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DOE OSTI2020

Dealing with Measurement Uncertainties as Nuisance Parameters in Bayesian Model Calibration

In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. Here, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Bayesian uncertainty quantification of tristructural isotropic particle fuel silver release: Decomposing model inadequacy plus experimental noise and parametric uncertainties

Tristructural isotropic (TRISO) particle fuel is one of the most promising fuel concepts enabling high temperature and high burnup reactor operation. One dominant source of radioactivity released from the TRISO particles is silver (Ag), which is subject to a high release fraction and long decay life compared to other fission products. Previous modeling efforts using the fuel performance code BISON indicated nonnegligible uncertainties in modeling the diffusion process of fission products in TRISO compared to the Advanced Gas Reactor experiments. The overall uncertainties observed when modeling the fission product diffusion can result from uncertainties in model parameters, noisy experimental measurements, and deficiencies in the developed models. The three types of underlying uncertainties have not yet been properly quantified in open literature. Here, this paper presents the Bayesian uncertainty quantification (UQ) using massively parallelizable Markov chain Monte Carlo samplers. The uncertainties due to model parameters, model inadequacy, and experimental measurement noise are quantified, with the σ term used to represent the sum of the model inadequacy and measurement noise uncertainties. It is worth noting that this is the first time the σ term is inferred for nuclear fuel experiments, as compared to using prescribed values for uncertainty quantification in previous work. The parallelizable Markov chain Monte Carlo samplers efficiently infer the model parameters and the σ term, giving insight into physical parameters like diffusion coefficients and the combined model discrepancy and measurement noise. A subsequent forward uncertainty quantification (UQ) is also performed based on the calibration results to generate more accurate predictions of the Ag release. The model inadequacy plus experimental noise is the most dominant source of uncertainty compared to the parametric uncertainty. All the UQ analyses presented in this work are based on the second series of the irradiation experiments in the Advanced Gas Reactor program.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

Modeling Radiation Detection Using a Mixed-Effects Statistical Model for Background Variation

In this paper, we consider radiation source localization in an urban environment as an inverse problem and use Bayesian parameter estimation techniques to infer the source location and intensity. Since parameter estimation generally requires a large number of model evaluations, we employ a simplified photon transport model, as in a 2017 paper by Stefanescu, et al., to reduce computational requirements. However, the model in the 2017 paper does not account for the physical reality that background radiation varies with position within an urban locale. We incorporate statistical mixed-effects modeling into the simplified transport equation from the Stefanescu, et al. paper to reflect individual variation among the background radiation measurements at multiple detector locations. With our new model, we use a Bayesian DRAM-within-Gibbs technique, which incorporates the Delayed Rejection Adaptive Metropolis (DRAM) algorithm, to estimate the mixed-effects parameters. We note that without adequate prior information, we were unable to simultaneously estimate the set of parameters corresponding to the source intensity, source location, and individual background radiation counts. By calibrating the background in the absence of a source, we obtained narrow prior distributions, which permitted us to jointly infer the source intensity and location and the background radiation distribution.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

Improved characterization of heterogeneous permeability in saline aquifers from transient pressure data during freshwater injection

Managing recharge of freshwater into saline aquifers requires accurate estimation of the heterogeneous permeability field for maximizing injection and recovery efficiency. Here we present a methodology for subsurface characterization in saline aquifers that takes advantage of the density difference between the injected freshwater and the ambient saline groundwater. We combine high-resolution forward modeling of density-driven flow with an efficient Bayesian geostatistical inversion algorithm. In the presence of a density difference between the injected and ambient fluids due to differences in salinity, the pressure field is coupled to the spatial distribution of salinity. This coupling renders the pressure field transient: the time evolution of the salinity distribution controls the density distribution which then leads to a time-evolving pressure distribution. We exploit this coupling between pressure and salinity to obtain an improved characterization of the permeability field without multiple pumping tests or additional salinity measurements. We show that the inversion performance improves with an increase in the mixed convection ratio—the relative importance between viscous forces from injection and buoyancy forces from density difference. Thus, our work shows that measuring transient pressure data at multiple sampling points during freshwater injection into saline aquifers can be an effective strategy for aquifer characterization, key to the successful management of aquifer recharge.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging

In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy laboratories.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Mapping Aedes aegypti (Diptera: Culicidae) and Aedes albopictus Vector Mosquito Distribution in Brownsville, TX

Abstract Aedes mosquitoes are vectors of several emerging diseases and are spreading worldwide. We investigated the spatiotemporal dynamics of Aedes aegypti (Linnaeus) and Aedes albopictus (Skuse) mosquito trap captures in Brownsville, TX, using high-resolution land cover, socioeconomic, and meteorological data. We modeled mosquito trap counts using a Bayesian hierarchical mixed-effects model with spatially correlated residuals. The models indicated an inverse relationship between temperature and mosquito trap counts for both species, which may be due to the hot and arid climate of southern Texas. The temporal trend in mosquito populations indicated Ae. aegypti populations peaking in the late spring and Ae. albopictus reaching a maximum in winter. Our results indicated that seasonal weather variation, vegetation height, human population, and land cover determine which of the two Aedes species will predominate.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Data-Driver Interpretation of Ultradeep Azimuthal Propagation

We report the interpretation of geological features around the borehole stresses on the search of true earth model parameters. Different from the conventional logging-while-drilling (LWD) technologies, such as wireline induction and propagation resistivity tools, the azimuthal resistivity measurement acquires the ability of directional sensitivity. Within this decade, this type of tools has been greatly enhanced with over hundred feet depth-of-detection (DoD). To resolve the interpretation of geological features within 100 feet from the borehole, the multiple-layer structure must be considered. However, the traditional methods can never handle the highly nonlinear inverse problems especially facing on the complicated earth structure. Meanwhile, no justifiable uncertainty of inverse parameters can be provided. The statistical methods have been adopted to search for the global statistical distribution and uncertainties of earth model parameters. However, the most attempts are still stuck in non-uniqueness of the solutions since the structure of earth model has been predefined, where the number of layers is assumed, which introduces another ambiguity into the model interpretation. This paper develops a general trans-dimensional Bayesian methodology to solve non-linear inverse problem of earth layer resistivity and depth to the layer boundaries, from the interpretation of ultra-deep azimuthal resistivity measurements. The presented work is a data-driven approach to search out the multi-dimensional parameter spaces. Finally, the simulations tell that the algorithm can efficiently solve the earth model interpretation within a hundred feet from borehole, and examine the uncertainty of earth model parameters.

58 GEOSCIENCES↗

DOE OSTI2026

Multi-Modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation

As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. Here, we demonstrate improved prediction accuracy and uncertainty quantification compared to unimodal surrogate models for both scalar and time series data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A Bayesian statistical approach to inferring particle dynamics from in-situ pump POC and chloropigment data from the Mediterranean Sea

Concentrations of chloropigments and particulate organic carbon (POC) in large-volume in-situ pump samples from the Mediterranean Sea were used to estimate rate constants of processes that control the fate of particles, and specifically chloropigments, in the water column. In this paper we introduce a Bayesian statistical inversion method that combines the data with a new box model and has the capacity to infer rate constants for POC respiration/dissolution, chlorophyll and pheopigment degradation, and particle aggregation and disaggregation. We use first-order kinetics to model disaggregation, and use both first-order and second-order kinetics to model aggregation. Using these methods, the estimated small-particle (1–70 μm) POC respiration rate constant was 2.44 -1.00 +1.69 yr -1 (0.41 yr). The estimated disaggregation and second-order aggregation rate constants were 85.6 -36.4 +63.4 yr -1 (1.17×10 -2 yr) and 2.78 -1.17 +2.01 μM -1 yr -1 , respectively. Using the optimal rate constants and the corresponding particle concentrations, disaggregation is ~4.2 times faster than the small-size POC dissolution rate, which indicates that disaggregation is a dominant processes at the time of sampling. More importantly, by comparing our results with those of previous studies, we conclude that sampling methods have less influence than tracers themselves on inferring particle dynamic rate constants. We previously introduced a somewhat similar approach to modeling SV sediment trap data, but large volume pumps are a much more common sample collection method in oceanographic surveys than SV sediment traps, and thus our new model should have a wider applicability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Tuning a RANS k-e model for jet-in-crossflow simulations.

We develop a novel calibration approach to address the problem of predictive k e RANS simulations of jet-incrossflow. Our approach is based on the hypothesis that predictive k e parameters can be obtained by estimating them from a strongly vortical flow, specifically, flow over a square cylinder. In this study, we estimate three k e parameters, C%CE%BC, Ce2 and Ce1 by fitting 2D RANS simulations to experimental data. We use polynomial surrogates of 2D RANS for this purpose. We conduct an ensemble of 2D RANS runs using samples of (C%CE%BC;Ce2;Ce1) and regress Reynolds stresses to the samples using a simple polynomial. We then use this surrogate of the 2D RANS model to infer a joint distribution for the k e parameters by solving a Bayesian inverse problem, conditioned on the experimental data. The calibrated (C%CE%BC;Ce2;Ce1) distribution is used to seed an ensemble of 3D jet-in-crossflow simulations. We compare the ensemble's predictions of the flowfield, at two planes, to PIV measurements and estimate the predictive skill of the calibrated 3D RANS model. We also compare it against 3D RANS predictions using the nominal (uncalibrated) values of (C%CE%BC;Ce2;Ce1), and find that calibration delivers a significant improvement to the predictive skill of the 3D RANS model. We repeat the calibration using surrogate models based on kriging and find that the calibration, based on these more accurate models, is not much better that those obtained with simple polynomial surrogates. We discuss the reasons for this rather surprising outcome.

Lefantzi, Sophia↗

DOE OSTI2017

Methane emissions from dairies in the Los Angeles Basin

We estimate the amount of methane (CH 4 ) emitted by the largest dairies in the southern California region by combining measurements from four mobile solar-viewing ground-based spectrometers (EM27/SUN), in situ isotopic 13/12 CH 4 measurements from a CRDS analyzer (Picarro), and a high-resolution atmospheric transport simulation with a Weather Research and Forecasting model in large-eddy simulation mode (WRF-LES). The remote sensing spectrometers measure the total column-averaged dry-air mole fractions of CH 4 and CO 2 (X CH 4 and X CO 2 ) in the near infrared region, providing information on total emissions of the dairies at Chino. Differences measured between the four EM27/SUN ranged from 0.2 to 22ppb (part per billion) and from 0.7 to 3ppm (part per million) for X CH 4 and X CO 2 , respectively. To assess the fluxes of the dairies, these differential measurements are used in conjunction with the local atmospheric dynamics from wind measurements at two local airports and from the WRF-LES simulations at 111m resolution. Our top-down CH 4 emissions derived using the Fourier transform spectrometers (FTS) observations of 1.4 to 4.8ppts -1 are in the low end of previous top-down estimates, consistent with reductions of the dairy farms and urbanization in the domain. However, the wide range of inferred fluxes points to the challenges posed by the heterogeneity of the sources and meteorology. Inverse modeling from WRF-LES is utilized to resolve the spatial distribution of CH 4 emissions in the domain. Both the model and the measurements indicate heterogeneous emissions, with contributions from anthropogenic and biogenic sources at Chino. A Bayesian inversion and a Monte Carlo approach are used to provide the CH 4 emissions of 2.2 to 3.5ppts -1 at Chino.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A hierarchical Bayesian model for background variation in radiation source localization

In this paper, we apply a new model to account for varying background radiation in radiological source localization. We present a hierarchical Bayesian model that simultaneously infers background and source location parameters without requiring separate estimation of the background radiation at each detector location. We employ a simplified photon transport model to reduce the computational expense of Bayesian model calibration. Furthermore, we demonstrate the model accuracy by localizing a cesium-137 source in a simulated city block, and we analyze experimental field measurements with varying background. In both cases, the model provides sufficient fidelity that we can locate the source while simultaneously estimating background radiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Accurate and Rapid Forecasts for Geologic Carbon Storage via Learning-Based Inversion-Free Prediction

Carbon capture and storage (CCS) is one approach being studied by the U.S. Department of Energy to help mitigate global warming. The process involves capturing CO 2 emissions from industrial sources and permanently storing them in deep geologic formations (storage reservoirs). However, CCS projects generally target “green field sites,” where there is often little characterization data and therefore large uncertainty about the petrophysical properties and other geologic attributes of the storage reservoir. Consequently, ensemble-based approaches are often used to forecast multiple realizations prior to CO 2 injection to visualize a range of potential outcomes. In addition, monitoring data during injection operations are used to update the pre-injection forecasts and thereby improve agreement between forecasted and observed behavior. Thus, a system for generating accurate, timely forecasts of pressure buildup and CO 2 movement and distribution within the storage reservoir and for updating those forecasts via monitoring measurements becomes crucial. This study proposes a learning-based prediction method that can accurately and rapidly forecast spatial distribution of CO 2 concentration and pressure with uncertainty quantification without relying on traditional inverse modeling. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO 2 storage site operators with an effective tool for timely and informative decision making based on limited simulation and monitoring data.

58 GEOSCIENCES↗

DOE OSTI2020

Bayesian Poroelastic Aquifer Characterization From InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate

Characterizing the properties of groundwater aquifers is essential for predicting aquifer response and managing groundwater resources. In this work, we develop a high-dimensional scalable Bayesian inversion framework governed by a three-dimensional quasi-static linear poroelastic model to characterize lateral permeability variations in groundwater aquifers. In this work, we determine the maximum a posteriori (MAP) point of the posterior permeability distribution from centimeter-level surface deformation measurements obtained from Interferometric Synthetic Aperture Radar (InSAR). The scalability of our method to high parameter dimension is achieved through the use of adjoint-based derivatives, inexact Newton methods to determine the MAP point, and a Mat´ern class sparse prior precision operator. Together, these guarantee that the MAP point is found at a cost, measured in number of forward/adjoint poroelasticity solves, that is independent of the parameter dimension. We apply our methodology to a test case for a municipal well in Mesquite, Nevada, in which InSAR and GPS surface deformation data are available. We solve problems with up to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs. A consistent treatment of noise level is employed so that the aquifer characterization result does not depend on the pixel spacing of surface deformation data. Our results show that the use of InSAR data significantly improves characterization of lateral aquifer heterogeneity, and the InSAR-based aquifer characterization recovers complex lateral displacement trends observed by independent daily GPS measurements.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

Top-down estimate of methane emissions in California using a mesoscale inverse modeling technique: The South Coast Air Basin

Methane (CH 4 ) is the primary component of natural gas and has a larger global warming potential than CO 2 . Some recent top-down studies based on observations showed CH 4 emissions in California's South Coast Air Basin (SoCAB) were greater than those expected from population-apportioned bottom-up state inventories. In this study, we quantify CH 4 emissions with an advanced mesoscale inverse modeling system at a resolution of 8 km × 8 km, using aircraft measurements in the SoCAB during the 2010 Nexus of Air Quality and Climate Change campaign to constrain the inversion. To simulate atmospheric transport, we use the FLEXible PARTicle-Weather Research and Forecasting (FLEXPART-WRF) Lagrangian particle dispersion model driven by three configurations of the Weather Research and Forecasting (WRF) mesoscale model. We determine surface fluxes of CH 4 using a Bayesian least squares method in a four-dimensional inversion. Simulated CH4 concentrations with the posterior emission inventory achieve much better correlations with the measurements (R2 = 0.7) than using the prior inventory (U.S. Environmental Protection Agency's National Emission Inventory 2005, R 2 = 0.5). The emission estimates for CH 4 in the posterior, 46.3 ± 9.2 Mg CH 4 /h, are consistent with published observation-based estimates. Changes in the spatial distribution of CH 4 emissions in the SoCAB between the prior and posterior inventories are discussed. Missing or underestimated emissions from dairies, the oil/gas system, and landfills in the SoCAB seem to explain the differences between the prior and posterior inventories. Furthermore, we estimate that dairies contributed 5.9 ± 1.7 Mg CH 4 /h and the two sectors of oil and gas industries (production and downstream) and landfills together contributed 39.6 ± 8.1 Mg CH 4 /h in the SoCAB.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2013

BAYESIAN ANALYSIS OF MULTIPLE HARMONIC OSCILLATIONS IN THE SOLAR CORONA

The detection of multiple mode harmonic kink oscillations in coronal loops enables us to obtain information on coronal density stratification and magnetic field expansion using seismology inversion techniques. The inference is based on the measurement of the period ratio between the fundamental mode and the first overtone and theoretical results for the period ratio under the hypotheses of coronal density stratification and magnetic field expansion of the wave guide. We present a Bayesian analysis of multiple mode harmonic oscillations for the inversion of the density scale height and magnetic flux tube expansion under each of the hypotheses. The two models are then compared using a Bayesian model comparison scheme to assess how plausible each one is given our current state of knowledge.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Estimating methane emissions in California's urban and rural regions using multitower observations

Here, we present an analysis of methane (CH 4 ) emissions using atmospheric observations from 36 thirteen sites in California during June 2013 – May 2014. A hierarchical Bayesian inversion 37 method is used to estimate CH 4 emissions for spatial regions (0.3° pixels for major regions) by 38 comparing measured CH 4 mixing ratios with transport model (WRF-STILT) predictions based 39 on seasonally varying California-specific CH 4 prior emission models. The transport model is 40 assessed using a combination of meteorological and carbon monoxide (CO) measurements 41 coupled with the gridded California Air Resources Board (CARB) carbon monoxide (CO) 42 emission inventory. Hierarchical Bayesian inversion suggests that state annual anthropogenic 43 CH 4 emissions are 2.42 ± 0.49 Tg CH 4 /yr (at 95% confidence, including transport bias 44 uncertainty), higher (1.2 - 1.8 times) than the CARB current inventory (1.64 Tg CH 4 /yr in 2013). 45 We note that the estimated CH 4 emissions drop to 1.0 - 1.6 times the CARB inventory if we 46 correct for the 10% median CH 4 emissions assuming the bias in CO analysis is applicable to 47 CH 4 . The CH 4 emissions from the Central Valley and urban regions (San Francisco Bay and 48 South Coast Air Basins) account for ~58% and 26% of the total posterior emissions, 49 respectively. This study suggests that the livestock sector is likely the major contributor to the 50 state total CH 4 emissions, in agreement with CARB’s inventory. Attribution to source sectors for 51 sub-regions of California using additional trace gas species would further improve the 52 quantification of California’s CH 4 emissions and mitigation efforts towards the California Global 53 Warming Solutions Act of 2006 (AB-32).

54 ENVIRONMENTAL SCIENCES↗