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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A Fast, Two-dimensional Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization

Gaussian processes (GPs) are commonly used as a model of stochastic variability in astrophysical time series. In particular, GPs are frequently employed to account for correlated stellar variability in planetary transit light curves. The efficient application of GPs to light curves containing thousands to tens of thousands of data points has been made possible by recent advances in GP methods, including the celerite method. Here we present an extension of the celerite method to two input dimensions where, typically, the second dimension is small. This method scales linearly with the total number of data points when the noise in each large dimension is proportional to the same celerite kernel and only the amplitude of the correlated noise varies in the second dimension. We demonstrate the application of this method to the problem of measuring precise transit parameters from multiwavelength light curves and show that it has the potential to improve transit parameters measurements by orders of magnitude. Applications of this method include transit spectroscopy and exomoon detection, as well a broader set of astronomical problems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Reinforcement Learning via Gaussian Processes with Neural Network Dual Kernels

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. Finally, we conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Gaussian-process generative model for the QCD equation of state

We develop a generative model for the nuclear matter equation of state at zero net baryon density using the Gaussian process regression method. We impose first-principles theoretical constraints from lattice quantum chromodynamics and hadron resonance gas at high- and low-temperature regions, respectively. By allowing the trained Gaussian process regression model to vary freely near the phase transition region, we generate random smooth crossover equations of state with different speeds of sound that do not rely on specific parametrizations. Here, we explore a collection of experimental observable dependencies on the generated equations of state, which paves the groundwork for future Bayesian inference studies to use experimental measurements from relativistic heavy-ion collisions to constrain the nuclear matter equation of state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Landmark-embedded Gaussian process with applications for functional data modeling

In practice, we often need to infer the value of a target variable from functional observation data. A challenge in this task is that the relationship between the functional data and the target variable is very complex: the target variable not only influences the shape but also the location of the functional data. In addition, due to the uncertainties in the environment, the relationship is probabilistic, that is, for a given fixed target variable value, we still see variations in the shape and location of the functional data. To address this challenge, we present a landmark-embedded Gaussian process model that describes the relationship between the functional data and the target variable. A unique feature of the model is that landmark information is embedded in the Gaussian process model so that both the shape and location information of the functional data are considered simultaneously in a unified manner. Gibbs-Metropolis-Hasting algorithm is used for model parameters estimation and target variable inference. The performance of the proposed framework is evaluated by extensive numerical studies and a case study of nano-sensor calibration.

42 ENGINEERING↗
DOE OSTI2022

Bayesian Active Learning for Scanning Probe Microscopy: From Gaussian Processes to Hypothesis Learning

Recent progress in machine learning methods and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs) have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. Here, the discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods and can be particularly impactful for destructive or irreversible measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Gaussian processes for inferring parton distributions

The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback-Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.

hadronic spectroscopy↗
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↗
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

Exploration with Scalable Gaussian Process Reinforcement Learning

Exploration is a challenging problem in reinforcement learning (RL), especially in environments with sparse rewards. Quantifying and utilizing the parametric uncertainty has been shown to be paramount for successful exploration [Osband et al., 2018]. Bayesian, or approximately Bayesian, methods present a principled means of estimating the parametric uncertainty in RL problems. Gaussian processes, nonparametric Bayesian models, are often impractical due to poor scalability and computational bottlenecks. We introduce a scalable Gaussian process RL (GPRL) method which directly induces sparsity in the covariance matrix to facilitate faster computation. This is a departure from previous GPRL methods which instead rely on data reduction and subsampling. We compare various covariance-based exploration techniques (Thompson sampling, upper confidence bound, and probabilistic maximum variance) which leverage our scalable GP framework in sparse reward environments. Finally, we show favorable comparison against the bootstrapped deep Q-Network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modelling stellar activity with Gaussian process regression networks

ABSTRACT Stellar photospheric activity is known to limit the detection and characterization of extrasolar planets. In particular, the study of Earth-like planets around Sun-like stars requires data analysis methods that can accurately model the stellar activity phenomena affecting radial velocity (RV) measurements. Gaussian Process Regression Networks (GPRNs) offer a principled approach to the analysis of simultaneous time series, combining the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian Processes. Using HARPS-N solar spectroscopic observations encompassing three years, we demonstrate that this framework is capable of jointly modelling RV data and traditional stellar activity indicators. Although we consider only the simplest GPRN configuration, we are able to describe the behaviour of solar RV data at least as accurately as previously published methods. We confirm the correlation between the RV and stellar activity time series reaches a maximum at separations of a few days, and find evidence of non-stationary behaviour in the time series, associated with an approaching solar activity minimum.

Camacho, J. D. (ORCID:0000000151215560)↗
DOE OSTI2026

Taming nuclear mass models with Gaussian processes

We propose a new set of nuclear mass predictions based on multiple theoretical mass models. By employing Gaussian process regression with the Matérn kernel, we achieved root-mean-square (rms) deviations below 100 keV for the training dataset. The best-performing mass models achieved rms deviations below 150 keV for the new precise mass data from AME2020, whereas the ensemble average showed robust performance across the nuclear chart. Our approach uniquely combines: (1) systematic refinement of eight mass models through their residuals, (2) physics-informed features, including magic numbers, nucleon parity numbers, neutron excess, and nuclear collectivity, and (3) theory-to-theory validation demonstrating robust extrapolation capability. We find that the Matérn kernel provides superior uncertainty quantification compared to the RBF kernel, with a length-scale analysis revealing enhanced inter-nuclei correlations. We provide complete mass predictions for all unknown nuclides in AME2020, offering valuable constraints for nuclear structure studies and astrophysical modeling when used with proper uncertainty propagation.

Gaussian processes↗
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 OSTI2022

Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

Chemistry↗
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

Gaussian Process Optimization of Sensitivity-Based Similarity Metrics between New Nuclear Applications and New/Existing Benchmarks [Slides]

This presentation discusses Nuclear Criticality Safety (NCS) and how designing safe, new nuclear criticality experiments requires expert judgement, which could take years of experience. Sensitivity/uncertainty (S/U) analysis can be utilized by less experienced individuals to conservatively estimate uncertainties in important parameters, such as k eff , in newly proposed nuclear experiments. The presentation poses the question of how this analysis can be performed and states that the answer lies in matching new nuclear experiments with existing benchmark experiments using similarity metrics. By increasing the criticality safety of the application in this work, higher mass limits could be used in PF-4 operations. Additionally, the presentation discusses MCNP6.2®, Whisper-1.1, the software that can be used in this analysis. Also discussed is the fact that International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmarks rarely match new nuclear applications and that there are significant differences in given set of materials and/or geometry. If there are no benchmarks that match the application, the presentation discusses the possibility of creating new benchmarks. In conclusion, this work presents a Gaussian process (GP) optimization scheme that was used to generate new benchmarks with the highest sensitivity-based similarity metrics to user-defined nuclear applications. The Gaussian process optimization successfully designed 3 new experimental benchmarks that were highly correlated to the application of interest and had k eff values near critical. Optimization over c k,i-r has shown that investigating specific isotope reactions for different applications is crucial to designing benchmark experiments. Partial contribution from Pu dominates c k similarity metric. Future work includes testing new stand-alone similarity metrics or new combinations of similarity metrics as the design criterion of this optimization – design criterion is application dependent.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗