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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Hayes, Kyle↗
DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fast Scanning Probe Microscopy via Machine Learning: Non-Rectangular Scans with Compressed Sensing and Gaussian Process Optimization

Fast scanning probe microscopy enabled via machine learning allows for a broad range of nanoscale, temporally resolved physics to be uncovered. However, such examples for functional imaging are few in number. Here, using piezoresponse force microscopy (PFM) as a model application, a factor of 5.8 reduction in data collection using a combination of sparse spiral scanning with compressive sensing and Gaussian process regression reconstruction is demonstrated. It is found that even extremely sparse spiral scans offer strong reconstructions with less than 6% error for Gaussian process regression reconstructions. Further, the error associated with each reconstructive technique per reconstruction iteration is analyzed, finding the error is similar past ≈15 iterations, while at initial iterations Gaussian process regression outperforms compressive sensing. Finally, this study highlights the capabilities of reconstruction techniques when applied to sparse data, particularly sparse spiral PFM scans, with broad applications in scanning probe and electron microscopies.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accurate and uncertainty-aware multi-task prediction of HEA properties using prior-guided deep Gaussian processes

Surrogate modeling techniques have become indispensable in accelerating the discovery and optimization of high-entropy alloys (HEAs), especially when integrating computational predictions with sparse experimental observations. This study systematically evaluates the training and testing performance of four prominent surrogate models—conventional Gaussian processes (cGP), Deep Gaussian processes (DGP), encoder-decoder neural networks for multi-output regression and eXtreme Gradient Boosting (XGBoost)—applied to a hybrid dataset of experimental and computational properties of the 8-component HEA system Al-Co-Cr-Cu-Fe-Mn-Ni-V. We specifically assess their capabilities in predicting correlated material properties, including yield strength, hardness, modulus, ultimate tensile strength, elongation, and average hardness under dynamic/quasi-static conditions, alongside auxiliary computational properties. The comparison highlights the strengths of hierarchical deep modeling approaches in handling heteroscedastic, heterotopic, and incomplete data commonly encountered in materials science. Our findings illustrate that combined surrogate models such as DGPs infused with machine-learned priors outperform other surrogates by effectively capturing inter-property correlations and by assimilating prior knowledge. This enhanced predictive accuracy positions the combined surrogate models as powerful tools for robust and data-efficient materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Gaussian Process Classification for Galaxy Blend Identification in LSST

Abstract A significant fraction of observed galaxies in the Rubin Observatory Legacy Survey of Space and Time (LSST) will overlap at least one other galaxy along the same line of sight, in a so-called “blend.” The current standard method of assessing blend likelihood in LSST images relies on counting up the number of intensity peaks in the smoothed image of a blend candidate, but the reliability of this procedure has not yet been comprehensively studied. Here we construct a realistic distribution of blended and unblended galaxies through high-fidelity simulations of LSST-like images, and from this we examine the blend classification accuracy of the standard peak-finding method. Furthermore, we develop a novel Gaussian process blend classifier model, and show that this classifier is competitive with both the peak finding method as well as with a convolutional neural network model. Finally, whereas the peak-finding method does not naturally assign probabilities to its classification estimates, the Gaussian process model does, and we show that the Gaussian process classification probabilities are generally reliable.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRSDate not supplied

A Gaussian Process Enhancement to Linear Parameter Varying Models

Simulation and analysis for modern engineering systems now routinely requires the merging of multiple disciplines, physical-domains, time-scales, and data sets — all at ever increasing levels. These capabilities are especially needed in the domain of Advanced Air Mobility, where rapidly emerging vehicle designs are significantly more complex, while having to be both cost-effective and safe. To meet these engineering challenges, machine learning methods are an attractive option for merging models and data across multiple areas while providing uncertainty quantification and maintaining computational efficiency. This paper examines the use of Gaussian process machine learning to generalize and enhance the commonly used class of quasi-Linear Parameter Varying models for fast full-envelope simulation while also supporting control system design and analysis with model uncertainty. Gaussian process machine learning is selected because it: can fuse multiple data sets, enables an easy trade-off between data fitting and smoothing, provides model uncertainty quantification, scales well with increasing complexity, and does not generally require starting from a large training data set. To demonstrate the benefits of the approach, a robust stability analysis with Gaussian process uncertainty is shown for a NASA reference design of an electric quad-rotor air-taxi concept vehicle with motor parameter uncertainty.

Gaussian Process↗
DOE OSTI2026

Extracting the Breakout Distance from the ECOT Trajectories: Gaussian Process Regression Approach

Enhanced Corner Turning (ECOT) experiments provide an important metric of performance of high explosive (HE) formulations. The breakout distance is a single scalar value that characterizes the corner turning efficiency of an HE. Extracting the breakout distance from the raw ECOT results, whether experimental or simulated, is a conceptually straightforward procedure which, however, is non-unique, especially in the presence of noise. More specifically, this procedure involves numerical smoothing and selecting particular values for parameters of this smoothing introduces human bias. In this work, we propose to use the Gaussian process regression to analyze ECOT results. This analysis involves the effective smoothing of the data, thus allowing for accurate extraction of the breakout distance. Most importantly, the parameters of this smoothing can be inferred from the ECOT data itself, rendering the approach effectively parameter-free and thus diminishing the human bias. An additional benefit of the Gaussian process regression, being a statistical inference method, is that not just the value of the breakout distance, but also its confidence interval can be extracted from the data. This report introduces the Gaussian process regression, as applied to ECOT, and demonstrates its usefulness by extracting the breakout distances for a selection of experimental and simulated data.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Multi-fidelity modeling to predict the rheological properties of a suspension of fibers using neural networks and Gaussian processes

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications. There are multiple factors, such as fiber aspect ratio and volume fraction, that play a significant role in altering the rheological behavior of suspensions. Three-dimensional (3D) numerical simulations of coupled differential equations of the suspension of fibers are computationally expensive and time-consuming. Machine learning algorithms can be trained on the available data and make predictions for the cases where no numerical data are available. However, some widely used machine learning surrogates, such as neural networks, require a relatively large training dataset to produce accurate predictions. Multi-fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified constitutive equations, can pave the way for more accurate predictions. Here, we focus on neural networks and the Gaussian processes with two levels of fidelity, i.e., high and low fidelity networks, to predict the steady-state rheological properties, and compare them to the single-fidelity network. High-fidelity data are obtained from direct numerical simulations based on an immersed boundary method to couple the fluid and solid motion. The low-fidelity data are produced by using constitutive equations. Multiple neural networks and the Gaussian process structures are used for the hyperparameter tuning purpose. Results indicate that with the best choice of hyperparameters, both the multi-fidelity Gaussian processes and neural networks are capable of making predictions with a high level of accuracy with neural networks demonstrating marginally better performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Wide neural networks with bottlenecks are deep Gaussian processes

There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not apply to architectures that require one or more of the hidden layers to remain narrow. In this paper, we consider the wide limit of BNNs where some hidden layers, called "bottlenecks", are held at finite width. The result is a composition of GPs that we term a "bottleneck neural network Gaussian process" (bottleneck NNGP). Although intuitive, the subtlety of the proof is in showing that the wide limit of a composition of networks is in fact the composition of the limiting GPs. We also analyze theoretically a single-bottleneck NNGP, finding that the bottleneck induces dependence between the outputs of a multi-output network that persists through extreme post-bottleneck depths, and prevents the kernel of the network from losing discriminative power at extreme post-bottleneck depths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gaussian processes for autonomous data acquisition at large-scale synchrotron and neutron facilities

The execution and analysis of complex experiments are challenged by the vast dimensionality of the underlying parameter spaces. Although an increase in data-acquisition rates should allow broader querying of the parameter space, the complexity of experiments and the subtle dependence of the model function on input parameters remains daunting owing to the sheer number of variables. New strategies for autonomous data acquisition are being developed, with one promising direction being the use of Gaussian process regression (GPR). GPR is a quick, non-parametric and robust approximation and uncertainty quantification method that can be applied directly to autonomous data acquisition. We review GPR-driven autonomous experimentation and illustrate its functionality using real-world examples from large experimental facilities in the USA and France. We introduce the basics of a GPR-driven autonomous loop with a focus on Gaussian processes, and then shift the focus to the infrastructure that needs to be built around GPR to create a closed loop. Finally, the case studies we discuss show that Gaussian-process-based autonomous data acquisition is a widely applicable method that can facilitate the optimal use of instruments and facilities by enabling the efficient acquisition of high-value datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with intractable likelihoods, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in nonconvex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.

Bayesian inference↗
DOE OSTI2023

Multi-Fidelity Gaussian Process for Distribution System Voltage Probabilistic Estimation with PVs

The increasing penetration of behind-the-meter PVs causes challenges to maintain voltage security due to the lack of distribution system visibility. This paper proposes a nonlinear autoregressive Gaussian process (NARGP) approach to fuse limited number of SCADA/AMI data together with historical pseudo measurements for distribution node voltage probabilistic estimation. The high-fidelity SCADA data are fused with the low-fidelity AMI and pseudo measurements by the autoregressive algorithm embedded in the Gaussian process. This allows us to use multi-fidelity data to achieve entire distribution system voltage visibility. Numerical results carried out on the IEEE 123node system demonstrate that the NARGP method is able to obtain high accuracy in estimating bus voltage and quantifying estimation uncertainties as compared to other approaches.

distribution system estimation↗
DOE OSTI2022

Single Gaussian process method for arbitrary tokamak regimes with a statistical analysis

Abstract Gaussian process regression is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including intrinsic uncertainty quantification and robustness to over-fitting. This work investigates the use of a new method, the change-point method, for handling the varying length scales found in different tokamak regimes. The use of the Student’s t-distribution for the Bayesian likelihood probability is also investigated and shown to be advantageous in providing good fits in profiles with many outliers. To compare different methods, synthetic data generated from analytic profiles is used to create a database enabling a quantitative statistical comparison of which methods perform the best. Using a full Bayesian approach with the change-point method, Matérn kernel for the prior probability, and Student’s t-distribution for the likelihood is shown to give the best results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The PAU Survey: narrow-band photometric redshifts using Gaussian processes

Here, we study the performance of the hybrid template machine learning photometric redshift (photo- z ) algorithm delight , which uses Gaussian processes, on a subset of the early data release of the Physics of the Accelerating Universe Survey (PAUS). We calibrate the fluxes of the 40 PAUS narrow bands with six broad-band fluxes ( uBVriz ) in the Cosmic Evolution Survey (COSMOS) field using three different methods, including a new method that utilizes the correlation between the apparent size and overall flux of the galaxy. We use a rich set of empirically derived galaxy spectral templates as guides to train the Gaussian process, and we show that our results are competitive with other standard photometric redshift algorithms. delight achieves a photo- z 68th percentile error of σ 68 = 0.0081(1 + z ) without any quality cut for galaxies with i auto < 22.5 as compared to 0.0089(1 + z ) and 0.0202(1 + z ) for the bpz and annz 2 codes, respectively. delight is also shown to produce more accurate probability distribution functions for individual redshift estimates than bpz and annz 2. Common photo- z outliers of delight and bcnz 2 (previously applied to PAUS) are found to be primarily caused by outliers in the narrow-band fluxes, with a small number of cases potentially indicating spectroscopic redshift failures in the reference sample. In the process, we introduce performance metrics derived from the results of bcnz 2 and delight , allowing us to achieve a photo- z quality of σ 68 < 0.0035(1 + z ) at a magnitude of i auto < 22.5 while keeping 50 per cent objects of the galaxy sample.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Incorporating physical constraints into Gaussian process surrogate models (LDRD Project Summary)

This report summarizes work done under the Laboratory Directed Research and Development (LDRD) project titled "Incorporating physical constraints into Gaussian process surrogate models?' In this project, we explored a variety of strategies for constraint implementations. We considered bound constraints, monotonicity and related convexity constraints, Gaussian processes which are constrained to satisfy linear operator constraints which represent physical laws expressed as partial differential equations, and intrinsic boundary condition constraints. We wrote three papers and are currently finishing two others. We developed initial software implementations for some approaches. This report summarizes the work done under this LDRD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Gaussian Process Prediction with MuyGPs

This code provides fast Gaussian process prediction algorithms based on the MuyGPs scalable hyperparameter optimization algorithm. This code is the companion to a research paper preprint soon to be made publicly available.

Priest, BenjaminW↗