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All sources NASA NTRS DOE OSTI

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 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

Physics makes the difference: Bayesian optimization and active learning via augmented Gaussian process

Abstract Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of interest in the image space or parameter space of computational models. The direct grid search of the parameter space tends to be extremely time-consuming, leading to the development of strategies balancing exploration of unknown parameter spaces and exploitation towards required performance metrics. However, classical Bayesian optimization (BO) strategies based on the Gaussian process (GP) do not readily allow for the incorporation of the known physical behaviors or past knowledge. Here we explore a hybrid optimization/exploration algorithm created by augmenting the standard GP with a structured probabilistic model of the expected system’s behavior. This approach balances the flexibility of the non-parametric GP approach with a rigid structure of physical knowledge encoded into the parametric model. The fully Bayesian treatment of the latter allows additional control over the optimization via the selection of priors for the model parameters. The method is demonstrated for a noisy version of a standard univariate test function used to evaluate optimization algorithms and further extended to physical lattice models. This methodology is expected to be universally suitable for injecting prior knowledge in the form of physical models and past data in the BO framework.

42 ENGINEERING↗

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 OSTI2026

HostSub_GP: Precise Galaxy Background Subtraction in Transient Long-slit Spectroscopy with Gaussian Processes

We present a novel host galaxy subtraction technique in long-slit spectroscopy for extragalactic transients. Unlike classic methods which generally estimate the background using simple interpolation of local galaxy flux in the 2D spectrum, our approach leverages multi-band archival images of the host galaxies to model the background emission from the galaxy in the 2D spectrum. Such imaging encodes the wavelength-dependent galaxy profile along the slit, and is readily accessible through wide-field imaging surveys. We construct a smooth prior for the 2D galaxy profile with a Gaussian process (GP) based on these reference images, and use another GP to model the correlated deviations from the prior in the observed spectrum. This enables accurate inference of the galaxy flux blended with the transient. On synthetic long-slit data of a spiral galaxy extracted from a Multi Unit Spectroscopic Explorer hyper-spectral cube, the GP method remains robust as long as the host galaxy is spatially resolved and consistently outperforms classic methods. We apply the method to archival Keck spectra of two real transients, SN 2019eix and AT 2019qiz, to further demonstrate how the method uniquely recovers weak spectral features amid strong galaxy contamination, enabling refined constraints on the properties of both transients. We have released the software implementation, HostSub_GP, a scalable toolkit that leverages JAX, with an MIT license.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Estimation of the Ambient Wind Field From Wind Turbine Measurements Using Gaussian Process Regression

In the search for a lower levelized cost of wind energy, one approach is to increase the accuracy of wind turbine measurements such as wind speed and wind direction. The sensors available on wind turbines are susceptible to local turbulence and measurement bias, which can result in suboptimal turbine performance. As an alternative, recent research has considered using the sensor measurements in a coordinated manner. With such a cooperative approach, the local wind conditions can be estimated more accurately and reliably without the need for additional measurement equipment. In this paper, a novel wind field estimation approach is presented that estimates the local wind conditions based on turbine measurements using Gaussian processes. We show that the estimation framework is able to improve the accuracy of the wind direction estimate both in an offline and online manner, as well as identify possible biases in the sensors and reduce unnecessary wind turbine yaw activity.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

DOE OSTI2024

A Gaussian process based surrogate approach for the optimization of cylindrical targets

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular, surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this study, we apply surrogate modeling and optimization techniques that are well established in the existing literature to one-dimensional simulation data of a new cylindrical target design containing deuterium–tritium fuel. These models predict yields without the need for expensive simulations. We find that Bayesian optimization with Gaussian process surrogates enhances sampling efficiency in low-dimensional design spaces but becomes less efficient as dimensionality increases. Nonetheless, optimization routines within two-dimensional and five-dimensional design spaces can identify designs that maximize yield, while also aligning with established physical intuition. Optimization routines, which ignore constraints on hydrodynamic instability growth, are shown to lead to unstable designs in 2D, resulting in yield loss. However, routines that utilize 1D simulations and impose constraints on the in-flight aspect ratio converge on novel cylindrical target designs that are stable against hydrodynamic instability growth in 2D and achieve high yield.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Estimation of hydraulic conductivity in a watershed using sparse multi-source data via Gaussian process regression and Bayesian experimental design

Enhanced water management systems depend on accurate estimation of subsurface hydraulic properties. However, geologic formations can vary significantly, so information from a single source (e.g., widely spaced boreholes) is insufficient in characterizing subsurface aquifer properties. Therefore, multiple sources of information are needed to complement the hydrogeology understanding of a region. Here, this study presents a numerical framework in which information from different measurement sources is combined to characterize the 3D random field in a multi-fidelity prediction model. Coupled with the model, a Bayesian experimental design was used to determine the best future sampling locations. The Upper Sangamon watershed in east-central Illinois was selected as the case study site, where the multi-fidelity Gaussian process model was used to estimate the hydraulic conductivity in the region of interest. Multi-source observation data were obtained from electrical resistivity and borehole pumping tests. The accuracy of the model prediction is dependent on the locations and the distribution of both high- and low-fidelity data. Furthermore, the multi-fidelity model was compared with the single-fidelity model. The uncertainties and confidence in the measurements and parameter estimates were quantified and used to design future cycles of data collection to further improve the confidence intervals.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

DOE OSTI2023

GPLaSDI: Gaussian Process Latent Space Dynamics Identification

GPLaSDI is a software that introduces GPLaSDI, a novel LaSDI-based framework that relies on Gaussian process (GP) for latent space ODE interpolations. Using GPs offers two significant advantages. First, it enables the quantification of uncertainty over the reduced order model (ROM) predictions. Second, leveraging this prediction uncertainty allows for efficient adaptive training through a greedy selection of additional training data points. This approach does not require prior knowledge of the underlying PDEs. Consequently, GPLaSDI is inherently non-intrusive and can be applied to problems without a known PDE or its residual. We demonstrate the effectiveness of our approach on the Burgers equation, Vlasov equation for plasma physics, and a rising thermal bubble problem. Our proposed method achieves between 200 and 100,000 times speed-up, with up to 7% relative error.

Choi, Youngsoo↗

DOE OSTI2023

Proxy quality control of biomass particles using thermogravimetric analysis and Gaussian process regression models

Abstract The temperature experienced by reactants during preparation in a reactor is a key component in determining the yield and homogeneity of usable chemical products such as biomass particles. Thermocouples with sensors can be used to monitor spatial temperature gradients within reactors but these sensors are often too expensive and/or invasive. The present work proposes a strategy to identify optimal machine learning models to infer the maximum effective temperature experienced by particles during oxidative biomass torrefaction using key thermochemical combustion parameters. The maximum rate of weight loss, the corresponding temperature, and fixed carbon content on a dry‐ash‐free basis are used as literature‐based predictor variables obtained from thermogravimetric analysis. The evaluation of 24 machine‐learning models using the standard tenfold cross‐validation method suggests that the exponential Gaussian process regression (GPR) model is the most effective, followed by other GPR models. These high‐performing GPR models were also utilized to predict the effective preparation temperature distribution of reactor‐produced biomass particles under eight conditions of varying residence time and air‐to‐biomass ratio. The effective preparation temperature and residence time of individual biomass particles were then encoded into the torrefaction severity factor and used to estimate the energy yield of the reactor output as a novel quality control method. © 2023 The Authors. Biofuels, Bioproducts and Biorefining published by Society of Industrial Chemistry and John Wiley & Sons Ltd.

09 BIOMASS FUELS↗

DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗

DOE OSTI2026

Multi-Fidelity Bayesian Optimization with Gaussian Processes for Double Shell Inertial Confinement Fusion Target Design

Reliable, secure access to energy is a major focus for national security efforts. One potential route to such energy is through fusion reactions in inertial confinement fusion (ICF) experiments. Such experiments are carried out at facilities such as the National Ignition Facility (NIF) in Livermore, California, where high powered lasers are used to compress a DT fuel-containing target to the necessary high temperature, high pressure conditions. These experiments are limited in number, which creates a heavy dependence on high fidelity predictive physics simulations and analysis performed “pre shot,” or before the experiment occurs. Many of these simulations in higher dimensions (2D and 3D) are computationally expensive, so finding optimal simulation-based designs presents its own challenges. In this work, we present our multi-fidelity Bayesian optimization with Gaussian processes (GPs) for ICF double shell targets, where a 1D surrogate model is used to help find a 2D surrogate model, enabling us to find optimal targets in the higher fidelity (2D), while saving computational cost.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Efficient Data Query for Gaussian Process Compressed Data through Value Range Estimation [Slides]

When the resolution of the data increases, data reduction methods are applied to simulation output, including Gaussian process, neural representation and compression algorithms. Lots of data analysis/visualization techniques requires data query, but data query from reduced representation is still challenging. This report will provide examples and provide possible answers to why data query from reduced representation is still challenging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

DOE OSTI2021

Constraining the Milky Way’s ultraviolet-to-infrared SED with Gaussian process regression

ABSTRACT Improving our knowledge of global Milky Way (MW) properties is critical for connecting the detailed measurements only possible from within our Galaxy to our understanding of the broader galaxy population. We here train Gaussian process regression (GPR) models on SDSS (Sloan Digital Sky Survey) galaxies to map from galaxy properties (stellar mass, apparent axial ratio, star formation rate, bulge-to-total ratio, disc scale length, and bar vote fraction) to ultraviolet (UV; GALEX FUV/NUV), optical (SDSS ugriz), and infrared (IR; 2MASS JHKs and WISE W1/W2/W3/W4) fluxes and uncertainties. With these models, we estimate the photometric properties of the MW, resulting in a full UV-to-IR spectral energy distribution (SED) as it would be measured externally, viewed face-on. We confirm that the MW lies in the green valley in optical diagnostic diagrams, but show for the first time that the MW is in the star-forming region in standard UV and IR diagnostics – characteristic of the population of red spiral galaxies. Although our GPR method predicts one band at a time, the resulting MW UV–IR SED is consistent with SEDs of local spirals with characteristics broadly similar to the MW, suggesting that these independent predictions can be combined reliably. Our UV–IR SED will be invaluable for reconstructing the MW’s star formation history using the same tools employed for external galaxies, allowing comparisons of results from in situ measurements to those from the methods used for extragalactic objects.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Bayesian Gaussian process inference for neutron spin echo measurement

Neutron spin echo (NSE) spectroscopy provides unique access to microscopic dynamics, but its application is often constrained by low neutron flux, long acquisition times, and significant noise. Here, we present a Bayesian inference approach based on Gaussian process regression (GPR) to reconstruct high-quality spin echo signals from sparse and noisy data by exploiting correlations in reciprocal space. Benchmarks on synthetic datasets and validation with experimental NSE measurements of dendrimers show that GPR suppresses noise, interpolates missing intensity values, and accommodates irregular observations. The method improves accuracy, shortens acquisition times, and enables high-throughput and real-time studies. Beyond NSE, the framework is broadly applicable to other low signal-to-noise ratio scattering techniques, thereby extending the scope of neutron spectroscopy.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗