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DOE OSTI2022

Proxy-Based Bayesian Inversion Of Poroelastic Simulations To Interpret Strain Tensor Data Measured During Well Testing

The long runtimes of 3D poroelastic numerical simulators makes it impractical to interpret deformation datasets using many inversion schemes. Recent advances in instrumentation have made it possible to measure the strain tensor during well testing, but the lack of robust inversion methods is limiting the ability to interpret these data. We have developed an inversion workflow that reduces the number of computations required to complete a Bayesian inversion using DREAMzs. The workflow trains a KNN model using output from the poroelastic simulator, and then uses the KNN model as a proxy for the simulator during inversion. The workflow also includes a strategy for ensuring the results from the proxy model converge to the results from the simulator, ensuring the accuracy of the final results. An idealized example configured to represent a well test in a deep aquifer is used to verify that the workflow correctly identifies parameters and characterizes noise. Field data measured using strainmeters during an injection test at an oil reservoir in Oklahoma are used to evaluate performance with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), and the results are used to characterize posterior parameter distribution and evaluate the prediction uncertainty. This approach makes it feasible to invert strain data measured during well testing and this has the potential to improve the characterization of aquifers and reservoirs.

Roudini, Soheil↗

NASA NTRS2012

A Regional CO2 Observing System Simulation Experiment Using ASCENDS Observations and WRF-STILT Footprints

Knowledge of the spatiotemporal variations in emissions and uptake of CO2 is hampered by sparse measurements. The recent advent of satellite measurements of CO2 concentrations is increasing the density of measurements, and the future mission ASCENDS (Active Sensing of CO2 Emissions over Nights, Days and Seasons) will provide even greater coverage and precision. Lagrangian atmospheric transport models run backward in time can quantify surface influences ("footprints") of diverse measurement platforms and are particularly well suited for inverse estimation of regional surface CO2 fluxes at high resolution based on satellite observations. We utilize the STILT Lagrangian particle dispersion model, driven by WRF meteorological fields at 40-km resolution, in a Bayesian synthesis inversion approach to quantify the ability of ASCENDS column CO2 observations to constrain fluxes at high resolution. This study focuses on land-based biospheric fluxes, whose uncertainties are especially large, in a domain encompassing North America. We present results based on realistic input fields for 2007. Pseudo-observation random errors are estimated from backscatter and optical depth measured by the CALIPSO satellite. We estimate a priori flux uncertainties based on output from the CASA-GFED (v.3) biosphere model and make simple assumptions about spatial and temporal error correlations. WRF-STILT footprints are convolved with candidate vertical weighting functions for ASCENDS. We find that at a horizontal flux resolution of 1 degree x 1 degree, ASCENDS observations are potentially able to reduce average weekly flux uncertainties by 0-8% in July, and 0-0.5% in January (assuming an error of 0.5 ppm at the Railroad Valley reference site). Aggregated to coarser resolutions, e.g. 5 degrees x 5 degrees, the uncertainty reductions are larger and more similar to those estimated in previous satellite data observing system simulation experiments.

Wang, James S.↗

NASA NTRS1986

Dislocation model for aseismic crustal deformation at Hollister, California

A model of crustal deformation during the interseismic phase is developed and applied (using the improved Bayesian inversion algorithm described by Jackson and Matsu'ura, 1985) to trilateration data for the USGS Hollister (CA) network. In the model, rigid blocks in motion relative to each other experience friction only in a brittle upper zone, while their ductile lower zones slide freely; the Hollister model comprises five blocks and nine rectangular fault patches. The data and results are presented in tables, graphs, and maps and characterized in detail. The model predicts steady block motion on time scales between 10 yr and 1 Myr, with net motion across the San Andreas/Calaveras fault system 38 + or - 3 mm/yr and brittle/ductile transition depths ranging from 0.4 to 11 km. Two San Andreas segments with higher probabilities of moderate-to-large earthquakes are identified.

Matsuura, Mitsuhiro↗

DOE OSTI2021

Towards robust autonomous impedance spectroscopy analysis: A calibrated hierarchical Bayesian approach for electrochemical impedance spectroscopy (EIS) inversion

Distribution-based analyses, such as the distribution of relaxation times (DRT) and the distribution of diffusion times (DDT), present model-free alternatives to equivalent circuit modeling for analysis of electrochemical impedance spectroscopy (EIS) data. However, reconstructing such distributions from noisy impedance data is an ill-posed problem that must be solved with specialized inversion algorithms, requiring careful control and tuning. Furthermore, most inversion algorithms developed to date can only solve problems of limited complexity. Herein, we present a new hierarchical Bayesian method for EIS inversion, leveraging efficient algorithms for optimization and Hamiltonian Monte Carlo (HMC) sampling to solve models of arbitrary complexity. We overcome the challenge of ad-hoc parameter tuning by encoding intrinsic characteristics of the DRT and DDT into flexible prior distributions and “pre-calibrating” the model to simulated data. This approach is versatile, highly robust to noise, and provides quantitative estimates of both the error structure of the data and the uncertainty in the recovered distributions. The model is validated with simulated data to demonstrate accurate recovery of the DRT and the DDT. The method also shows promise for simultaneous recovery of multiple distributions, raising the intriguing possibility of semi-autonomous EIS analysis and ad-hoc model construction. Finally, the practical utility of the method is illustrated with experimental data. Throughout, we draw comparisons to several recently published EIS inversion methodologies.

36 MATERIALS SCIENCE↗

DOE OSTI2026

The Influence of Shallow Subsurface Properties on Particle Motion in Acoustic-Seismic Coupling

Atmospheric acoustic waves transmit energy into the solid Earth through air-to-ground coupling. These waves are recorded by seismic sensors and provide insight into both atmospheric phenomena and subsurface properties. Interpreting these signals is often challenging because they are modulated by subsurface structure and the incidence angle of the acoustic wave. This study examines acoustic--seismic coupling generated by the 2012 Camp Minden Explosion, which was recorded by hundreds of seismoacoustic stations. We apply a novel technique to quantify the seismic particle motion, model coupled waves with a propagator matrix approach, and apply a Bayesian inversion to infer properties of the shallow subsurface. Our analysis reveals that prograde motion is widespread and focused in low shear-wave velocity regions, such as the Mississippi Embayment, and retrograde motion is more common in higher shear-velocity areas. Inversion results at some stations produce plausible subsurface models with strong waveform fits, while inversions at other sites are less successful. These results indicate prograde particle motion in air-to-ground coupled waves is more prevalent than previously recognized and may serve as a diagnostic for shallow velocity structure. Our comprehensive modeling and inversion framework provides a potential method to extract layered near-surface properties from acoustic-seismic coupling observations.

58 GEOSCIENCES↗

DOE OSTI2020

Geometric Scale-up Experiments on Fluidization of Geldart B Glass Beads

The objective of this work is to provide a valuable database from controlled experiments for validating computational models. Recently, coarse-grained techniques such as particle-in-cell (PIC) or coarse-grained discrete element modeling (DEM) have gained popularity due to their computational efficiency while modeling large-scale systems; however, the influence of model parameters and their sensitivities at different geometric scales and flow conditions remain to be analyzed. These datasets are critical for the multiphase flow research community to assess predictive capability of modeling techniques as well as elucidate the hydrodynamic behavior in these systems. This study performed fluidization experiments using three different test sections with internal diameters of 2.5, 4, and 6 in. The operating conditions, bed material, and range of flow velocities at the inlet were constant in all the units, which were not hydrodynamically scaled. Glass beads having a Sauter Mean Diameter of 332 μm were used. Superficial velocity was varied from 2.97 to 5.35 times the minimum fluidization velocity and the initial static bed height was 0.1524 m. The order in which the experiments were performed was randomized and replicates were included to provide uncertainty in measurements. Statistics of differential pressure and bed height from these tests were reported. Future plans include validating PIC methodology in the open-source software, MFiX (Multiphase Flow with Interphase Exchanges) using results from this study. This could further be extended to determine optimal model parameters using inverse techniques such as deterministic calibration or Bayesian inference.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2020

Geometric Scale-up Experiments on Fluidization of Geldart B Glass Beads

42 ENGINEERING↗

DOE OSTI2023

Quantifying uncertainty in analysis of shockless dynamic compression experiments on platinum. II. Bayesian model calibration

Dynamic shockless compression experiments provide the ability to explore material behavior at extreme pressures but relatively low temperatures. Typically, the data from these types of experiments are interpreted through an analytic method called Lagrangian analysis. Here, in this work, alternative analysis methods are explored using modern statistical methods. Specifically, Bayesian model calibration is applied to a new set of platinum data shocklessly compressed to 570 GPa. Several platinum equation-of-state models are evaluated, including traditional parametric forms as well as a novel non-parametric model concept. The results are compared to those in Paper I obtained by inverse Lagrangian analysis. The comparisons suggest that Bayesian calibration is not only a viable framework for precise quantification of the compression path, but also reveals insights pertaining to trade-offs surrounding model form selection, sensitivities of the relevant experimental uncertainties, and assumptions and limitations within Lagrangian analysis. The non-parametric model method, in particular, is found to give precise unbiased results and is expected to be useful over a wide range of applications. The calibration results in estimates of the platinum principal isentrope over the full range of experimental pressures to a standard error of 1.6%, which extends the results from Paper I while maintaining the high precision required for the platinum pressure standard.

Brown, Justin Lee↗

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 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 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 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↗

NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗

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 OSTI2023

Bayesian inference for the seismic moment tensor using regional waveforms and a data-derived distribution of velocity models

The largest source of uncertainty in any source inversion is the velocity model used to construct the transfer function employed in the forward model that relates observed ground motion to the seismic moment tensor. However, standard inverse procedures often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. We attempt to incorporate this uncertainty into an estimation of the seismic moment tensor using a distribution of velocity models calculated in a prior effort based on different and complementary data sets. The posterior distribution of velocity models is then used to construct Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional waveform data. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and can be interpreted in terms of most-probable source-type.

58 GEOSCIENCES↗

NASA NTRS1989

Confidence set inference with a prior quadratic bound

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Backus, George E.↗