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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mapping Stellar Surfaces. II. An Interpretable Gaussian Process Model for Light Curves

The use of Gaussian processes (GPs) as models for astronomical time series data sets has recently become almost ubiquitous, given their ease of use and flexibility. In particular, GPs excel at marginalization over the stellar signal when the variability due to starspots is treated as a nuisance, as in exoplanet transit modeling. However, these effective models are less useful in cases where the starspot signal is of primary interest, since it is not obvious how the parameters of the GP relate to physical parameters like the spot size, contrast, and latitudinal distribution. Instead, it is common practice to explicitly model the effect of individual starspots on the light curve and attempt to infer their properties via optimization or posterior inference. Unfortunately, this process is ill-posed and often computationally intractable when applied to stars with more than a few spots and/or to ensembles of many stars. Here we derive a closed-form expression for a GP that describes the light curve of a rotating, evolving stellar surface conditioned on a given distribution of starspot sizes, contrasts, and latitudes. We demonstrate that this model is correctly calibrated, allowing one to robustly infer physical parameters of interest from one or more light curves, including the typical spot radii and latitudes. Our GP has far-ranging implications for understanding the variability and magnetic activity of stars from light curves and radial velocity measurements, as well as for modeling correlated noise in exoplanet searches. Our implementation is efficient, user-friendly, and open-source, available in the package starry-process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Tensor Basis Gaussian Process Models of Hyperelastic Materials

In this study, we develop Gaussian process regression (GPR) models of isotropic hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this approach that embeds rotational invariance of the stress-stretch constitutive relation in the GPR representation. This approach requires fewer training examples and achieves higher accuracy while maintaining invariance to rotations exactly. Finally, we consider an approach that recovers the strain-energy density function and derives the stress tensor from this potential. Although the error of this model for predicting the stress tensor is higher, the strain-energy density is recovered with high accuracy from limited training data. The approaches presented here are examples of physics-informed machine learning. They go beyond purely data-driven approaches by embedding the physical system constraints directly into the Gaussian process representation of materials models.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Abstract Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics‐based justification and have achieved promising performance. Two versions use LVs in Cartesian (LV‐Car) space and hyperspherical (LV‐sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed‐variable GP models, from which we conclude that the LV‐sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank‐based perspective like in the theorem, we propose a new alternative model named LV‐mix that combines the LV‐based correlation structures from both LV‐Car and LV‐sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV‐mix achieves higher average accuracy compared with the existing two.

Tao, Siyu↗
DOE OSTI2023

Physics-constrained Gaussian process model for prediction of hydrodynamic interactions between wave energy converters in an array

To improve the efficiency of wave farms and achieve maximum power generation, the layout of wave energy converters (WECs) in an array needs to be carefully designed so that the hydrodynamic interactions can be positively exploited. For this, the hydrodynamic characteristics of the WEC array in different layouts need to be calculated. However, such calculations using numerical models usually entail significant computational cost, especially for large arrays of WECs. To address the computational challenge, a physics-constrained Gaussian process (GP) model is proposed to replace the original expensive numerical model and predict the hydrodynamic characteristics of the WECs for any array layout. By exploring the relationship between the WEC array (i.e., the input) and different hydrodynamic characteristics (i.e., the output), here we summarize a set of physical constraints/features, including invariance, symmetry, and additivity. This prior knowledge about the input-output relationship is then directly embedded in the constructed GP model through the design of physics-constrained kernels. In particular, a double-sum invariant kernel is first developed to incorporate the invariance and symmetry features, and then an additive kernel is developed to incorporate the additive feature of the problem. The invariant kernel and the additive kernel are then integrated to construct the physics-constrained GP model. Compared to the standard GP model, the proposed physics-constrained GP models require less training data to achieve the desired accuracy in predicting the hydrodynamic characteristics and are also less vulnerable to the curse of dimensionality (i.e., good scalability for large arrays) due to the use of an additive kernel. The efficiency, accuracy, and scalability of the proposed approach are demonstrated through an application to predict the hydrodynamic characteristics for WEC arrays of different sizes and layouts.

16 TIDAL AND WAVE POWER↗
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 OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Genetic Algorithm for Hyperparameter Optimization in Gaussian Process Modeling

A genetic algorithm is developed and applied to optimize hyperparameters of convolutional recursively determined dual neural network-Gaussian process (NNGP) kernels. As a specific application of the combined GPNN-GA algorithm, it is applied to image classification in publicly available data of Hyper Suprime-Cam Subaru Strategic Program. Matthews correlation coefficient is calculated based on results of binary star-galaxy classification and used as a fitting function of the GA module of the algorithm. The simulation results confirm significant improvement of the classification accuracy with optimized hyperparameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Imaging mechanism for hyperspectral scanning probe microscopy via Gaussian process modelling

We investigate the ability to reconstruct and derive spatial structure from sparsely sampled 3D piezoresponse force microcopy data, captured using the band-excitation (BE) technique, via Gaussian Process (GP) methods. Even for weakly informative priors, GP methods allow unambiguous determination of the characteristic length scales of the imaging process both in spatial and frequency domains. We further show that BE data set tends to be oversampled in the spatial domains, with ~30% of original data set sufficient for high-quality reconstruction, potentially enabling faster BE imaging. At the same time, reliable reconstruction along the frequency domain requires the resonance peak to be within the measured band. This behavior suggests the optimal strategy for the BE imaging on unknown samples. Finally, we discuss how GP can be used for automated experimentation in SPM, by combining GP regression with non-rectangular scans.

47 OTHER INSTRUMENTATION↗
NASA NTRSDate not supplied

Multihierarchy Gaussian Process Models for Probabilistic Aerodynamic Databases using Uncertain Nominal and Off-Nominal Configuration Data

Probabilistic aerodynamic databases are a crucial component of the development lifecycle for aerospace vehicles. A key challenge when building aerodynamic databases is that most data used to construct them represent various simplifications of the real flight vehicle. For example, wind tunnel models often simplify the vehicle geometry and surface roughness characteristics, while CFD computations often make simplifications to the physics being modeled, such as fully laminar or turbulent calculations. Multifidelity data fusion models rely on a user being able to define a hierarchy of fidelity levels anchored to some "truth" data. This approach is unsatisfactory when no data can be considered to accurately reflect real flight conditions. In this work, we provide an alternative approach by presenting a consistent mathematical framework for building probabilistic aerodynamic databases in the form of a conditional probability distribution described by an ensemble of multifidelity Gaussian Processes. Instead of relying on a single hierarchy of data fidelity levels, the presented framework identifies a "nominal" configuration and potential corrections to the nominal which represent specific physical phenomena not represented in the nominal data. The nominal and correction functions themselves are constructed as multifidelity Gaussian Processes and linearly combined to form an ensemble model which fuses the uncertainties associated nominal and correction models. Results obtained using the proposed framework on a simplified Orion Crew Module wind tunnel dataset demonstrate the predictive capability of the multihierarchy framework. We further demonstrate the benefits of such a probabilistic aerodynamic database approach through function sampling and computing the conditional distributions of derived quantities, such as the trim angle of attack and aerodynamic coefficients at trim.

Gaussian Processes↗
DOE OSTI2024

Non-uniform active learning for Gaussian process models with applications to trajectory informed aerodynamic databases

The ability to non-uniformly weight the input space is desirable for many applications, and has been explored for space-filling approaches. Increased interests in linking models, such as in a digital twinning framework, increases the need for sampling emulators where they are most likely to be evaluated. In particular, here we apply non-uniform sampling methods for the construction of aerodynamic databases. This paper combines non-uniform weighting with active learning for Gaussian Processes (GPs) to develop a closed-form solution to a non-uniform active learning criterion. We accomplish this by utilizing a kernel density estimator as the weight function. We demonstrate the need and efficacy of this approach with an atmospheric entry example that accounts for both model uncertainty as well as the practical state space of the vehicle, as determined by forward modeling within the active learning loop.

42 ENGINEERING↗
DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗