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DOE OSTI2021

Retrospective Analysis and Bayesian Model Averaging of CMIP6 Precipitation in the Nile River Basin

The Nile River basin is one of the global hotspots vulnerable to climate change impacts because of a fast-growing population and geopolitical tensions. Previous studies demonstrated that general circulation models (GCMs) frequently show disagreement in the sign of change in annual precipitation projections. Here, we first evaluate the performance of 20 GCMs from phase six of the Coupled Model Intercomparison Project (CMIP6) benchmarked against a high-spatial-resolution precipitation dataset dating back to 1983 from Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Climate Data Record (PERSIANN-CDR). Next, a Bayesian model averaging (BMA) approach is adopted to derive probability distributions of precipitation projections in the Nile basin. Retrospective analysis reveals that most GCMs exhibit considerable (up to 64% of mean annual precipitation) and spatially heterogenous bias in simulating annual precipitation. Moreover, it is shown that all GCMs underestimate interannual variability; thus, the ensemble range is underdispersive and is a poor indicator of uncertainty. The projected changes from the BMA model show that the value and sign of change vary considerably across the Nile basin. Specifically, it is found that projected changes in the two headwaters basins, namely, the Blue Nile and Upper White Nile, are 0.03% and -1.65%, respectively; both are statistically insignificant at α = 0.05. The uncertainty range estimated from the BMA model shows that the probability of a precipitation decrease is much higher in the Upper White Nile basin whereas projected change in the Blue Nile is highly uncertain both in magnitude and sign of change.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

STARS DO NOT EAT THEIR YOUNG MIGRATING PLANETS: EMPIRICAL CONSTRAINTS ON PLANET MIGRATION HALTING MECHANISMS

The discovery of ''hot Jupiters'' very close to their parent stars confirmed that Jovian planets migrate inward via several potential mechanisms. We present empirical constraints on planet migration halting mechanisms. We compute model density functions of close-in exoplanets in the orbital semi-major axis-stellar mass plane to represent planet migration that is halted via several mechanisms, including the interior 1:2 resonance with the magnetospheric disk truncation radius, the interior 1:2 resonance with the dust sublimation radius, and several scenarios for tidal halting. The models differ in the predicted power-law dependence of the exoplanet orbital semi-major axis as a function of stellar mass, and thus we also include a power-law model with the exponent as a free parameter. We use a Bayesian analysis to assess the model success in reproducing empirical distributions of confirmed exoplanets and Kepler candidates that orbit interior to 0.1 AU. Our results confirm a correlation of the halting distance with stellar mass. Tidal halting provides the best fit to the empirical distribution of confirmed Jovian exoplanets at a statistically robust level, consistent with the Kozai mechanism and the spin-orbit misalignment of a substantial fraction of hot Jupiters. We can rule out migration halting at the interior 1:2 resonances with the magnetospheric disk truncation radius and the interior 1:2 resonance with the dust disk sublimation radius, a uniform random distribution, and a distribution with no dependence on stellar mass. Note that our results do not rule out Type-II migration, but rather eliminate the role of a circumstellar disk in stopping exoplanet migration. For Kepler candidates, which have a more restricted range in stellar mass compared to confirmed planets, we are unable to discern between the tidal dissipation and magnetospheric disk truncation braking mechanisms at a statistically significant level. The power-law model favors exponents in the range of 0.38-0.9. This is larger than that predicted for tidal halting (0.23-0.33), which suggests that additional physics may be missing in the tidal halting theory.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

THE ALBEDOS OF KEPLER'S CLOSE-IN SUPER-EARTHS

Exoplanet research focusing on the characterization of super-Earths is currently limited to the handful of targets orbiting bright stars that are amenable to detailed study. This Letter proposes to look at alternative avenues to probe the surface and atmospheric properties of this category of planets, known to be ubiquitous in our galaxy. I conduct Markov Chain Monte Carlo light-curves analyses for 97 Kepler close-in R{sub P} ≲ 2.0 R {sub ⊕} super-Earth candidates with the aim of detecting their occultations at visible wavelengths. Brightness temperatures and geometric albedos in the Kepler bandpass are constrained for 27 super-Earth candidates. A hierarchical Bayesian modeling approach is then employed to characterize the population-level reflective properties of these close-in super-Earths. I find median geometric albedos A{sub g} in the Kepler bandpass ranging between 0.16 and 0.30, once decontaminated from thermal emission. These super-Earth geometric albedos are statistically larger than for hot Jupiters, which have medians A{sub g} ranging between 0.06 and 0.11. A subset of objects, including Kepler-10b, exhibit significantly larger albedos (A{sub g} ≳ 0.4). I argue that a better understanding of the incidence of stellar irradation on planetary surface and atmospheric processes is key to explain the diversity in albedos observed for close-in super-Earths.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2004

Putting Priors in Mixture Density Mercer Kernels

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Srivastava, Ashok N.↗

DOE OSTI2021

Bayesian inference of the incompressibility, skewness and kurtosis of nuclear matter from empirical pressures in relativistic heavy-ion collisions

Within the Bayesian statistical framework we infer the incompressibility K 0 , skewness J 0 and kurtosis Z 0 parameters of symmetric nuclear matter (SNM) at its saturation density ρ 0 using the constraining bands on the pressure in cold SNM in the density range of 1.3ρ 0 to 4.5ρ 0 from transport model analyses of kaon production and nuclear collective flow in relativistic heavy-ion collisions. As the default option assuming the K 0 , J 0 and Z 0 have Gaussian prior probability distribution functions (PDFs) with the means and variances of 235±30, -200±200 and -146±1728 MeV, their posterior most probable values are narrowed down to 192$^{+12}_{-16}$ MeV, -180$^{+100}_{-110}$ MeV and ${\mathrm{200}}_{-250}^{+250}$ at 68% confidence level, respectively. The results are largely independent of the prior PDFs of J 0 and Z 0 used. However, if one adopts the strong belief that the incompressibility K 0 has a uniform prior PDF within its absolute boundary of 220–260 MeV as one can find easily in the literature, the posterior most probable values of K 0 , J 0 and Z 0 shift to ${K}_{0}=22{0}_{-0}^{+6}$ MeV, ${J}_{0}=-39{0}_{-70}^{+60}$ MeV and ${Z}_{0}=60{0}_{-200}^{+200}$ MeV, respectively. While the posterior PDFs of the SNM EOS parameters depend somewhat on the prior PDF of K 0 used, the results from using different prior PDFs are qualitatively consistent. The uncertainties of all three parameters are significantly reduced especially for the J 0 and Z 0 parameters compared to their current values.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Implementation of a Bayesian Engine for Uncertainty Analysis

In probabilistic risk assessment, it is important to have an environment where analysts have access to a shared and secured high performance computing and a statistical analysis tool package. As part of the advanced small modular reactor probabilistic risk analysis framework implementation, we have identified the need for advanced Bayesian computations. However, in order to make this technology available to non-specialists, there is also a need of a simplified tool that allows users to author models and evaluate them within this framework. As a proof-of-concept, we have implemented an advanced open source Bayesian inference tool, OpenBUGS, within the browser-based cloud risk analysis framework that is under development at the Idaho National Laboratory. This development, the “OpenBUGS Scripter” has been implemented as a client side, visual web-based and integrated development environment for creating OpenBUGS language scripts. It depends on the shared server environment to execute the generated scripts and to transmit results back to the user. The visual models are in the form of linked diagrams, from which we automatically create the applicable OpenBUGS script that matches the diagram. These diagrams can be saved locally or stored on the server environment to be shared with other users.

99 GENERAL AND MISCELLANEOUS↗

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 OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗

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

Bayesian projection pursuit regression

In projection pursuit regression (PPR), a univariate response variable is approximated by the sum of $M$ “ridge functions,” which are flexible functions of one-dimensional projections of a multivariate input variable. Traditionally, optimization routines are used to choose the projection directions and ridge functions via a sequential algorithm, and $M$ is typically chosen via cross-validation. Here, we introduce a novel Bayesian version of PPR, which has the benefit of accurate uncertainty quantification. To infer appropriate projection directions and ridge functions, we apply novel adaptations of methods used for the single ridge function case ($M$=1), called the Bayesian Single Index Model; and use a Reversible Jump Markov chain Monte Carlo algorithm to infer the number of ridge functions $M$. We evaluate the predictive ability of our model in 20 simulated scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Finally, we generalize this methodology and demonstrate the ability to accurately model multivariate response variables. Its effective performance indicates that Bayesian Projection Pursuit Regression is a valuable addition to the existing regression toolbox.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Empirical radius formulas for canonical neutron stars from bidirectionally selecting features of equations of state in extended Bayesian analyses of observational data

Significant advancement in Bayesian inference of nuclear equation of state (EOS) from gravitational wave and x-ray observations of neutron stars (NSs) has been made by the nuclear astrophysics community especially since GW170817. By extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not), we search for a data-driven and robust empirical formula for the radius 𝑅 1.4 of canonical NSs in terms of the characteristic EOS parameters (features). We also identify the single most important but currently poorly known EOS parameter for determining the 𝑅 1.4 . Using three regression-model-building methodologies: bidirectional stepwise feature selection, least absolute shrinkage selection operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding 𝑅 1.4 values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable 𝑅 1.4 formulas with varying statistical accuracy and technical complexity. Here, the most important EOS parameters for determining 𝑅 1.4 are found consistently in each of the feature selection processes to be (in order of decreasing importance): curvature 𝐾 sym , slope 𝐿, skewness 𝐽 sym of nuclear symmetry energy, skewness 𝐽 0 , incompressibility 𝐾 0 of symmetric nuclear matter, and the magnitude 𝐸 sym ⁡(𝜌 0 ) of symmetry energy at the saturation density 𝜌 0 of nuclear matter.

Bayesian methods↗

DOE OSTI2025

Analysis and optimization of seismic monitoring networks with Bayesian optimal experimental design

SUMMARY Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network’s ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. This framework requires five elements: (i) A likelihood function that describes the distribution of detection and traveltime data from the sensor network, (ii) A prior distribution that describes a priori belief about seismic events, (iii) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, (iv) An algorithm to compute EIG about seismic events over a data set of hypothetical prior events, (v) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number and locations influence uncertainty; and how prior models and constraints influence sensor placement.

58 GEOSCIENCES↗

DOE OSTI2017

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.

42 ENGINEERING↗

DOE OSTI2022

Photometric redshift uncertainties in weak gravitational lensing shear analysis: models and marginalization

ABSTRACT Recovering credible cosmological parameter constraints in a weak lensing shear analysis requires an accurate model that can be used to marginalize over nuisance parameters describing potential sources of systematic uncertainty, such as the uncertainties on the sample redshift distribution n(z). Due to the challenge of running Markov chain Monte Carlo (MCMC) in the high-dimensional parameter spaces in which the n(z) uncertainties may be parametrized, it is common practice to simplify the n(z) parametrization or combine MCMC chains that each have a fixed n(z) resampled from the n(z) uncertainties. In this work, we propose a statistically principled Bayesian resampling approach for marginalizing over the n(z) uncertainty using multiple MCMC chains. We self-consistently compare the new method to existing ones from the literature in the context of a forecasted cosmic shear analysis for the HSC three-year shape catalogue, and find that these methods recover statistically consistent error bars for the cosmological parameter constraints for predicted HSC three-year analysis, implying that using the most computationally efficient of the approaches is appropriate. However, we find that for data sets with the constraining power of the full HSC survey data set (and, by implication, those upcoming surveys with even tighter constraints), the choice of method for marginalizing over n(z) uncertainty among the several methods from the literature may modify the 1σ uncertainties on Ωm–S8 constraints by ∼4 per cent, and a careful model selection is needed to ensure credible parameter intervals.

Zhang, Tianqing (ORCID:000000025596198X)↗

DOE OSTI2014

A continuation multilevel Monte Carlo algorithm

Here, we propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. Moreover, the actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding variance and weak error. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Our numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

ON THE RELIABILITY OF POLARIZATION ESTIMATION USING ROTATION MEASURE SYNTHESIS

We benchmark the reliability of the rotation measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower signal-to-noise ratio (S/N) if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrained solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence, it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Formal Experimentation and Analysis of Handheld RFID Readers as a Tool for Nuclear Material Accounting

Commercial, off-the-shelf Radio Frequency Identification (RFID) systems have been successfully deployed for inventory tracking in numerous industries, but their viability in the tracking of complex environments containing nuclear material is less understood. Of primary interest in this setting is a RFID tracking system for nuclear material accounting which can reliably identify as many tags as possible with high accuracy, while also reducing an operator’s exposure to radiation. In this work, we develop a formal statistical approach to identify relevant handheld RFID reader settings which optimize tagging performance. To achieve this goal, we design a full factorial split-plot experiment for a static shelf configuration scene with 50 randomly placed nuclear material containers affixed with RFID tags. We use Bayesian inference to fit a second-order response surface model which expresses the probability of a successful match for each container as a function of the experimental factors. Such effects are allowed to vary across individual containers and the containers’ population in its entirety to estimate overall effects. Uncertainties of estimates and predictions are quantified via their corresponding posterior distributions. Following extensive model checking and validation, the fitted model is used to identify experimental factors which maximize matching probabilities at both the container-level and for the full shelf configuration scene. We also analyze sensitivity of performance to relevant factors.

25 ENERGY STORAGE↗