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DOE OSTI2023

Code for multi-shape Gaussian process (GP) fitting with uncertainty quantification (UQ)

This is code associated with the publication “Nonparametric Multi-shape Modeling with Uncertainty Quantification,” authored by Hengrui Luo (Lawrence Berkeley National Laboratory) and Justin Strait (Los Alamos National Laboratory). The code is used to fit multiple-output Gaussian process (GP) models of planar closed curves to collections of ordered point sets, allowing for flexible nonlinear prediction of the underlying curve under dense or sparse point set samplings and with or without noise, as well as tractable uncertainty quantification. To do this, we employ use of a periodic kernel to account for the nonlinear input space of closed curves, and combine with coregionalization models to account for dependence both (i) between curve coordinates, and (ii) between pairs of curves. Functions in the code are capable of fitting these models, as well as performing additional tasks with the fitted curves such as (a) shape registration and alignment, (b) shape averaging, and (c) fitting for curve sub-populations / clusters.

Strait, Justin↗

DOE OSTI2023

Validating the Use of Gaussian Process Regression for Adaptive Mapping of Residual Stress Fields

Probing the stress state using a high density of measurement points is time intensive and presents a limitation for what is experimentally feasible. Alternatively, individual strain fields used for determining stresses can be reconstructed from a subset of points using a Gaussian process regression (GPR). Results presented in this paper evidence that determining stresses from reconstructed strain fields is a viable approach for reducing the number of measurements needed to fully sample a component’s stress state. The approach was demonstrated by reconstructing the stress fields in wire-arc additively manufactured walls fabricated using either a mild steel or low-temperature transition feedstock. Effects of errors in individual GP reconstructed strain maps and how these errors propagate to the final stress maps were assessed. Implications of the initial sampling approach and how localized strains affect convergence are explored to give guidance on how best to implement a dynamic sampling experiment.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

Analysis of cosmic shear is an integral part of understanding structure growth across cosmic time, which in turn provides us with information about the nature of dark energy. Conventional methods generate shear maps from which we can infer the matter distribution in the universe. Current methods (e.g., Kaiser–Squires inversion) for generating these maps, however, are tricky to implement and can introduce bias. Recent alternatives construct a spatial process prior for the lensing potential, which allows for inference of the convergence and shear parameters given lensing shear measurements. Realizing these spatial processes, however, scales cubically in the number of observations—an unacceptable expense as near-term surveys expect billions of correlated measurements. Therefore, we present a linearly scaling shear map construction alternative using a scalable Gaussian process prior called MuyGPs. MuyGPs avoids cubic scaling by conditioning interpolation on only nearest neighbors and fits hyperparameters using batched leave-one-out cross-validation. This work is the first step toward a full, scalable mass mapping method. We work in a simplified regime where we validate our method by interpolating and analyzing maps given noisy point-estimate data from all three shear fields, taken from a suite of N -body ray-tracing simulations. We also show that we can perform these operations at the scale of billions of galaxies on high-performance computing platforms.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Gaussian process for calibration and control of GlueX Central Drift Chamber

We have developed and implemented a machine learning based system to calibrate and control the GlueX Central Drift Chamber at Jefferson Lab, VA, in near real-time. The system monitors environmental and experimental conditions during data taking and uses those as inputs to a Gaussian process (GP) with learned prior. The GP predicts calibration constants in order to recommend a high voltage (HV) setting for the detector that maintains consistent detector performance (gain and resolution) throughout data taking. This approach is in stark contrast to traditional detector operations in which the detector operates at fixed HV and its calibration parameters vary quite considerably with time. Additionally, the ML based system utilizes uncertainty quantification to correct the recommended control parameters when appropriate. We will present results from the ML system autonomously during the Charged Pion Polarizability (CPP) experiment conducted in Hall D at Jefferson Lab.

McSpadden, Helen↗

DOE OSTI2022

Gaussian process for calibration and control of GlueX Central Drift Chamber

McSpadden, Helen↗

DOE OSTI2020

Autonomous materials discovery driven by Gaussian process regression with inhomogeneous measurement noise and anisotropic kernels

Abstract A majority of experimental disciplines face the challenge of exploring large and high-dimensional parameter spaces in search of new scientific discoveries. Materials science is no exception; the wide variety of synthesis, processing, and environmental conditions that influence material properties gives rise to particularly vast parameter spaces. Recent advances have led to an increase in the efficiency of materials discovery by increasingly automating the exploration processes. Methods for autonomous experimentation have become more sophisticated recently, allowing for multi-dimensional parameter spaces to be explored efficiently and with minimal human intervention, thereby liberating the scientists to focus on interpretations and big-picture decisions. Gaussian process regression (GPR) techniques have emerged as the method of choice for steering many classes of experiments. We have recently demonstrated the positive impact of GPR-driven decision-making algorithms on autonomously-steered experiments at a synchrotron beamline. However, due to the complexity of the experiments, GPR often cannot be used in its most basic form, but rather has to be tuned to account for the special requirements of the experiments. Two requirements seem to be of particular importance, namely inhomogeneous measurement noise (input-dependent or non-i.i.d.) and anisotropic kernel functions, which are the two concepts that we tackle in this paper. Our synthetic and experimental tests demonstrate the importance of both concepts for experiments in materials science and the benefits that result from including them in the autonomous decision-making process.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Model selection and signal extraction using Gaussian Process regression

We present a novel computational approach for extracting localized signals from smooth background distributions. We focus on datasets that can be naturally presented as binned integer counts, demonstrating our procedure on the CERN open dataset with the Higgs boson signature, from the ATLAS collaboration at the Large Hadron Collider. Our approach is based on Gaussian Process (GP) regression — a powerful and flexible machine learning technique which has allowed us to model the background without specifying its functional form explicitly and separately measure the background and signal contributions in a robust and reproducible manner. Unlike functional fits, our GP-regression-based approach does not need to be constantly updated as more data becomes available. We discuss how to select the GP kernel type, considering trade-offs between kernel complexity and its ability to capture the features of the background distribution. We show that our GP framework can be used to detect the Higgs boson resonance in the data with more statistical significance than a polynomial fit specifically tailored to the dataset. Finally, we use Markov Chain Monte Carlo (MCMC) sampling to confirm the statistical significance of the extracted Higgs signature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Gaussian process analysis of electron energy loss spectroscopy data: multivariate reconstruction and kernel control

Abstract Advances in hyperspectral imaging including electron energy loss spectroscopy bring forth the challenges of exploratory and physics-based analysis of multidimensional data sets. The multivariate linear unmixing methods generally explore similarities in the energy dimension, but ignore correlations in the spatial domain. At the same time, Gaussian process (GP) explicitly incorporate spatial correlations in the form of kernel functions but is computationally intensive. Here, we implement a GP method operating on the full spatial domain and reduced representations in the energy domain. In this multivariate GP, the information between the components is shared via a common spatial kernel structure, while allowing for variability in the relative noise magnitude or image morphology. We explore the role of kernel constraints on the quality of the reconstruction, and suggest an approach for estimating them from the experimental data. We further show that spatial information contained in higher-order components can be reconstructed and spatially localized.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Control and Calibration of GlueX Central Drift Chamber Using Gaussian Process Regression

The Gluonic Excitations (GlueX) experiment is designed to search for exotic hybrid mesons using photoproduction, and to study the hybrid meson spectrum predicted from Lattice Quantum Chromodynamics. For the first time, the GlueX Central Drift Chamber was controlled autonomously using machine learning (ML) to calibrate in real time while recording cosmic ray tracks. We demonstrate the ability of a Gaussian Process to predict the gain correction calibration factor used to determine a high voltage setting that will stabilize the CDC gain in response to changing environmental conditions; this is in contrast to the traditional, computationally expensive method of calibrating raw data after data collection is complete.

McSpadden, Helen↗

DOE OSTI2025

Computationally efficient subglacial drainage modelling using Gaussian process emulators: GlaDS-GP v1.0

Subglacial drainage models represent water flow at the ice–bed interface through coupled distributed and channelized systems to determine water pressure, discharge, and drainage system geometry. While they are used to understand processes such as the relationship between surface melt and ice flow, the number of uncertain model parameters and the computational cost of running models makes it difficult to adequately explore the high-dimensional parameter space and evaluate uncertainty in model predictions. Here, we develop Gaussian process (GP) emulators that make fast predictions with associated uncertainty of subglacial drainage model outputs. Using a truncated principal component (PC) basis representation, we construct a GP emulator for diurnally averaged subglacial water pressure. We also explore emulation of scalar variables describing drainage efficiency and configuration. We train the emulators using ensembles of up to 512 simulations varying eight parameters of the Glacier Drainage System (GlaDS) model on a synthetic domain intended to represent an ice-sheet margin. The emulators make predictions ∼ 1000 times faster than GlaDS simulations, with errors <3 % for the water pressure field and ∼ 5 %–9 % for drainage efficiency and configuration. We apply the emulators to explore the eight-dimensional parameter space by computing variance-based parameter sensitivity indices, finding that three parameters (ice flow coefficient, bed bump aspect ratio, and the subglacial cavity system conductivity) explain 90 % of the variance in modelled water pressure in response to parameter changes. The GP emulator approach described here is well suited to integrating observational data with models to make calibrated, credible predictions of subglacial drainage.

58 GEOSCIENCES↗

DOE OSTI2022

Accelerating cosmological inference with Gaussian processes and neural networks – an application to LSST Y1 weak lensing and galaxy clustering

ABSTRACT Studying the impact of systematic effects, optimizing survey strategies, assessing tensions between different probes and exploring synergies of different data sets require a large number of simulated likelihood analyses, each of which cost thousands of CPU hours. In this paper, we present a method to accelerate cosmological inference using emulators based on Gaussian process regression and neural networks. We iteratively acquire training samples in regions of high posterior probability which enables accurate emulation of data vectors even in high dimensional parameter spaces. We showcase the performance of our emulator with a simulated 3×2 point analysis of LSST-Y1 with realistic theoretical and systematics modelling. We show that our emulator leads to high-fidelity posterior contours, with an order of magnitude speed-up. Most importantly, the trained emulator can be re-used for extremely fast impact and optimization studies. We demonstrate this feature by studying baryonic physics effects in LSST-Y1 3×2 point analyses where each one of our MCMC runs takes approximately 5 min. This technique enables future cosmological analyses to map out the science return as a function of analysis choices and survey strategy.

Astronomy & Astrophysics↗

DOE OSTI2022

Accelerating Noisy VQE Optimization with Gaussian Processes

Hybrid variational quantum algorithms, which combine a classical optimizer with evaluations on a quantum chip, are the most promising candidates to show quantum advantage on current noisy, intermediate-scale quantum (NISQ) devices. The classical optimizer is required to perform well in the presence of noise in the objective function evaluations, or else it becomes the weakest link in the algorithm. We introduce the use of Gaussian Processes (GP) as surrogate models to reduce the impact of noise and to provide high quality seeds to escape local minima, whether real or noise-induced. We build this as a framework on top of local optimizations, for which we choose Implicit Filtering (ImFil) in this study. ImFil is a state-of-the-art, gradient-free method, which in comparative studies has been shown to outperform on noisy VQE problems. The result is a new method: "GP+ImFil". We show that when noise is present, the GP+ImFil approach finds results closer to the true global minimum in fewer evaluations than standalone ImFil, and that it works particularly well for larger dimensional problems. Using GP to seed local searches in a multi-modal landscape shows mixed results: although it is capable of improving on ImFil standalone, it does not do so consistently and would only be preferred over other, more exhaustive, multistart methods if resources are constrained.

Muller, Juliane↗

DOE OSTI2026

Automated scanning probe microscopy of combinatorial ferroelectric libraries: Gaussian-process-guided exploration and noise-aware experiment planning

Combinatorial materials libraries provide an efficient route for mapping composition–property relationships, but their broader impact depends on rapid, quantitative, and functionally relevant characterization. Scanning Probe Microscopy (SPM), including piezoresponse force microscopy (PFM), offers significant potential for quantitative, functionally relevant combi-library readouts. Here, we implement a fully automated SPM workflow for ferroelectric combinatorial libraries and benchmark Gaussian-process-based Bayesian optimization strategies for autonomous experiment planning. The workflow integrates automated probe motion, contact optimization, imaging, and dual amplitude resonance tracking-PFM spectroscopy, and uses scalarized spectroscopic observables to guide subsequent measurements. Stage motion, probe engagement, in-contact tuning, imaging, spectroscopy, and the choice of the next measurement location all proceed without human input. We demonstrate the approach on Sm-doped BiFeO 3 and Zn x Mg 1−x O libraries. By comparing vanilla Bayesian optimization with a measured-noise variant, we show that explicit treatment of local reproducibility can improve modeling of composition-dependent response when the measured variance is physically meaningful, but can also reduce robustness when variability is dominated by outliers or topographic artifacts. Furthermore, these results establish automated SPM as a bridge between combinatorial synthesis and quantitative functional characterization.

Liu, Yu [University of Tennessee, Knoxville, TN (U↗

DOE OSTI2026

Desmearing Bonse–Hart USANS data using Bayesian Gaussian process regression

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

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

DOE OSTI2024

Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.

Science & Technology - Other Topics↗

DOE OSTI2022

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Physics-constrained machine learning is emerging as an important topic in the field of machine learning for physics. One of the most significant advantages of incorporating physics constraints into machine learning methods is that the resulting model requires significantly less data to train. By incorporating physical rules into the machine learning formulation itself, the predictions are expected to be physically plausible. Gaussian process (GP) is perhaps one of the most common methods in machine learning for small datasets. In this paper, we investigate the possibility of constraining a GP formulation with monotonicity on three different material datasets, where one experimental and two computational datasets are used. The monotonic GP is compared against the regular GP, where a significant reduction in the posterior variance is observed. The monotonic GP is strictly monotonic in the interpolation regime, but in the extrapolation regime, the monotonic effect starts fading away as one goes beyond the training dataset. Imposing monotonicity on the GP comes at a small accuracy cost, compared to the regular GP. The monotonic GP is perhaps most useful in applications where data are scarce and noisy, and monotonicity is supported by strong physical evidence.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Gaussian Process Regression for Aggregate Baseline Load Forecasting

Demand response (DR) is one of the most effective ways to maintain the reliability and improve the flexibility of power systems. Accurate forecasts of baseline loads are essential for DR programs. In the era of big data, machine learning-based approaches present a unique opportunity for baseline load forecasting. Thus, this paper presents a machine learning-based approach using a relatively less explored algorithm, Gaussian process regression (GPR), to forecast aggregate baseline loads. As such, a dataset was generated using a set of EnergyPlus simulations. Using the generated dataset, a GPR-based forecasting model was developed. In addition, support vector regression (SVR)-, artificial neural network (ANN)-, and averaging-based models were developed as baseline models for comparison. These models were compared in terms of accuracy, simplicity, and integrity. The prediction performance of the models showed that the GPR-based model is more accurate and reliable than the others. Such high performance shows the potential of the GPR in baseline load forecasting. GPR, therefore, can be used for DR applications.

Amasyali, Kadir↗

DOE OSTI2021

Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

25 ENERGY STORAGE↗