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DOE OSTI2021

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Probabilistic Groundwater Modeling of the RDX Plume at Los Alamos National Laboratory to Support Risk Assessment - 20359

A plume of the contaminant hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) with concentrations greater than the New Mexico tap water drinking standard (9.66 ppb) is present in the regional aquifer near the southwestern boundary of Los Alamos National Laboratory (LANL). A risk assessment is performed for exposure to regional aquifer groundwater, with long-term predictions of RDX concentrations provided by a calibrated, probabilistic, numerical fate and transport model. The structure of the model is hierarchical, with the RDX Regional Aquifer (RA) groundwater model acting as the primary tool for analysis of downgradient RDX concentrations. The RA model is deeply informed by the conceptual site model (CSM) and is calibrated using site RDX concentration data and hydraulic head measurements, along with other analyses. The model is calibrated using data through December 2019. Where data are scarce other lines of evidence are used to inform inputs, including the multiphase RDX Vadose Zone (VZ) model and Pipe and Disk analytical screening tool. Model inputs are described with informative prior distributions using a robust approach to development that incorporates all available lines of evidence for every parameter used as an input to the RA model. Calibration is performed using a classical nonlinear optimization routine, which is then used to initialize a Bayesian calibration. The Bayesian calibration constrains the uncertainty in the classical calibration, ultimately providing posterior distributions for all model parameters. The challenges of the calibration include high-dimensional parameter space, including spatially heterogeneous hydraulic conductivities, comparatively sparse data, and low RDX concentrations. Posterior parameter distributions developed in the calibration process are then used for stochastic predictive model runs into the future. The result of the forward runs is spatially and temporally explicit estimates of head and concentration with uncertainty at all points in space and time. The probabilistic modeling approach presented here includes innovative computational and statistical methods that leverage high-performance computing (HPC) resources. It makes use of prior modeling work performed at the chromium plume site in the central LANL area, with extensive updates. The risk assessment will ultimately be used to support decision-making at the site, using multiple appropriately weighted sources of information, as well as uncertainty, sensitivity, and value-of-information analyses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Fast strength model characterization using Bayesian statistics

A variety of flow stress models exist with new models constantly being developed. These models aim to approximate the strength of materials in a variety of regimes from quasistatic loading through shock scenarios. All models contain an array of parameters which need to be tuned to the material under study. Some models perform well under limited conditions, requiring adjustment of the parameters when venturing outside of those predefined ranges. Other models perform well over a wide range of conditions with a set of parameters, but may be outperformed by other models optimized on a tighter range of conditions. Recent research by Los Alamos demonstrated the ability to optimize the Johnson Cook (JC) model using a set of 3 plate-impact experiments on Aluminum. They utilized Bayesian statistics and emulation to determine optimal parameters for the model with a quantification of parameter uncertainty. We present an extension of this capability to incorporate velocimetry from plate-impact tests, stress-strain data from split Hopkinson pressure bar and quasistatic compression tests, plus profiles from Taylor cylinders in a unified fashion. Statistically robust comparisons of the performance and uncertainty of different realizations of the JC flow stress model were carried out based on calibration to several possible combinations of these three different experiment types.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Sequential Bayesian inference of transition rates in the hidden Markov model for multi-state system degradation

The more easily available system performance data and advances in data analytics have provided us with opportunities to optimize maintenance programs for engineered systems, for example nuclear power plants. One key task in maintenance optimization is to obtain an accurate model for system degradation. Here, in this research, we propose a Bayesian method to address this problem. Noting that systems usually exhibit multiple states and that the actual state of a system usually is not directly observable, in the method we first model the system degradation process and the observation process based on a hidden Markov model. Then we develop a sequential Bayesian inference algorithm based on importance sampling and the forward algorithm to infer the posterior distributions of the transition rates in the hidden Markov model based on available observations. The proposed Bayesian method allows us to take advantage of evidence from multiple sources, and also allows us to perform Bayesian inference sequentially, without the need to use the entire history of observations every time new observations are collected. We demonstrate the proposed method using both synthetic data for a nuclear power plant feedwater pump and realistic data for a nuclear power plant chemistry analytical device.

42 ENGINEERING↗

DOE OSTI2021

Uncertainty Quantification in High Explosives Equations of State [Slides]

In order to fit models to data, we need a way to simulate the data given a model. Our projects involved simulators for the Manganin gauge experiment and for cylinder tests, which we use to calibrate models to experiments. We call the parameters we seek to optimize the degrees of freedom (DOF). We use a Bayesian approach with its associated UQ benefits.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Improvements to CTF Closure Models for Modelling of Two-Phase Flow

This report documents the efforts to improve the CTF prediction of void fraction and two-phase pressure drop by improving two-phase closure models. Previous validation activities have revealed that CTF tends to overpredict void fraction and two-phase pressure drop. In response to this, two approaches were taken to improve CTF’s predictive capabilities. Based on findings that the interfacial drag and subcooled boiling models significantly impact void prediction, alternative closure models for these physical effects were found and implemented into the code. An extensive assessment was performed by using the existing and newly added two-phase experimental data, which showed that void prediction, wall temperature, and two-phase pressure-drop results are improved by using the newly implemented models. A second approach for improving CTF modeling accuracy involved the use of a Bayesian calibration process that uses CTF validation data to optimize selected modeling coefficients and closure model multipliers to achieve a more accurate prediction of experimental results. A similar assessment was performed with calibrated models that improved the void and pressure-drop prediction for test cases that were both included and not included in the calibration dataset. Results of this study will be used to change the models used in CTF to achieve more accurate BWR analyses moving forward. This study also identified opportunities for improving additional closure models and other opportunities to use calibration techniques to improve CTF.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

pygwb: A Python-based Library for Gravitational-wave Background Searches

The collection of gravitational waves (GWs) that are either too weak or too numerous to be individually resolved is commonly referred to as the gravitational-wave background (GWB). A confident detection and model-driven characterization of such a signal will provide invaluable information about the evolution of the universe and the population of GW sources within it. We present a new, user-friendly, Python-based package for GW data analysis to search for an isotropic GWB in ground-based interferometer data. We employ cross-correlation spectra of GW detector pairs to construct an optimal estimator of the Gaussian and isotropic GWB, and Bayesian parameter estimation to constrain GWB models. The modularity and clarity of the code allow for both a shallow learning curve and flexibility in adjusting the analysis to one’s own needs. We describe the individual modules that make up pygwb, following the traditional steps of stochastic analyses carried out within the LIGO, Virgo, and KAGRA Collaboration. We then describe the built-in pipeline that combines the different modules and validate it with both mock data and real GW data from the O3 Advanced LIGO and Virgo observing run. We successfully recover all mock data injections and reproduce published results.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Bayesian performance evaluation of evapotranspiration models based on eddy covariance systems in an arid region

Abstract. Evapotranspiration (ET) is a major component of the land surface processinvolved in energy fluxes and energy balance, especially in the hydrologicalcycle of agricultural ecosystems. While many models have been developed aspowerful tools to simulate ET, there is no agreement on which model bestdescribes the loss of water to the atmosphere. This study focuses on twoaspects, evaluating the performance of four widely used ET models andidentifying parameters, and the physical mechanisms that havesignificant impacts on the model performance. The four tested models arethe Shuttleworth–Wallace (SW) model, Penman–Monteith (PM) model,Priestley–Taylor and Flint–Childs (PT–FC) model, and advection–aridity (AA)model. By incorporating the mathematically rigorous thermodynamicintegration algorithm, the Bayesian model evidence (BME) approach is adoptedto select the optimal model with half-hourly ET observations obtained at aspring maize field in an arid region. Our results reveal that the SW model has thebest performance, and the extinction coefficient is not merely partitioningthe total available energy into the canopy and surface but also includingthe energy imbalance correction. The extinction coefficient is wellconstrained in the SW model and poorly constrained in the PM model but notconsidered in PT–FC and AA models. This is one of the main reasons that theSW model outperforms the other models. Meanwhile, the good fitting of SWmodel to observations can counterbalance its higher complexity. In addition,the detailed analysis of the discrepancies between observations and modelsimulations during the crop growth season indicate that explicit treatmentof energy imbalance and energy interaction will be the primary way offurther improving ET model performance.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

On-the-fly closed-loop materials discovery via Bayesian active learning

Active learning—the field of machine learning (ML) dedicated to optimal experiment design—has played a part in science as far back as the 18th century when Laplace used it to guide his discovery of celestial mechanics. In this work, we focus a closed-loop, active learning-driven autonomous system on another major challenge, the discovery of advanced materials against the exceedingly complex synthesis-processes-structure-property landscape. We demonstrate an autonomous materials discovery methodology for functional inorganic compounds which allow scientists to fail smarter, learn faster, and spend less resources in their studies, while simultaneously improving trust in scientific results and machine learning tools. This robot science enables science-over-the-network, reducing the economic impact of scientists being physically separated from their labs. The real-time closed-loop, autonomous system for materials exploration and optimization (CAMEO) is implemented at the synchrotron beamline to accelerate the interconnected tasks of phase mapping and property optimization, with each cycle taking seconds to minutes. We also demonstrate an embodiment of human-machine interaction, where human-in-the-loop is called to play a contributing role within each cycle. This work has resulted in the discovery of a novel epitaxial nanocomposite phase-change memory material.

36 MATERIALS SCIENCE↗

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 OSTI2023

Operation Optimization Using Reinforcement Learning with Integrated Artificial Reasoning Framework

In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.

Kim, Junyung↗

NASA NTRS2005

Point process algorithm: a new Bayesian approach for TPF-I planet signal extraction

TPF-I capability for planetary signal extraction, including both detection and spectral characterization, can be optimized by taking proper account of instrumental characteristics and astrophysical prior information. We have developed the Point Process Algorithm, a Bayesian technique for estracting planetary signals using the sine/cosine chopped outputs of a dual nulling interferometer.

stars↗

DOE OSTI2019

Bayesian modeling of inconsistent plastic response due to material variability

The advent of fabrication techniques such as additive manufacturing has focused attention on the considerable variability of material response due to defects and other microstructural aspects. This variability motivates the development of an enhanced design methodology that incorporates inherent material variability to provide robust predictions of performance. In this work, we develop plasticity models capable of representing the distribution of mechanical responses observed in experiments using traditional plasticity models of the mean response and recently developed uncertainty quantification (UQ) techniques. To account for material response variability through variations in physical parameters, we adapt a recent Bayesian embedded modeling error calibration technique. We use Bayesian model selection to determine the most plausible of a variety of plasticity models and the optimal embedding of parameter variability. To expedite model selection, we develop an adaptive importance-sampling-based numerical integration scheme to compute the Bayesian model evidence. In conclusion, we demonstrate that the new framework provides predictive realizations that are superior to more traditional ones, and how these UQ techniques can be used in model selection and assessing the quality of calibrated physical parameters.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Analytic Neural Network Gaussian Process Enabled Chance-Constrained Voltage Regulation for Active Distribution Systems with PVs, Batteries and EVs

This paper proposes an analytic neural network Gaussian process (NNGP)-based chance-constrained real-time voltage regulation method for active distribution systems with photovoltaics (PVs), batteries, and electric vehicles (EVs). NNGP can utilize historical measurement data to achieve real-time probabilistic node voltage estimation through Bayesian inference. Then, NNGP is fully analytically embedded into the optimal power flow model to perform voltage regulation and adapt to various topological changes. The uncertainties of voltage estimations are easily considered via the chance constraint, and it has been shown that the adoption of this chance constraint can significantly improve the reliability of voltage regulation under various scenarios. The comparison results with other methods, carried out on a real 759-node distribution system located in western Colorado, U.S., show that the proposed method can achieve accurate voltage estimation across different topologies and reliably perform voltage regulation considering PVs, batteries, and EVs.

active distribution systems↗

NASA NTRS1977

Modeling human decision making behavior in supervisory control

An optimal decision control model was developed, which is based primarily on a dynamic programming algorithm which looks at all the available task possibilities, charts an optimal trajectory, and commits itself to do the first step (i.e., follow the optimal trajectory during the next time period), and then iterates the calculation. A Bayesian estimator was included which estimates the tasks which might occur in the immediate future and provides this information to the dynamic programming routine. Preliminary trials comparing the human subject's performance to that of the optimal model show a great similarity, but indicate that the human skips certain movements which require quick change in strategy.

Tulga, M. K.↗

NASA NTRS2010

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Mengshoel, Ole J.↗

DOE OSTI2020

GIS-Based Modeling of Contaminated Soil Volumes at Multiple Sites in the Formerly Utilized Sites Remedial Action Program - 20149

The remediation of hazardous, toxic, and radioactive waste (HTRW) sites produces cost-related risks associated with the estimation of contaminated soil or debris volumes. Historical risk-management techniques include cost contingencies to cover volume uncertainties that affect project budgeting and decision-making. The Buffalo District teamed with project partners to lessen volume uncertainty and reduce project risks at multiple HTRW sites managed under the Formerly Utilized Sites Remedial Action Program (FUSRAP). Historical remedial investigations under FUSRAP commonly identified the presence of radiological material in site media, the associated human health risk, and then areas of remediation. To manage remedial execution and reduce risk, pre-design or remediation-phase sampling essentially 'chased' contamination, which was not conducive to efficient predictive budgeting derived from Feasibility Study (FS) cost analyses. The Buffalo District first optimized their approach to better understand volume uncertainty by utilizing the Argonne National Laboratory's Bayesian Approaches for Adaptive Spatial Sampling (BAASS) software [1]. BAASS processed soft data (e.g., gamma walk-over data) and spatial sampling data to estimate the lateral extent of contaminated soil irrespective of depth (i.e., gross contamination extent) and define areas of contaminant uncertainty. The software performed a binary transformation of contaminant concentrations at all sampling points based upon remedial action goals or a sum of ratios approach (i.e., clean, impacted, or range of impacts in soil). The model produced two-dimensional (horizontal) contaminant probability contours and statistical uncertainty in the sampling coverage and resulting contaminant extents. This method was translated vertically by partitioning the sampling data into depth brackets that produced a stacked representation of contaminant extents and uncertainty in the subsurface (i.e., similar to construction lifts). The results commonly led to a better understanding of project uncertainty and the need for sampling strategies that produce high-confidence soil volumes, which control costs. The BAASS-based delineations were eventually replaced by Empirical Bayesian Kriging (EBK) methods available in ArcGIS Spatial or 3D Analysts [2]. The EBK method calculates contaminant probability zones derived from user-controlled semivariograms of the spatial datasets. The resulting probability zones (e.g., 50% or 80% of contaminant probability) represent the two-dimensional surface delineation of the overall horizontal remedial area, similarly to BAASS. However, unlike BAASS, the vertical sampling data within these probability zones became vertical control points to contour a subterranean surface that connects subsurface points to the land-surface delineations of contamination. The resulting representation of horizontal and vertical impacts within an enclosed envelop (volume) of soil included uncertainty distributions that are used to plan uncertainty-reduction sampling. These data-driven and math-based models of three-dimensional sampling results produced well-bounded remedial volumes for project planning and better uncertainty predictions during project budgeting. The EBK method was applied to several FUSRAP sites managed by the Buffalo District and compared to less rigorously modeled sites previously remediated by the District. The comparison of modeled to actual remediated volumes provide a basis for validating the volume-estimation method. This comparison is important to ensure modeled volumes match physical boundaries of site remediation. FUSRAP sites with denser investigative sampling and lesser volume uncertainty proved useful in remedial planning and contracting. The Buffalo District noted that historical sites with sparser sampling arrays had greater disparity between estimated volumes and final remedial volumes. The benefit achieved over the cost of detailed soil sampling appears positive for FUSRAP projects, especially where impacts vary widely and appear unbounded by investigation-phase sampling. The subsequent Empirical Bayesian Kriging of contamination coupled with vertical contouring for soil estimations reduces uncertainty in soil volumes or indicates where sampling is required to reduce uncertainty, which together optimize remedial planning and budgeting. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Optimizing Carbon Cycle Parameters Drastically Improves Terrestrial Biosphere Model Underestimates of Dryland Mean Net CO 2 Flux and its Inter-Annual Variability

Drylands occupy ~40% of the land surface and are thought to dominate global carbon (C) cycle inter-annual variability (IAV). Therefore, it is imperative that global terrestrial biosphere models (TBMs), which form the land component of IPCC earth system models, are able to accurately simulate dryland vegetation and biogeochemical processes. However, compared to more mesic ecosystems, TBMs have not been widely tested or optimized using in situ dryland CO 2 fluxes. Here, for this work, we address this gap using a Bayesian data assimilation system and 89 site-years of daily net ecosystem exchange (NEE) data from 12 southwest US Ameriflux sites to optimize the C cycle parameters of the ORCHIDEE TBM. The sites span high elevation forest ecosystems, which are a mean sink of C, and low elevation shrub and grass ecosystems that are either a mean C sink or “pivot” between an annual C sink and source. We find that using the default (prior) model parameters drastically underestimates both the mean annual NEE at the forested mean C sink sites and the NEE IAV across all sites. Our analysis demonstrated that optimizing phenology parameters are particularly useful in improving the model's ability to capture both the magnitude and sign of the NEE IAV. At the forest sites, optimizing C allocation, respiration, and biomass and soil C turnover parameters reduces the underestimate in simulated mean annual NEE. Our study demonstrates that all TBMs need to be calibrated for dryland ecosystems before they are used to determine dryland contributions to global C cycle variability and long-term carbon-climate feedbacks.

59 BASIC BIOLOGICAL SCIENCES↗