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Results for “Markov Chain Monte Carlo”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mobility assessment of the BCC and carbide phases in the C-Nb, C-U and Nb-U systems

Uranium carbides with refractory metal additions are considered for Gen IV nuclear reactors and nuclear thermal propulsion as fuels for their high-temperature and corrosion resistant properties. Understanding kinetic effects that dictate microstructural evolution during fabrication and operating conditions is essential to advance technological development of these fuels. This work presents the development of an atomic mobility database for C-Nb-U systems based off available experimental data supported with ab-initio methods. The mobility assessments and uncertainty quantification (using Markov chain Monte Carlo) were conducted in the Kawin software. Carbon diffusion is considered dominant, as metal diffusion is much slower, with niobium diffusion being even slower and rate limiting than uranium metal. We provide a comprehensive and self-consistent thermo-kinetic database that is validated by diffusion couple simulations through Kawin. In conclusion, this enables prediction of microstructural and phase evolution critical for the development and lifetime assessment of next generation nuclear fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications

Here, this paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems — Sampler, MultiApp, Reporter, and Surrogate — in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference; very rare events analysis in nuclear microreactors using active learning; advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction; fluid flow using deep GPs (DGPs); and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. These capabilities are part of the MOOSE framework.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Improvement of two-phase closure models in CTF using Bayesian inference

Under the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, extensive capabilities have been developed in CTF to analyze light-water reactors (LWRs) for normal operating conditions, departure from nucleate boiling (DNB), and system transients. However, further improvements are required in the modeling and simulation of boiling water reactors (BWRs), which is a focus of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, CTF validation results were used to optimize selected modeling coefficients by calibrating to experimental data using a Bayesian inference approach. Here, calibration studies were conducted to improve (vapor) void fraction prediction without worsening the two-phase pressure drop prediction, as well as to improve the two-phase pressure drop prediction. Calibration was performed for interfacial drag and wall shear models. Surrogates were developed to alleviate the computational expense required for sampling the parameter space using Markov chain Monte Carlo (MCMC). An assessment performed with calibrated models demonstrated an improvement of CTF in its prediction of key parameters such as void fraction and two-phase pressure drop.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Discrepancy quantification between experimental and simulated data of CO 2 adsorption isotherm using hierarchical Bayesian estimation

Here, to quantitatively analyze the inconsistencies commonly observed between experimental and simulated adsorption isotherms, parameter estimation of adsorption isotherm models was conducted by hierarchical Bayesian estimation with parameter uncertainties being quantified as probability distributions. The estimation method was implemented using Markov Chain Monte Carlo (MCMC) to analyze multiple data sets obtained from different sources, including a publicly available database. To describe the discrepancies of experimental and simulated adsorption data, the simulation data was set as the reference to which experimental measurements were compared. We applied the proposed approach to analyze CO 2 adsorption isotherms that are measured and simulated on zeolite 13X and MIL-101(Cr). In these case studies, the discrepancy of CO 2 adsorption isotherm was successfully quantified between experimental measurements and predictions given by molecular simulations using Grand Canonical Monte Carlo (GCMC), where uncertainties were quantified as probability distributions. Furthermore, experimental data sets that agree well with the GCMC simulation have been identified, providing insights into experimental and measurement methods as well as choosing the right assumptions in the molecular simulation.

42 ENGINEERING↗
DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Bayesian model for multivariate discrete data using spatial and expert information with application to inferring building attributes

When modeling sparsely observed multivariate data, strong prior information elicited from experts can be used to bolster predictive accuracy and counteract sampling bias. Similarly, modeling autocorrelation in space can help make use of co-occurrence patterns present in many types of spatial data. To make use of both expert prior information and spatial structure, we propose a novel graphical model for a spatial Bayesian network developed specifically to address challenges in inferring the attributes of buildings from geographically sparse observational data. This model is implemented as the sum of a spatial multivariate Gaussian random field and a tabular conditional probability function in real-valued space prior to projection onto the probability simplex. This modeling form is especially suitable for the usage of prior information in the form of sets of atomic rules obtained from experts. To perform inference with missing data, we implement a Markov chain Monte Carlo scheme composed of alternating steps of Gibbs sampling of missing entries and Hamiltonian Monte Carlo for model parameters. A case study in building attribution is presented to highlight the advantages and limitations of this approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Emulator-based Bayesian calibration of a subglacial drainage model

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

58 GEOSCIENCES↗
DOE OSTI2025

Pervaporative Dehydration of 2,3-Butanediol by Dense Poly(vinylidene fluoride) Hollow Fiber Membranes: Parameter Estimation, Process Design, and Technoeconomic Evaluation under Uncertainty

Pervaporation, combined with other separation processes, can effectively remove water from fermentation product streams, making it highly suitable for purifying alcohols like 2,3-butanediol (BDO). In this study, a dense poly(vinylidene fluoride) (PVDF) hollow fiber membrane module prototype was fabricated for BDO dehydration, achieving >0.2 LMH total flux and >95% BDO rejection. With a Markov chain Monte Carlo (MCMC) approach, Bayesian inference was used to quantify the uncertainty of the permeance parameters. A membrane cascade model was developed to scale up a process that purifies a preconcentrated BDO feed (70 wt %) to high purity (90 wt %). Through propagation of the uncertainty of the parameters and sensitivity analyses of the process variables, a cascade design was recommended. Despite data and model limitations, the framework enabled a reliable system analysis and economic evaluation, validated through tight confidence intervals in key process metrics, establishing the foundation for future applications of Bayesian methods in membrane-based processes.

Animal feed↗
DOE OSTI2022

Electrical Conductivities and Association Constants in Dilute Aqueous NdCl 3 Solutions from 298 to 523 K along an Isobar of 25 MPa

Here, electrical measurements were performed in dilute aqueous NdCl 3 solutions from 298 to 523 K along the 25 MPa isobar to obtain limiting conductivities and association constants. The specific conductivity data were estimated using a continuous flow cell and a Markov Chain Monte Carlo (MCMC) correction algorithm. The limiting conductivities for the salts in water were derived by regressing the mean spherical approximation model and speciation analyses based on the MCMC algorithm and the deep earth water model. The limiting conductivities derived from the experimental data were correlated using the Zimmerman-Arcis-Tremaine correlation and agreed well with a predictive correlation proposed by Smolyakov, Anderko, and Lencka. Only the first association constant between neodymium and chloride could be derived at low temperatures (<373 K) due to the apparent large statistical uncertainty of the second association constant. Above 373 K, both association constants could be derived and show a reasonable agreement with Migdisov and Williams-Jones and Gammons et al.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Measuring Relative Energies of Ligand Binding Conformations on Nanocluster Surfaces with Temperature-Dependent FTIR Spectroscopy

We present a method to measure relative energies between binding conformations of carboxylate ligands on InP magic-sized clusters in solution. Using Markov chain Monte Carlo global fitting analysis on temperature-dependent vibrational spectra of cluster-bound ligands, we observe significantly different relative energies between various bidentate and monodentate binding motifs. Relative to the monodentate motif, the chelating conformation is 0.7 ± 0.3 kcal/mol more stable and the syn–syn bridging conformation is 1.1 ± 0.5 kcal/mol more stable, but the syn–anti bridging conformation exhibits no significant difference. Our results demonstrate that the relative energy between monodentate-bound carboxylates and unbound carboxylic acids is 4.52 ± 0.05 kcal/mol, or 1582 ± 19 cm –1 , nearly identical to the carboxylate asymmetric stretching frequency. Here, we suggest that the ligand vibrational energy may play a key role in ligand dissociation by compensating for energy differences between bound and dissociated ligand states. This approach gives important experimental insights into ligand binding and can inform future nanocrystal surface engineering.

Conformation↗
DOE OSTI2021

Joint Bayesian Inference for Near-Surface Explosion Yield and Height-of-Burst

Forensic capabilities to understand chemical and nuclear explosions are greatly aided by an accurate estimate of explosive yield with uncertainty. The relationship between explosive size and geophysical observations of seismic, acoustic, and optical waves can be exploited to provide an estimate of yield. Any near-surface yield estimate is complicated by the surface interaction, so an estimate for the explosion height-of-burst is necessarily included in the relationship. Additionally, the relationship dictates a trade-off between estimates of yield and height-of-burst. Fortunately, the surface interaction for each type of observation is different, which breaks the trade-off, and the inclusion of height-of-burst with multiple data types improves yield estimation. We define simple parametric forward models to relate seismoäcoustoöptic observations from a data set of known explosive yields and height-of-bursts. The parameters of the models and a prediction for the yield and height-of-burst of a new event can then be estimated given new observations via Bayesian inference. We report posterior distribution estimates of the parametric models using a Markov chain Monte Carlo sampling technique. These models are then used to predict the yield and height-of-burst of SUGAR, a historical near-surface nuclear explosion, using its reported historical observations. The reported yield of 1.2 ktonne Trinitrotoluene (TNT)-equivalent (Department of Energy, 2015) is within the estimated posterior. Yield uncertainty can be estimated from the spread of the posterior, which is between 0.9 and 2.1 ktonne TNT-equivalent. The posterior for height-of-burst has a wider range between 10 m below and 8 m above ground that includes the true height-of-burst of 1 m.

58 GEOSCIENCES↗
DOE OSTI2021

Slope-Aspect Induced Climate Differences Influence How Water Is Exchanged Between the Land and Atmosphere

Cross-slope climate differences in the midlatitudes are ecologically important, and impact vegetation-mediated water balance between the earth surface and the atmosphere. We made high-resolution in situ observations of air temperature, relative humidity, soil moisture, insolation, and sap velocity observations on 14 Pacific madrone trees (Arbutus menziesii) spanning adjacent north and south slopes at the University of California's Angelo Coast Range Reserve. To understand the cross-slope response of sap velocity, a proxy for transpiration, to microclimate, we modeled the sap velocity on each slope using a transpiration model driven by ambient environment and parameterized with a Markov Chain Monte Carlo parameter estimation process. The results show that trees on opposing slopes do not follow a shared pattern of physiological response to transpiration drivers. This means that the observed sap velocity differences are not due entirely to observed microclimate differences, but also due to population-level physiological differences, which indicates acclimation to inhabited microclimate. While our present data set and analytical tools do not identify mechanisms of acclimation, we speculate that differing proportions of sun-adapted and shade-adapted leaves, differences in stomatal regulation, and cross-slope root zone moisture differences could explain some of the observed and modeled differences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

On the Reliability of Parameter Inferences in a Multiscale Model for Transport in Stream Corridors

Nonreacting tracer tests capture information about physical processes in transient storage zones including the hyporheic zone (HZ). However, reliably extracting this information from breakthrough curves (BTCs) and distinguishing the effects of in-channel dispersion and transient storage are well-known challenges. Using BTCs from a nonreacting tracer test monitored at multiple locations, we explore ways for reliable parameter estimations. The identifiability of parameters is greatly influenced by the choice of forward and inverse modeling frameworks in addition to the quality of the data. Our forward model is a recently proposed multiscale model that uses subgrid transport models written in the Lagrangian form to represent transport along a diverse set of HZ pathways with a shape-free distribution of travel times. Joint distributions of HZ and channel parameters are estimated using the Markov Chain Monte Carlo technique. Numerical experiments show ambiguity between channel dispersion and HZ transport when the reach length is too short to allow significant solute-HZ interaction, the observation period is too brief to observe the tailing behavior, or the solute source is spread in time. In contrast, we obtained reliable parameter estimates by simultaneously fitting BTCs observed at different locations in the test reach using a single set of HZ parameters and section-specific channel areas and dispersion coefficients. Furthermore, this study demonstrates the estimation of travel time distributions, HZ exchange rates, and channel parameters in a new multiscale approach and offers guidance for extracting reliable parameter estimates from multiple BTCs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Intra-Specific Variability in Plant Hydraulic Parameters Inferred From Model Inversion of Sap Flux Data

Understanding plant hydraulic regulation is critical for predicting plant and ecosystem responses to projected increases in drought stress. Plant hydraulic regulation is controlled by observable, diverse plant hydraulic traits that can vary as much across individuals of the same species as they do across different species. Direct measurements of plant hydraulic traits from a range of ecosystems remain limited in comparison to other, more readily measured traits (e.g., specific leaf area). Furthermore, plant hydraulic trait measurements, often made at leaf or branch levels, are not easily scaled to whole-plant values that are typically used to predict plant and ecosystem fluxes. In this study, multiple whole-plant hydraulic parameters are inferred from observations of plant water use (i.e., sap flow), soil properties, and meteorological data. We use a Markov Chain Monte Carlo model inversion approach to obtain the best estimates and uncertainty of plant hydraulic parameters that capture whole-plant effective embolism resistance and stomatal sensitivity to decreasing plant water potential. We then use the inferred values in the model to estimate whole-tree water use and isohydricity. This approach reliably infers whole-plant parameter values with enough specificity to resolve inter- and intra-specific differences, and thus supplements time- and labor-intensive direct measurements of traits.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. 2. Quantifying the Uncertainty

Uncertainty quantification of groundwater (GW) aquifer parameters is critical for efficient management and sustainable extraction of GW resources. These uncertainties are introduced by the data, model, and prior information on the parameters. We develop a Bayesian inversion framework that uses Interferometric Synthetic Aperture Radar (InSAR) surface deformation data to infer the laterally heterogeneous permeability of a transient linear poroelastic model of a confined GW aquifer. The Bayesian solution of this inverse problem takes the form of a posterior probability density of the permeability. Exploring this posterior using classical Markov chain Monte Carlo (MCMC) methods is computationally prohibitive due to the large dimension of the discretized permeability field and the expense of solving the poroelastic forward problem. However, in many partial differential equation (PDE)-based Bayesian inversion problems, the data are only informative in a few directions in parameter space. For the poroelasticity problem, we prove this property theoretically for a one-dimensional problem and demonstrate it numerically for a three-dimensional aquifer model. Here we design a generalized preconditioned Crank-Nicolson (gpCN) MCMC method that exploits this intrinsic low dimensionality by using a low-rank-based Laplace approximation of the posterior as a proposal, which we build scalably. The feasibility of our approach is demonstrated through a real GW aquifer test in Nevada. The inherently two-dimensional nature of InSAR surface deformation data informs a sufficient number of modes of the permeability field to allow detection of major structures within the aquifer, significantly reducing the uncertainty in the pressure and the displacement quantities of interest.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Constraining Bedrock Groundwater Residence Times in a Mountain System With Environmental Tracer Observations and Bayesian Uncertainty Quantification

Groundwater residence time distributions provide fundamental insights on the hydrological processes within watersheds. Yet, observations that can constrain groundwater residence times over broad timescales remain scarce in mountain catchment studies. We use environmental tracers (CFC-12, SF 6 , 3 H, and 4 He) to investigate groundwater residence times along a hillslope in the East River Watershed, Colorado, USA. We develop a Bayesian inference framework that applies a Markov-chain Monte Carlo (MCMC) approach to estimate noble gas recharge temperature, elevation, and excess-air parameters and the resulting environmental tracer concentrations. MCMC is then used to propagate the environmental tracer uncertainties to estimates of groundwater mean residence times inferred with lumped parameter models. All samples contain 3 H, CFC-12, and SF 6 in addition to terrigenic 4 He, suggesting a mixture of water characterized by modern and premodern residence times. 4He exponential mean residence times range from hundreds of years at the upslope well to thousands of years at the toe-slope well assuming average crustal production rates. We find that binary mixing residence time distributions with separate young and old mixing fractions are needed to predict the 4 He, CFC-12, SF 6 , and 3 H observations, supporting the importance of flow path mixing in this bedrock system. Our findings that the fractured bedrock hosts groundwater with a mixture of residence times ranging from decades to millennia suggest variable recharge dynamics and flow path mixing along the hillslope and highlight the importance of characterizing groundwater systems with observations that are sensitive to transport over a broad range of residence times.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A Diffusion‐Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration

Abstract Calibrating land surface models and accurately quantifying their uncertainty are crucial for improving the reliability of simulations of complex environmental processes. This, in turn, advances our predictive understanding of ecosystems and supports climate‐resilient decision‐making. Traditional calibration methods, however, face challenges of high computational costs and difficulties in accurately quantifying parameter uncertainties. To address these issues, we develop a diffusion‐based uncertainty quantification (DBUQ) method. Unlike conventional generative diffusion methods, which are computationally expensive and memory‐intensive, DBUQ innovates by formulating a parameterized generative model and approximates this model through supervised learning, which enables quick generation of parameter posterior samples to quantify its uncertainty. DBUQ is effective, efficient, and general‐purpose, making it suitable for site‐specific ecosystem model calibration and broadly applicable for parameter uncertainty quantification across various earth system models. In this study, we applied DBUQ to calibrate the Energy Exascale Earth System Model land model at the Missouri Ozark AmeriFlux forest site. Results indicated that DBUQ produced accurate parameter posterior distributions similar to those from Markov Chain Monte Carlo sampling but with 30 times less computing time. This significant improvement in efficiency suggests that DBUQ can enable rapid, site‐level model calibration at a global scale, enhancing our predictive understanding of climate impacts on terrestrial ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Using Machine Learning to Generate a GISS ModelE Calibrated Physics Ensemble (CPE)

A neural network (NN) surrogate of the NASA GISS ModelE atmosphere (version E3) is trained on a perturbed parameter ensemble (PPE) spanning 45 physics parameters and 36 outputs. The NN is leveraged in a Markov Chain Monte Carlo (MCMC) Bayesian parameter inference framework to generate a second posterior constrained ensemble coined a “calibrated physics ensemble,” or CPE. The CPE members are characterized by diverse parameter combinations and are, by definition, close to top-of-atmosphere radiative balance, and must broadly agree with numerous hydrologic, energy cycle and radiative forcing metrics simultaneously. Global observations of numerous cloud, environment, and radiation properties (provided by global satellite products) are crucial for CPE generation. The inference framework explicitly accounts for discrepancies (or biases) in satellite products during CPE generation. We demonstrate that product discrepancies strongly impact calibration of important model parameter settings (e.g., convective plume entrainment rates; fall speed for cloud ice). Structural improvements new to E3 are retained across CPE members (e.g., stratocumulus simulation). Notably, the framework improved the simulation of shallow cumulus and Amazon rainfall while not degrading radiation fields, an upgrade that neither default parameters nor Latin Hypercube parameter searching achieved. Analyses of the initial PPE suggested several parameters were unimportant for output variation. However, many “unimportant” parameters were needed for CPE generation, a result that brings to the forefront how parameter importance should be determined in PPEs. From the CPE, two diverse 45-dimensional parameter configurations are retained to generate radiatively-balanced, auto-tuned atmospheres that were used in two E3 submissions to CMIP6.

54 ENVIRONMENTAL SCIENCES↗