively short period of 21.1$_{−0.8}^{+2.0}$ yr. The orbit of β Pic c is eccentric with 0.206$_{−0.063}^{+0.074}$ with a period of 3.36 ± 0.03 yr. We find model-independent masses of 11.7 ± 1.4 and 8.5 ± 0.5 M Jup for β Pic b and c, respectively, assuming coplanarity. The mass of β Pic b is consistent with the hottest start evolutionary models, at an age of 25 ± 3 Myr. A direct detection of β Pic c would provide a second calibration measurement in a coeval system.

79 ASTRONOMY AND ASTROPHYSICS↗