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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 OSTI2021

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

In this note, we present a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

42 ENGINEERING↗

DOE OSTI2021

Robust Deep Gaussian Process-Based Probabilistic Electrical Load Forecasting Against Anomalous Events

The abnormal events, such as the unprecedented COVID-19 pandemic, can significantly change the load behaviors, leading to huge challenges for traditional short-term forecasting methods. This article proposes a robust deep Gaussian processes (DGP)-based probabilistic load forecasting method using a limited number of data. Since the proposed method only requires a limited number of training samples for load forecasting, it allows us to deal with extreme scenarios that cause short-term load behavior changes. In particular, the load forecasting at the beginning of abnormal event is cast as a regression problem with limited training samples and solved by double stochastic variational inference DGP. The mobility data are also utilized to deal with the uncertainties and pattern changes and enhance the flexibility of the forecasting model. The proposed method can quantify the uncertainties of load forecasting outcomes, which would be essential under uncertain inputs. Extensive comparison results with other state-of-the-art point and probabilistic forecasting methods show that our proposed approach can achieve high forecasting accuracies with only a limited number of data while maintaining the excellent performance of capturing the forecasting uncertainties.

anomalous events↗

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 OSTI2024

Analytic Neural Network Gaussian Process Enabled Chance-Constrained Voltage Regulation for Active Distribution Systems with PVs, Batteries and EVs

This paper proposes an analytic neural network Gaussian process (NNGP)-based chance-constrained real-time voltage regulation method for active distribution systems with photovoltaics (PVs), batteries, and electric vehicles (EVs). NNGP can utilize historical measurement data to achieve real-time probabilistic node voltage estimation through Bayesian inference. Then, NNGP is fully analytically embedded into the optimal power flow model to perform voltage regulation and adapt to various topological changes. The uncertainties of voltage estimations are easily considered via the chance constraint, and it has been shown that the adoption of this chance constraint can significantly improve the reliability of voltage regulation under various scenarios. The comparison results with other methods, carried out on a real 759-node distribution system located in western Colorado, U.S., show that the proposed method can achieve accurate voltage estimation across different topologies and reliably perform voltage regulation considering PVs, batteries, and EVs.

active distribution systems↗

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

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

Hierarchical Gaussian Random Field Sampling for Multilevel Markov Chain Monte Carlo: Coupling Stochastic Partial Differential Equation and the Karhunen–Loève Decomposition

This work introduces structure preserving hierarchical decompositions for sampling Gaussian random fields (GRFs) within the context of multilevel Bayesian inference in high-dimensional space. Existing scalable hierarchical sampling methods, such as those based on stochastic partial differential equations (SPDEs), often reduce the dimensionality of the sample space at the cost of accuracy of inference. Other approaches, such that those based on Karhunen-Loève (KL) expansions, offer sample space dimensionality reduction but sacrifice GRF representation accuracy and ergodicity of the Markov chain Monte Carlo (MCMC) sampler and are computationally expensive for high-dimensional problems. The proposed method integrates the dimensionality reduction capabilities of KL expansions with the scalability of SPDE-based sampling, thereby providing a robust, unified framework for high-dimensional uncertainty quantification (UQ) that is scalable and accurate, preserves ergodicity, and offers dimensionality reduction of the sample space. The hierarchy in our multilevel algorithm is derived from the geometric multigrid hierarchy. By constructing a hierarchical decomposition that maintains the covariance structure across the levels in the hierarchy, the approach enables efficient coarse-to-fine sampling while ensuring that all samples are drawn from the desired distribution. The effectiveness of the proposed method is demonstrated on a benchmark subsurface flow problem, demonstrating its effectiveness in improving computational efficiency and statistical accuracy. Furthermore, our proposed technique is more efficient and accurate and displays better convergence properties than existing methods for high-dimensional Bayesian inference problems.

Gaussian random fields↗

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 OSTI2023

Enter Gaussian Mixture Modeling Extensions for Improved False Discovery Rate Estimation in GC-MS Metabolomics

Identifying small molecules (e.g., metabolites) is key towards driving scientific advancement in metabolomics, and gas chromatography–mass spectrometry (GC-MS) is an analytic method that may be applied to facilitate this process. The typical GC-MS identification workflow involves quantifying the similarity of an observed sample spectrum and other features (e.g. retention index) to that of several references, noting the compound of the best-matching reference spectrum as the identified metabolite. While a deluge of similarity metrics exists, none characterize the error rate of generated identifications, thereby presenting an unknown risk of false identification or discovery. To quantify this unknown risk, we propose a model-based framework for estimating the false discovery rate (FDR) among a set of identifications. Extending the traditional mixture modeling framework, our method incorporates both similarity score and experimental information in estimating the FDR. We apply these models to identification lists derived from across 548 samples of varying complexity and sample type (e.g., fungal species, standard mixtures, etc.), comparing their performance to that of the traditional Gaussian mixture model (GMM). Through simulation, we additionally assess the impact of reference library size on the accuracy of FDR estimates. In comparing the best performing model extensions to the GMM, our results indicate relative decreases in median absolute estimation error (MAE) ranging from 12% to 70%, based on comparisons of the median MAEs across all hit-lists. Results indicate that these relative performance improvements generally hold despite library size, however FDR estimation error typically worsens as the set of reference compounds diminishes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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 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 OSTI2022

Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Computational models of atrial fibrillation have successfully been used to predict optimal ablation sites. A critical step to assess the effect of an ablation pattern is to pace the model from different, potentially random, locations to determine whether arrhythmias can be induced in the atria. In this work, we propose to use multi-fidelity Gaussian process classification on Riemannian manifolds to efficiently determine the regions in the atria where arrhythmias are inducible. We build a probabilistic classifier that operates directly on the atrial surface. We take advantage of lower resolution models to explore the atrial surface and combine seamlessly with high-resolution models to identify regions of inducibility. We test our methodology in 9 different cases, with different levels of fibrosis and ablation treatments, totalling 1,800 high resolution and 900 low resolution simulations of atrial fibrillation. When trained with 40 samples, our multi-fidelity classifier that combines low and high resolution models, shows a balanced accuracy that is, on average, 5.7% higher than a nearest neighbor classifier. We hope that this new technique will allow faster and more precise clinical applications of computational models for atrial fibrillation. All data and code accompanying this manuscript will be made publicly available at: https://github.com/fsahli/AtrialMFclass.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Comparative Performance of Gaussian Plume and Backward Lagrangian Stochastic Models for Near-Field Methane Emission Estimation Using a Single Controlled Release Experiment

Methane (CH 4 ) is a major component of natural gas and a potent greenhouse gas. Increasing atmospheric methane concentrations are attributed to emissive anthropogenic activities by an average of 13 ppb per yr since 2020 and are linked to a changing global climate. Mitigating CH 4 emissions from oil and gas production sites has recently become a target to reduce overall greenhouse gas emissions; however, monitoring the efficacy of mitigation strategies depends on accurate quantification of CH 4 emissions at the facility-level. Near-field quantification of methane (CH 4 ) emissions from oil and gas (O&G) facilities remains challenging due to the effects of atmospheric variability and sensor configuration on atmospheric dispersion models. This study evaluates the performance of two atmospheric dispersion models, the Gaussian plume (GP) and backward Lagrangian stochastic (bLS), by comparing calculated CH 4 emissions to controlled single-point emissions between 0.4 and 5.2 kg CH 4 h −1 . Emissions were calculated by both models using 121 individual sets of measurements comprising five-minute averaged downwind methane mixing ratios and matching meteorological data. The comparison shows that the bLS approach achieved a higher proportion of emission estimates within a factor of two (FAC2) of the known emission rates compared to the GP approach. The emissions calculated by the bLS model also had a lower multiplicative error and reduced bias relative to GP. Other error-based metrics further confirmed the bLS model performed better, as it yielded lower RMSE and MAE than GP. Statistical analysis of the emission data shows that the lateral and vertical alignment of the source and the sensor plays a critical role in emission estimations, as measurements made closer to the plume centerline and at a distance between 40 and 80 m downwind yielded the best FAC2 agreement. High wind meander degraded the ability of both approaches to generate representative emissions, particularly with the GP approach, as it violates the modeling approach’s assumption of steady-state emissions. Data suggest emissions calculated by the bLS model are comprehensively in better agreement, but the computational demands of the modeling approach and integration into fenceline systems limit real-time applicability. While these results provide insight into model performance under controlled near-field conditions, their applicability to more complex or heterogeneous oil and gas production environments (e.g., the regions Marcellus or Unita Basins) remains limited and uncertain.

gaussian plume↗

DOE OSTI2020

Dynamical Mass Estimates of the β Pictoris Planetary System through Gaussian Process Stellar Activity Modeling

Nearly 15 yr of radial velocity (RV) monitoring and direct imaging enabled the detection of two giant planets orbiting the young, nearby star β Pictoris. The δ Scuti pulsations of the star, which overwhelm planetary signals, need to be carefully suppressed. In this work, we independently revisit the analysis of the RV data following a different approach than available in the literature to model the activity of the star. We show that a Gaussian process (GP) with a stochastically driven damped harmonic oscillator kernel can model the δ Scuti pulsations. It provides similar results to parametric models but with a simpler framework, using only three hyperparameters. It also enables us to model poorly sampled RV data that were excluded from previous analyses, hence extending the RV baseline by nearly five years. Altogether, the orbit and mass of both planets can be constrained from RV only, which was not possible with the parametric modeling. To characterize the system more accurately, we also perform a joint fit of all available relative astrometry and RV data. Our orbital solutions for β Pic b favor a low eccentricity of 0.029$_{−0.024}^{+0.061}$ and a relatively short period of 21.1$_{−0.8}^{+2.0}$ yr. The orbit of β Pic c is eccentric with 0.206$_{−0.063}^{+0.074}$ with a period of 3.36 ± 0.03 yr. We find model-independent masses of 11.7 ± 1.4 and 8.5 ± 0.5 M Jup for β Pic b and c, respectively, assuming coplanarity. The mass of β Pic b is consistent with the hottest start evolutionary models, at an age of 25 ± 3 Myr. A direct detection of β Pic c would provide a second calibration measurement in a coeval system.

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 OSTI2021

A Gaussian Process Regression Reveals No Evidence for Planets Orbiting Kapteyn’s Star

Radial–velocity (RV) planet searches are often polluted by signals caused by gas motion at the star’s surface. Stellar activity can mimic or mask changes in the RVs caused by orbiting planets, resulting in false positives or missed detections. Here we use Gaussian process regression to disentangle the contradictory reports of planets versus rotation artifacts from Kapteyn’s star. To model rotation, we use joint quasiperiodic kernels for the RV and Hα signals, requiring that their periods and correlation timescales be the same. We find that the rotation period of Kapteyn’s star is 125 days, while the characteristic active-region lifetime is 694 days. Adding a planet to the RV model produces a best-fit orbital period of 100 yr, or 10 times the observing time baseline, indicating that the observed RVs are best explained by star rotation only. We also find no significant periodic signals in residual RV data sets constructed by subtracting off realizations of the best-fit rotation model and conclude that both previously reported “planets” are artifacts of the star’s rotation and activity. Our results highlight the pitfalls of using sinusoids to model quasiperiodic rotation signals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar Radial Velocities

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m s{sup −1}. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass (∼0.5 m s{sup −1}) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus (∼0.1 m s{sup −1}) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets.

47 OTHER INSTRUMENTATION↗