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Results for “Gaussian Process (GP)”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data

We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. The use of the Finnish Horseshoe as a sparsity-promoting prior for free model parameters also enables the discovery of parsimonious representations for the latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator–prey systems, systems biology and a 50-dimensional human motion dynamical system. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

Science & Technology - Other Topics↗
DOE OSTI2024

GP-BayesOpInf

SAND2025-01851O GP-BayesOpInf is a software tool that uses algorithms to combine Gaussian process regression, principal component analysis, and linear Bayesian inference to produce a probabilistic reduced-order model for time-dependent systems. Numerical examples include the compressible Euler equations for an ideal gas, a heat diffusion process with a nonlinear reaction term, and a set of ordinary differential equations describing a compartmental model in epidemiology. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
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 OSTI2026

Deep Gaussian process-based cost-aware batch Bayesian optimization for complex materials design campaigns

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Scaled Vecchia Approximation for Fast Computer-Model Emulation

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia’s ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction, and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2021

gp_blendclass_singleband

The code used for the data preprocessing, image simulation, and model training and analysis reported in the paper "Gaussian Process Classification for Galaxy Blend Identification in LSST" (arXiv:2107.09246).

Buchanan, JamesJ.↗
DOE OSTI2021

srMO-BO-3GP: A sequential regularized multi-objective Bayesian optimization for constrained design applications using an uncertain Pareto classifier

Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, and latent-variable modeling, have been proposed to address the limitations of the classical BO framework. In this work, we propose a novel multi-objective BO formalism, called srMO-BO-3GP, to solve multi-objective optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GPs is assigned with a different task. The first GP is used to approximate a single-objective computed from the multi-objective definition, the second GP is used to learn the unknown constraints, and the third one is used to learn the uncertain Pareto frontier. At each iteration, a multi-objective augmented Tchebycheff function is adopted to convert multi-objective to single-objective, where the regularization with a regularized ridge term is also introduced to smooth the single-objective function. Finally, we couple the third GP along with the classical BO framework to explore the convergence and diversity of the Pareto frontier by the acquisition function for exploitation and exploration. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.

42 ENGINEERING↗
DOE OSTI2026

Fermilab Booster loss modelling and rebalancing using Bayesian methods

To meet PIP-II upgrade requirements, Fermilab Booster losses need to be reduced by 50% compared to present levels. So far, simulations are not good enough to predict loss patterns. Thus, an extensive Booster tune up will be necessary to achieve required performance. In this paper we present an effort to build a data-driven loss model using Bayesian techniques, and subsequently to rebalance losses for higher trip margins. We first created several sets of spatially and temporally isolated orbit and optics knobs, and trained Gaussian process models for each beam loss monitor as well as beam current. Novel techniques of uncertainty constraints and approximate GP fitting were introduced to handle safety and timing requirements. We then performed single and multi-objective tuning using scalarized objectives comprised of critical beam loss locations. We achieved significant rebalancing of losses, increasing margins by 25%, as well as an overall improvement in transmission efficiency of 0.4%. Automated data collection is being developed so that more accurate surrogate models can be trained over time.

Kuklev, N. [Fermilab]↗
DOE OSTI2022

aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture

High-fidelity complex engineering simulations are often predictive, but also computationally expensive and often require substantial computational efforts. The mitigation of computational burden is usually enabled through parallelism in high-performance cluster (HPC) architecture. Optimization problems associated with these applications is a challenging problem due to the high computational cost of the high-fidelity simulations. In this paper, an asynchronous parallel constrained Bayesian optimization method is proposed to efficiently solve the computationally expensive simulation-based optimization problems on the HPC platform, with a budgeted computational resource, where the maximum number of simulations is a constant. The advantage of this method are three-fold. Firstly, the efficiency of the Bayesian optimization is improved, where multiple input locations are evaluated parallel in an asynchronous manner to accelerate the optimization convergence with respect to physical runtime. This efficiency feature is further improved so that when each of the inputs is finished, another input is queried without waiting for the whole batch to complete. Second, the proposed method can handle both known and unknown constraints. Third, the proposed method samples several acquisition functions based on their rewards using a modified GP-Hedge scheme. The proposed framework is termed aphBO-2GP-3B, which means asynchronous parallel hedge Bayesian optimization with two Gaussian processes and three batches. The numerical performance of the proposed framework aphBO-2GP-3B is comprehensively benchmarked using 16 numerical examples, compared against other 6 parallel Bayesian optimization variants and 1 parallel Monte Carlo as a baseline, and demonstrated using two real-world high-fidelity expensive industrial applications. The first engineering application is based on finite element analysis (FEA) and the second one is based on computational fluid dynamics (CFD) simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(n log 2 n). We show that this approximation’s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multi-objective Bayesian alloy design using multi-task Gaussian processes

In design applications, correlations among material properties (such as the tendency for stronger materials to be less ductile) are often neglected. This approach is echoed in multi-objective optimization techniques which treat each performance characteristic as an independent objective, aiming to optimize scalar functions and find optimal Pareto fronts. However, this overlooks the statistical relationships between performance characteristics inherent in a material system. To address this, we propose the use of Bayesian optimization, a highly efficient black-box optimization algorithm known for constructing Gaussian processes (GPs) – uncorrelated surrogates - to model objective functions. Rather than evaluating multiple GPs for each objective function separately, we argue for a shift towards jointly modeling these objective functions, considering their statistical correlations. This integrated approach utilizes naturally occurring relationships among material properties, providing additional information to enhance the performance of the design framework. This requires the replacement of multiple independent GPs with a single multi-task GP, employing a correlation matrix to construct a multi-task kernel function, wherein each task corresponds to a single objective function. Here, we anticipate this refined methodology will better leverage material correlations, improving design optimization results.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fast Gaussian Process Estimation for Large-Scale In Situ Inference using Convolutional Neural Networks

Exascale computing will bring with it significant I/O limitations. One foreseeable consequence of such restrictions is that the user can save only a small fraction of complex simulation data to disk for subsequent analysis. An alternative is to fit statistical models to data in situ, that is, inside the simulation as it runs. This option requires extremely fast statistical estimation to avoid slowing down the simulation. Gaussian processes (GPs) have state-of-the-art predictive performance for modeling spatial data. However, standard estimation methods for GPs scale quite poorly to large data sets as parameter estimation requires inverting a covariance matrix to the size of the data set. In the presented work, we use a convolutional neural network (CNN) to predict the GP parameters for a spatial data set, from a simulation or otherwise, rather than optimize the parameters directly. Here, our presented case study models spatial data from E3SM, the Department of Energy’s Exascale climate model. The CNN is trained on synthetic data simulated from GP models with known parameters and then applied to data from the climate simulation. In the presented examples, the neural network scheme produces parameter estimates that compare well with standard methods such as maximum likelihood estimation in predictive performance but is obtained four orders of magnitude faster.

big data↗
DOE OSTI2020

Applying Constrained Bayesian Optimization to the Design of Critical Experiments

Often when planning a criticality experiment, many design configurations are iteratively investigated with a Monte Carlo transport code. The goal is that the experiment will be optimal with respect to some variable, like the fraction of fissions occurring at a certain energy range, while simultaneously being critical. Unfortunately, the Monte Carlo transport simulations are expensive, which can ultimately limit the number of configurations that can be explored. In this work, we present how Gaussian processes (GPs) can be used as a reduced-order model in a constrained Bayesian optimization (CBO) algorithm to design a criticality experiment. The GPs replace the Monte Carlo transport simulations that explore the design space. The CBO algorithm efficiently identifies new points in the design space to run the Monte Carlo transport code while respecting the criticality constraint. It does so in a manner that both improves the accuracy of the GP and finds the approximate global optimum. We demonstrate the performance of CBO with the design of a Thermal Epithermal eXperiment (TEX) for the criticality safety validation of nuclear waste models of the Hanford Tank Farm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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 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 OSTI2024

Non-smooth Bayesian optimization in tuning scientific applications

Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Here, motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.

97 MATHEMATICS AND COMPUTING↗
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↗