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DOE OSTI2019

Reconstructing probability distributions with Gaussian processes

Modern cosmological analyses constrain physical parameters using Markov Chain Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques are computationally expensive to run and require up to thousands of CPU hours to complete. Here we present a method for reconstructing the log-probability distributions of completed experiments from an existing chain (or any set of posterior samples). Here, the reconstruction is performed using Gaussian process regression for interpolating the log-probability. This allows for easy resampling, importance sampling, marginalization, testing different samplers, investigating chain convergence, and other operations. As an example use case, we reconstruct the posterior distribution of the most recent Planck 2018 analysis. We then resample the posterior, and generate a new chain with 40 times as many points in only 30 min. Our likelihood reconstruction tool is made publicly available online.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

NASA NTRS2022

Searching for Quasi-periodic Oscillations in Astrophysical Transients Using Gaussian Processes

Analyses of quasi-periodic oscillations(QPOs)are important to understanding the dynamic behavior in manyastrophysical objects during transient events like gamma-ray bursts, solarflares, magnetarflares, and fast radiobursts. Astrophysicists often search for QPOs with frequency-domain methods such as(Lomb–Scargle)periodograms, which generally assume power-law models plus some excess around the QPO frequency. Time-series data can alternatively be investigated directly in the time domain using Gaussian process(GP)regression.While GP regression is computationally expensive in the general case, the properties of astrophysical data andmodels allow fast likelihood strategies. Heteroscedasticity and nonstationarity in data have been shown to causebias in periodogram-based analyses. GPs can take account of these properties. Using GPs, we model QPOs as astochastic process on top of a deterministicflare shape. Using Bayesian inference, we demonstrate how to infer GPhyperparameters and assign them physical meaning, such as the QPO frequency. We also perform model selectionbetween QPOs and alternative models such as red noise and show that this can be used to reliablyfind QPOs. Thismethod is easily applicable to a variety of different astrophysical data sets. We demonstrate the use of this methodon a range of short transients: a gamma-ray burst, a magnetarflare, a magnetar giantflare, and simulated solarflare data.

Moritz Hubner↗

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↗

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 OSTI2026

Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

DOE OSTI2023

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data

In this work, we present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules in which Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Non-uniform active learning for Gaussian process models with applications to trajectory informed aerodynamic databases

The ability to non-uniformly weight the input space is desirable for many applications, and has been explored for space-filling approaches. Increased interests in linking models, such as in a digital twinning framework, increases the need for sampling emulators where they are most likely to be evaluated. In particular, here we apply non-uniform sampling methods for the construction of aerodynamic databases. This paper combines non-uniform weighting with active learning for Gaussian Processes (GPs) to develop a closed-form solution to a non-uniform active learning criterion. We accomplish this by utilizing a kernel density estimator as the weight function. We demonstrate the need and efficacy of this approach with an atmospheric entry example that accounts for both model uncertainty as well as the practical state space of the vehicle, as determined by forward modeling within the active learning loop.

42 ENGINEERING↗

DOE OSTI2025

Enabling Robust Exoplanet Atmospheric Retrievals with Gaussian Processes

Atmospheric retrievals are essential tools for interpreting exoplanet transmission and eclipse spectra, enabling quantitative constraints on the chemical composition, aerosol properties, and thermal structure of planetary atmospheres. The James Webb Space Telescope (JWST) offers unprecedented spectral precision, resolution, and wavelength coverage, unlocking transformative insights into the formation, evolution, climate, and potential habitability of planetary systems. However, this opportunity is accompanied by challenges: modeling assumptions and unaccounted-for noise or signal sources can bias retrieval outcomes and their interpretation. To address these limitations, we introduce a Gaussian process (GP)-aided atmospheric retrieval framework that flexibly accounts for unmodeled features and correlated noise in exoplanet spectra. We validate this method on synthetic JWST observations, and show that GP-aided retrievals reduce bias in inferred abundances and better capture model–data mismatches than traditional approaches. We also introduce the concept of mean squared error to quantify the trade-off between bias and variance, arguing that this metric more accurately reflects retrieval performance than bias alone. We then reanalyze the NIRISS/SOSS JWST transmission spectrum of WASP-96 b, finding that GP-aided retrievals yield broader constraints on CO 2 and H 2 O, possibly alleviating tension between previous retrieval results and equilibrium predictions. Our GP framework provides precise and accurate constraints while highlighting regions where models fail to explain the data. As JWST matures and future facilities come online, a deeper understanding of the limitations of both data and models will be essential, and GP-enabled retrievals like the one presented here offer a principled path forward.

Rotman, Yoav [Arizona State Univ., Tempe, AZ (Unit↗

DOE OSTI2020

Efficient neutrino oscillation parameter inference using Gaussian processes

The unified approach of Feldman and Cousins allows for exact statistical inference of small signals that commonly arise in high energy physics. It has gained widespread use, for instance, in measurements of neutrino oscillation parameters in long-baseline experiments. However, the approach relies on the Neyman construction of the classical confidence interval and is computationally intensive as it is typically done in a grid-based fashion over the entire parameter space. In this article, we propose an efficient algorithm for the Feldman-Cousins approach using Gaussian processes to construct confidence intervals iteratively. Further, we show that in the neutrino oscillation context, one can obtain confidence intervals fives times faster in one dimension and ten times faster in two dimensions, while maintaining an accuracy above 99.5%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Quantifying experimental edge plasma evolution via multidimensional adaptive Gaussian process regression

The edge density and temperature of tokamak plasmas are strongly correlated with energy and particle confinement and their quantification is fundamental to understanding edge dynamics. These quantities exhibit behaviours ranging from sharp plasma gradients and fast transient phenomena (e.g. transitions between low and high confinement regimes) to nominal stationary phases. Analysis of experimental edge measurements therefore require robust fitting techniques to capture potentially stiff spatiotemporal evolution. Additionally, fusion plasma diagnostics inevitably involve measurement errors and data analysis requires a statistical framework to accurately quantify uncertainties. This paper outlines a generalized multidimensional adaptive Gaussian process routine capable of automatically handling noisy data and spatiotemporal correlations. We focus on the edge-pedestal region in order to underline advancements in quantifying time-dependent plasma profiles including transport barrier formation on the Alcator C-Mod tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

WearGP: A computationally efficient machine learning framework for local erosive wear predictions via nodal Gaussian processes

Computational fluid dynamics (CFD)-based wear predictions are computationally expensive to evaluate, even with a high-performance computing infrastructure. Thus, it is difficult to provide accurate local wear predictions in a timely manner. Data-driven approaches provide a more computationally efficient way to approximate the CFD wear predictions without running the actual CFD wear models. In this paper, a machine learning (ML) approach, termed WearGP, is presented to approximate the 3D local wear predictions, using numerical wear predictions from steady-state CFD simulations as training and testing datasets. The proposed framework is built on Gaussian process (GP) and utilized to predict wear in a much shorter time. The WearGP framework can be segmented into three stages. At the first stage, the training dataset is built by using a number of CFD simulations in the order of O (10 2 ). At the second stage, the data cleansing and data mining process are performed, where the nodal wear solutions are extracted from the solution database to build a training dataset. At the third stage, the wear predictions are made, using trained GP processes. Two CFD case studies including 3D slurry pump impeller and casing are used to demonstrate the WearGP framework, in which 144 training and 40 testing data points are used to train and test the proposed method, respectively. The numerical accuracy, computational effiency and effectiveness between the WearGP framework and CFD wear model for both slurry pump impellers and casings are compared. It is shown that the WearGP framework can achieve highly accurate results that are comparable with the CFD results, with a relatively small size training dataset, with a computational time reduction in an order of 10 5 to 10 6 .

42 ENGINEERING↗