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

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DOE OSTI2024

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

In this work we present a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

42 ENGINEERING↗
DOE OSTI2021

Making sense of uncertain nuclear data

At its core, and in an imperfect world, the scientific method relies heavily on the concept of uncertain knowledge. Understanding the nature and magnitude of our lack of knowledge on nuclear data has important ramifications on a wide range of nuclear technologies that encompass defense, energy, medicine, astrophysics, among others. Over the span of a long and fruitful carrier, Dr. Massimo Salvatores has made significant contributions to the fields of nuclear reactor physics, nuclear data, and uncertainty quantification and propagation. Advances in machine learning techniques and computational capabilities are enabling a new level of confidence in our ability to predict key nuclear metrics as well as their associated uncertainties across many applications. Here this short article reviews some of those concepts with an eye towards developing a new paradigm to provide nuclear data libraries of benefit to various applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Accelerating uncertainty quantification in incremental dynamic analysis using dimension reduction-based surrogate modeling

We propose a surrogate modeling framework based on dimension reduction to facilitate the quantification of seismic risk of structural systems in performance-based earthquake engineering. The framework adopts incremental dynamic analysis (IDA) for addressing hazard variability, and promotes significant computational efficiency improvement for propagating epistemic uncertainties associated with the structural models. It utilizes both linear and nonlinear dimension reduction approaches, equipped with inverse mappings, to learn a functional between the input parameter space (e.g., the epistemic uncertainties of the structure) to the high-dimensional output space created through the IDA implementation across different ground motions and seismic intensity levels. Polynomial chaos expansion is adopted as the surrogate model to learn this functional in the reduced space. A nine-story steel moment-resisting frame with uncertain structural properties is used as a testbed. Furthermore, we select the seismic fragility curves as a measure of the structure’s seismic performance, since it provides an estimate of the probability of entering specified damage states for given levels of ground shaking.

42 ENGINEERING↗
DOE OSTI2022

Robust two-colour pyrometry uncertainty analysis to acquire spatially-resolved measurements

Two-colour pyrometry (2CP) has been used over several decades to study engine-relevant combustion processes, but results are generally regarded as qualitative or semi-quantitative. In many current 2CP systems, large measurement errors are introduced by parallax because the two measured wavelengths are not from the same line of sight. Here this work presents a spatially-resolved 2CP system with the objective of quantifying and reducing measurement uncertainty. An optical setup that eliminates parallax in 2CP is used together with pixel-by-pixel calibration of the camera sensor to increase measurement accuracy. Primary uncertainty terms are identified, and an error propagation analysis is performed to compute uncertainties in the final results of soot temperature, soot concentration parameter, KL, and soot mass. These methodologies are applied to investigate an auto-igniting fuel spray in a constant pressure flow rig at diesel-like conditions of high ambient pressure and temperature. Results show bias uncertainty of around 200 K (≈10%) for temperature and about 40%–60% for KL. High uncertainty was found to occur on the diffusion flame front where both optical thickness and soot concentrations are small. However, these uncertain measurement zones with relatively low soot concentrations contribute minimally to the total soot mass present in the reacting jet during the temporal evolution of the flame.

42 ENGINEERING↗
DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗
DOE OSTI2024

MLUQ (Uncertainty quantification for ML closure models) [SWR-24-36]

Data-based closure models are increasingly being used to replace physic-based closure models because of their flexibility and the growing availability of data. However, closure models are subject to uncertainty because of lack of data in parts of the input space (epistemic uncertainty) or because of noise in the data (aleatoric uncertainty). This software contains a toolbox for training bayesian neural nets that can estimate both uncertainties. A specific treatment is provided to ensure accuracy outside of the data distribution. A set of tools are provided to reduce the dimensionality of the uncertain parameter space, thereby enabling fast uncertainty propagation.

Hassanaly, Malik↗
DOE OSTI2026

Comparative Performance of Gaussian Plume and Backward Lagrangian Stochastic Models for Near-Field Methane Emission Estimation Using a Single Controlled Release Experiment

Methane (CH 4 ) is a major component of natural gas and a potent greenhouse gas. Increasing atmospheric methane concentrations are attributed to emissive anthropogenic activities by an average of 13 ppb per yr since 2020 and are linked to a changing global climate. Mitigating CH 4 emissions from oil and gas production sites has recently become a target to reduce overall greenhouse gas emissions; however, monitoring the efficacy of mitigation strategies depends on accurate quantification of CH 4 emissions at the facility-level. Near-field quantification of methane (CH 4 ) emissions from oil and gas (O&G) facilities remains challenging due to the effects of atmospheric variability and sensor configuration on atmospheric dispersion models. This study evaluates the performance of two atmospheric dispersion models, the Gaussian plume (GP) and backward Lagrangian stochastic (bLS), by comparing calculated CH 4 emissions to controlled single-point emissions between 0.4 and 5.2 kg CH 4 h −1 . Emissions were calculated by both models using 121 individual sets of measurements comprising five-minute averaged downwind methane mixing ratios and matching meteorological data. The comparison shows that the bLS approach achieved a higher proportion of emission estimates within a factor of two (FAC2) of the known emission rates compared to the GP approach. The emissions calculated by the bLS model also had a lower multiplicative error and reduced bias relative to GP. Other error-based metrics further confirmed the bLS model performed better, as it yielded lower RMSE and MAE than GP. Statistical analysis of the emission data shows that the lateral and vertical alignment of the source and the sensor plays a critical role in emission estimations, as measurements made closer to the plume centerline and at a distance between 40 and 80 m downwind yielded the best FAC2 agreement. High wind meander degraded the ability of both approaches to generate representative emissions, particularly with the GP approach, as it violates the modeling approach’s assumption of steady-state emissions. Data suggest emissions calculated by the bLS model are comprehensively in better agreement, but the computational demands of the modeling approach and integration into fenceline systems limit real-time applicability. While these results provide insight into model performance under controlled near-field conditions, their applicability to more complex or heterogeneous oil and gas production environments (e.g., the regions Marcellus or Unita Basins) remains limited and uncertain.

gaussian plume↗
DOE OSTI2020

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. Here, this work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

NRAP-Open-IAM: NRAP Open Source Integrated Assessment Model

Note: This is the last version (a2.6.1) of NRAP-Open-IAM released during NRAP Phase II in 2022. The latest version of NRAP-Open-IAM is available here: https://edx.netl.doe.gov/dataset/phase-iii-nrap-open-iam NRAP-Open-IAM is an open-source software product that enables quantification of containment effectiveness and leakage risk at storage sites in the context of system uncertainties and variability. NRAP-Open-IAM represents the next-generation in a line of systems-based computational models developed for quantitative geological carbon storage (GCS) risk assessment. The model comprises a set of reduced-order and analytical models of various components of the GCS system, potential leakage pathways, receptors of concern including impact to groundwater resources and the atmosphere, a framework to support stochastic simulation, time stepping, uncertainty quantification, other analytical functionality for scenario and risk-performance evaluation, and a basic graphical user interface to support scenario development, data input simulation definition, and basic post-processing and results display. As the NRAP Open-IAM functionality continues to evolve, we continue to add to its capability to develop quantitative, probabilistic, and time-dependent profiles of the evolution of risk at a GCS site and evaluate the influence of uncertain parameters on uncertainty in predicted risk. It can be used to quantify the dynamics of reservoir saturation plume and pressure-affected area, for evaluation of the area of potential groundwater impact (i.e., Area of Review) and monitoring requirements to support cost and regulatory analysis, and for consideration of different post-injection site care and closure scenarios. This submission contains the current version of NRAP-Open-IAM available for evaluation and testing. To use the NRAP-Open-IAM, download the source code (https://edx.netl.doe.gov/dataset/08f396c8-bc5f-44ad-a028-6e98a6ea6d70/resource/4c24a3da-3b40-4ffe-9892-c807ae9f8760) then open the NRAP-Open-IAM user's guide (https://edx.netl.doe.gov/dataset/08f396c8-bc5f-44ad-a028-6e98a6ea6d70/resource/8b27335a-343c-4836-b8a3-3ad0bdc9e669) to read more about the tool. Installation instructions for Windows, Mac, and Linux can be found in the "installers" folder of the extracted NRAP-Open-IAM folder and describe setup of environment (e.g., Python libraries) needed for proper work of the tool. Test of installation can be done by running "python openiam_setup_tests.py" in the "setup" folder. The installation test also runs a test suite to see if the NRAP-Open-IAM has been installed correctly. To run the test suite separately, run "python iam_test.py" in the "test" folder. User's guide: https://edx.netl.doe.gov/dataset/08f396c8-bc5f-44ad-a028-6e98a6ea6d70/resource/8b27335a-343c-4836-b8a3-3ad0bdc9e669 Developer's guide: https://edx.netl.doe.gov/dataset/08f396c8-bc5f-44ad-a028-6e98a6ea6d70/resource/3bc6ee7d-609d-4eb6-80ba-fa6130ee0313 Reservoir simulation data used in some examples distributed with NRAP-Open-IAM: - Kimberlina: https://edx.netl.doe.gov/dataset/08f396c8-bc5f-44ad-a028-6e98a6ea6d70/resource/eb62cece-61b2-4037-9b6d-32407dde2ab8 - Kimberlina (compartmentalized): https://edx.netl.doe.gov/dataset/08f396c8-bc5f-44ad-a028-6e98a6ea6d70/resource/366f9530-3b32-4b84-affe-ab2df1d9a8b5 - FutureGen 2.0: https://edx.netl.doe.gov/dataset/futuregen-2-0-1008-simulation-reservoir-lookup-table NRAP-Open-IAM GitLab repository: https://gitlab.com/NRAP/OpenIAM Related publications: - Bacon, D., Yonkofski, C., Brown, C., Demirkanli, D. and Whiting, J., 2019. Risk-based post injection site care and monitoring for commercial-scale carbon storage: Reevaluation of the FutureGen 2.0 site using NRAP-Open-IAM and DREAM. International Journal of Greenhouse Gas Control 90: 102784. - Bacon, D. Demirkanli, D., and White, S., 2020. Probabilistic risk-based Area of Review (AoR) determination for a deep-saline carbon storage site. International Journal of Greenhouse Gas Control 102: 103153. - Harp, D., Oldenburg, C., and Pawar, R., 2019. A metric for evaluating conformance robustness during geologic CO2 sequestration operations. International Journal of Greenhouse Gas Control 85: 100-108. - Lackey, G., Vasylkivska, V., Huerta, N., King, S., and Dilmore, R., 2019. Managing well leakage risks at a geologic carbon storage site with many wells, International Journal of Greenhouse Gas Control, 88 :182-194. - Vasylkivska, V., Dilmore, R., Lackey, G., Zhang, Y., King, S., Bacon, D., Chen, B., Mansoor, K., and Harp, D., 2021. NRAP-Open-IAM: A flexible open-source integrated assessment model for geologic carbon storage risk assessment and management, Environmental Modelling & Software, 143: 105114. Presentations: - Chen, B., Harp, D., and Pawar, R., A data assimilation approach (ES-MDA) coupling with NRAP-Open-IAM for quantifying uncertainty reduction in geological CO2 sequestration. AGUFM 2019: T44A-02. - Chen, B., and Harp, D., Improving risk analysis precision for geologic CO2 sequestration by quantifying the uncertainty reduction before and after acquiring monitoring data. 14th Greenhouse Gas Control Technologies Conference, Melbourne, Australia, 2018, pp. 21-26. - Harp, D., National Risk Assessment Partnership Task 2: Containment Assurance. No. LA-UR-19-28654, Los Alamos National Laboratory (LANL), Los Alamos, NM (United States), 2019. - Vasylkivska, V., King, S., Bacon, D., Harp, D., Chen, B., Mansoor, K., Onishi, T., Yang, Y., Zhang, Y., and Keating, E., NRAP-Open-IAM: An open-source integrated assessment model, poster, Mastering the Subsurface Through Technology Innovation, Partnerships and Collaboration: Carbon Storage and Oil and Natural Gas Technologies Review Meeting, Pittsburgh, PA, August 13-16, 2018. - Vasylkivska, V., Lackey, G., King, S., Wentworth, A., Huerta, N., Creason, C., DiGiulio, J., Yang, Y., and Dilmore, R., Long-term risk analysis of a geologic CO2 storage project during the post-injection period, SIAM Conference on Computational Science and Engineering, Spokane, WA, February 25-March 1, 2019. - Vasylkivska, V., Overview of the NRAP-Open-IAM tool for carbon storage (beta release), 2019 Annual NRAP Tool Users Meeting, Pittsburgh, PA, August 27, 2019. - Vasylkivska, V., Bacon, D., Chen, B., Dilmore, R., Harp, D., King, S., Lackey, G., Lindner, E., Liu, G., Mansoor, K. and Zhang, Y., NRAP-Open-IAM: A new, open-source code for integrated assessment of geologic carbon storage containment effectiveness and leakage risk, poster, American Geophysical Union Fall Meeting 2020 (virtual meeting), December 2020. - Vasylkivska, V., NRAP open-source integrated assessment model and relevant application, oral presentation, NRAP workshop "NRAP Tools for Geologic Carbon Storage Risk-Based Decision Making" held in conjunction with Groundwater Protection Council (GWPC) 2021 Annual Forum (virtual meeting), Salt Lake City, UT, September 2021. - Vasylkivska, V., NRAP-Open-IAM: open-source integrated assessment model, digital poster/demonstration, software demonstration session, 2022 Carbon Management Project Review Meeting, August 16, 2022

AoR↗
DOE OSTI2023

Parameter estimation with maximal updated densities

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of “true” parameter values under the assumption that such uncertainties should be reduced as more data are incorporated into the problem, i.e., the uncertainty is considered epistemic. A major contribution of this work is the formulation and solution of such a parameter identification problem (PIP) within the measure-theoretic framework developed for the SIP. The approach is novel in that it utilizes a solution to a stochastic forward problem (SFP) to update an initial density only in the parameter directions informed by the model output data. In other words, this method performs “selective regularization” only in the parameter directions not informed by data. Further, the solution is defined by a maximal updated density (MUD) point where the updated density defines the measure-theoretic solution to the PIP. Another significant contribution of this work is the full theory of existence and uniqueness of MUD points for linear maps with Gaussian distributions. Data-constructed Quantity of Interest (QoI) maps are also presented and analyzed for solving the PIP within this measure-theoretic framework as a means of reducing uncertainties in the MUD estimate. We conclude with a demonstration of the general applicability of the method on two problems involving either spatial or temporal data for estimating uncertain model parameters. The first problem utilizes spatial data from a stationary partial differential equation to produce a MUD estimate of an uncertain boundary condition. The second problem utilizes temporal data obtained from the state-of-the-art ADvanced CIRCulation (ADCIRC) model to obtain a MUD estimate of uncertain wind drag coefficients for a simulated extreme weather event near the Shinnecock Inlet located in the Outer Barrier of Long Island, NY, USA.

42 ENGINEERING↗
DOE OSTI2020

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

We use a conditional Karhunen-Lo` eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, Y (x). We assume that a small number of Y (x) measurements are available and model Y (x) with a KL expansion. We achieve reduction in uncertainty by conditioning the KL expansion coefficients on measurements. We consider two approaches for conditioning the KL expansion: In Approach 1, we condition the KL model first and then truncate it. In Approach 2, we first truncate the KL expansion and then condition it. We employ the conditional KL expansion together with Monte Carlo and sparse grid collocation methods to compute the moments of the solution of the SPDE problem. Uncertainty of the problem is further reduced by adaptively selecting additional observation locations using two active learning methods. Method 1 minimizes the variance of the PDE coefficient, while Method 2 minimizes the variance of the solution of the PDE. We demonstrate that conditioning leads to dimension reduction of the KL representation of Y (x). For a linear diffusion SPDE with uncertain log-normal coefficient, we show that Approach 1 provides a more accurate approximation of the conditional log-normal coefficient and solution of the SPDE than Approach 2 for the same number of random dimensions in a conditional KL expansion. Furthermore, Approach 2 provides a good estimate for the number of terms of the truncated KL expansion of the conditional field of Approach 1. Finally, we demonstrate that active learning based on Method 2 is more efficient for uncertainty reduction in the SPDE’s states (i.e., it leads to a larger reduction of the variance) than active learning using Method 2.

Conditioned Karhunen-Lo` eve expanion, machine lea↗
DOE OSTI2019

Elastic strain tensor of zirconium hydrides in Zr2.5%Nb pressure tubes by synchrotron X-ray diffraction

Zirconium alloys are used in fuel cladding and structural components of nuclear power plants. Hydrogen enters the Zr matrix during plant operation and precipitates as hydride particles that degrade the mechanical properties of the alloy, limiting service life. Knowledge of the stress state within hydride precipitates is important to understand stress-induced degradation mechanisms such as delayed hydride cracking, but no direct quantification has yet been reported in the literature. Here, measurements are reported of the average elastic strain tensor within δ zirconium hydride precipitates in Zr2.5%Nb pressure tube material from CANDU power plants. Complete intensity and strain pole figures for the hydride were obtained by synchrotron X-ray diffraction experiments on specimens with hydrogen contents ranging from ~100 wt p.p.m. hydrogen to nearly 100% δ-hydride. Zirconium hydride precipitates by a process involving a martensitic transformation, with two hydride variants possible from a single α-Zr grain. A synthetic model of the hydride crystallographic texture allowed the interpretation of the measured strain pole figures and quantification of the elastic strain tensor for both texture components. It was found that the two variants appear in nearly equal proportion but with different stress states, differing in the sign of the shear strain components (~±3000 µ$\epsilon$). This difference is possibly associated with the shear movement of Zr atoms during the phase transformation. This suggests that hydride clusters are composed of stacks of smaller hydrides in alternating hydride variants. Stresses were estimated from a set of rather uncertain hydride elastic constants. Overall, both variants showed compressive strains along the tube axial direction (~5000 µ$\epsilon$). For low hydrogen concentrations, the hydrides' stress tensor is dominated by compressive stresses of ~300 MPa along the axial direction, probably caused by the elongated morphology of hydride clusters along this direction, and variant-dependent shear stresses of ~±100 MPa, probably from the shear movement of the Zr atoms involved in the phase transformation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sequential Bayesian Experimental Design for Calibration of Expensive Simulation Models

Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at different parameter settings. Using intelligent and adaptive selection of parameters to build the emulator can drastically improve the efficiency of the calibration process. The article proposes a sequential framework with a novel criterion for parameter selection that targets learning the posterior density of the parameters. The emergent behavior from this criterion is that exploration happens by selecting parameters in uncertain posterior regions while simultaneously exploitation happens by selecting parameters in regions of high posterior density. Furthermore, the advantages of the proposed method are illustrated using several simulation experiments and a nuclear physics reaction model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Characterization of uncertainties in electron-argon collision cross sections

Abstract The predictive capability of a plasma discharge model depends on accurate representations of electron-impact collision cross sections, which determine the corresponding reaction rates and electron transport properties. The values of cross sections can be known only approximately either through experiments or simulations and are thus subject to uncertainties. Quantifying the uncertainties in plasma simulations allows us to assess the reliability of simulations and to provide a basis for interpreting discrepancies between simulations and experiments. For such uncertainty quantification of plasma simulations, it is essential to quantify the uncertainties of the underlying cross sections. Although much effort has been committed to calibrate the cross section values, their uncertainties are not well investigated. We characterize uncertainties in electron-argon atom collision cross sections using a Bayesian framework. Six collision processes—elastic momentum transfer, ionization, and four excitations—are characterized with semi-empirical models, which effectively capture the features important to the macroscopic properties of the plasma. A probability model for the uncertain parameters of these semi-empirical models is developed. Specifically, a Gaussian-process likelihood model is proposed to capture discrepancies among data sets, as well as the model-form inadequacies of the semi-empirical models. Two other likelihood models are compared with the proposed Gaussian-process model, to illustrate the importance of the choice of the likelihood model. The cross section models are calibrated using the electron-beam experiments and ab-inito quantum simulations. The resulting calibrated uncertainties capture well the scattering among the data sets. The calibrated cross section models are further validated against swarm-parameter experiments and zero-dimensional Boltzmann equation simulations of widely used cross section datasets.

Chung, Seung Whan (ORCID:0000000302501549)↗
DOE OSTI2022

Data-Driven Probabilistic Voltage Risk Assessment of MiniWECC System with Uncertain PVs and Wind Generations using Realistic Data

Here, it is found from actual data that due to generation dispatch and uncertain renewable generations and loads with complicated correlations, inferring the probabilistic distributions for uncertain inputs is challenging. Many probabilistic power flow approaches have been developed in the literature but their validations using realistic systems and data are lacking. This paper proposes a data-driven probabilistic analysis approach for system risk assessment of the miniWECC system using actual data. The sparse Gaussian process (SGP) is advocated to quantify the impacts of uncertain inputs on voltage security. SGP does not need the probability distribution function of uncertain inputs, can handle correlations and is highly computationally efficient. Results on the miniWECC system using realistic data show that SGP outperforms existing approaches and is able to quantify the voltage violation risks.

17 WIND ENERGY↗
DOE OSTI2020

Uncertainty Quantification of Global Net Methane Emissions From Terrestrial Ecosystems Using a Mechanistically Based Biogeochemistry Model

Quantification of methane (CH4) emissions from wetlands and its sinks from uplands is still fraught with large uncertainties. Here, a methane biogeochemistry model was revised, parameterized, and verified for various wetland ecosystems across the globe. The model was then extrapolated to the global scale to quantify the uncertainty induced from four different types of uncertainty sources including parameterization, wetland type distribution, wetland area distribution, and meteorological input. We found that global wetland emissions are 212 ± 62 and 212 ± 32 Tg CH4 year -1 (1Tg = 10 12 g) due to uncertain parameters and wetland type distribution, respectively, during 2000–2012. Using two wetland distribution data sets and three sets of climate data, the model simulations indicated that the global wetland emissions range from 186 to 212 CH 4 year -1 for the same period. The parameters were the most significant uncertainty source. After combining the global methane consumption in the range of -34 to -46 Tg CH 4 year -1 , we estimated that the global net land methane emissions are 149–176 Tg CH 4 year -1 due to uncertain wetland distribution and meteorological input. Spatially, the northeast United States and Amazon were two hotspots of methane emission, while consumption hotspots were in the Eastern United States and eastern China. During 1950–2016, both wetland emissions and upland consumption increased during El Niño events and decreased during La Niña events. This study highlights the need for more in situ methane flux data, more accurate wetland type, and area distribution information to better constrain the model uncertainty.

58 GEOSCIENCES↗
DOE OSTI2024

Uncertainty Quantification and Sensitivity Analysis of Non-Nuclear Advanced Controls Testbed Reactor Mockup

The research presented in this report describes our progress in applying stochastic methods and uncertainty quantification, parametric study, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated with Griffin, with the goal of developing a reduced order (surrogate) model which can be rapidly sampled while perturbing multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums, which are controlled by a hybrid proportional, integral and derivative (PID) controller, actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time and $\beta$ from a transient Griffin simulation executed with the improved quasi-static method to provide the kinetic parameters) as inputs to functions which control the CD rotation angle. Using a number of stochastic method approaches, we developed a dual purpose training-surrogate model of the NTP system using polynomial regression. The trained model can be rapidly sampled while simultaneously perturbing various input parameters of the model, such as coefficients on the PID control, or temperature (directly affect the neutron cross section). The surrogate model delivers accurate results orders-of-magnitude faster (minutes, not days) than the base model. Once the base model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs and their effect on the output. For example, coefficients used in the PID control system may vary due to some physical interference, or there may be uncertainty in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters and operational boundaries can be determined. The goal of this work is to support development of an advanced control system to operate CDs in a functioning NTP system.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗