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DOE OSTI2025

Computational Fluid Dynamics-Based Modeling of Methane Flows Around Oil and Gas Equipment

Recent studies estimate that emissions from oil and gas production facilities contribute between 20 and 50% of the total methane ( CH 4 ) emitted in the US; therefore, quantifying and reducing these emissions are crucial for achieving climate goals. Methane quantification depends on both measuring methane concentrations and converting them to emissions through a modeling framework. Currently, simple atmospheric dispersion models are primarily used to quantify emissions and concentrations, but these estimates are highly uncertain when quantifying emissions from complex aerodynamic sources, such as oil and gas facilities. This investigation used a CFD modeling approach, which can account for aerodynamic complexity but has hitherto not been used to model methane concentrations downwind of a methane release of a known rate, and compared it against in situ measurements. High-time-resolution (1 Hz) methane concentration and meteorological data were measured during experiments conducted at the METEC on 21 March and 11 July 2024. The METEC site configuration, measured wind data, and controlled emission rates were used as input for the CONVERGE CFD model to model downwind CH 4 concentration. The modeling was carried out between 20 and 70 m, from two different points of release in two separate controlled-release experiments, one from a separator and another from a wellhead. In these experiments, we found that the CFD model could predict the CH 4 concentrations downwind of the release to a good degree. The model was evaluated on multiple metrics to assess its performance in estimating methane concentrations at typical fence line distances (∼30 m). These results help us to understand external flows and the ability of CFD models to predict downwind concentrations in aerodynamically complex environments.

03 NATURAL GAS↗

DOE OSTI2024

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗

NASA NTRS2015

Modelling Freshwater Resources at the Global Scale: Challenges and Prospects

Quantification of spatially and temporally resolved water flows and water storage variations for all land areas of the globe is required to assess water resources, water scarcity and flood hazards, and to understand the Earth system. This quantification is done with the help of global hydrological models (GHMs). What are the challenges and prospects in the development and application of GHMs? Seven important challenges are presented. (1) Data scarcity makes quantification of human water use difficult even though significant progress has been achieved in the last decade. (2) Uncertainty of meteorological input data strongly affects model outputs. (3) The reaction of vegetation to changing climate and CO2 concentrations is uncertain and not taken into account in most GHMs that serve to estimate climate change impacts. (4) Reasons for discrepant responses of GHMs to changing climate have yet to be identified. (5) More accurate estimates of monthly time series of water availability and use are needed to provide good indicators of water scarcity. (6) Integration of gradient-based groundwater modelling into GHMs is necessary for a better simulation of groundwater-surface water interactions and capillary rise. (7) Detection and attribution of human interference with freshwater systems by using GHMs are constrained by data of insufficient quality but also GHM uncertainty itself. Regarding prospects for progress, we propose to decrease the uncertainty of GHM output by making better use of in situ and remotely sensed observations of output variables such as river discharge or total water storage variations by multi-criteria validation, calibration or data assimilation. Finally, we present an initiative that works towards the vision of hyper resolution global hydrological modelling where GHM outputs would be provided at a 1-km resolution with reasonable accuracy.

Global hydrological model↗

DOE OSTI2026

Uncertainty quantification and reliability assessment for intermodal freight transportation

Intermodal freight optimization models support cost-effective, low-emission, and timely goods movement by coordinating trucks, rail, and barges. These models determine optimal flows, routing, and modal switches while respecting infrastructure and operational constraints. However, their real-world utility is often undermined by pervasive uncertainties-such as fluctuating transportation costs and emissions, variable terminal capacities, and uncertain freight demand-that distort key performance outcomes, including total system cost, carbon footprint, and transit time reliability. This study presents a structured framework for quantifying uncertainty in intermodal freight transportation (IFT) optimization. The framework evaluates how input uncertainty affects system performance and reliability, a critical need for ensuring that model-based decisions remain robust under real-world variability, especially amid volatile fuel prices, shifting demand, and growing disruptions. It integrates three complementary methods: (1) Sobol-based global sensitivity analysis to identify influential parameters affecting cost, emissions, and transit time, (2) Monte Carlo-based capacity perturbation analysis to assess robustness under probabilistic facility disruptions, and (3) Monte Carlo filtering with Bayesian inference to detect threshold-based performance vulnerabilities. The results highlight diesel truck unit cost as the dominant driver of variability. To improve system resilience, planners should prioritize uncertainty in fuel-related parameters when designing intermodal strategies.

Intermodal freight transportation↗

NASA NTRS2018

Quantifying Methane Leak Emissions by Fused Airborne Imaging Spectroscopy with in Situ Surface Mobile and Airborne Observations of a California Producing Oil Field

Methane (CH4) emission budgets remain uncertain and are projected to grow as oil and gas production from short-lived wells increases and their subsequent transport through aging gas distribution networks. Orders-of-magnitude variations in temporal, spatial, and emission scales present a key challenge to leak detection and quantification. Also, the probability distributions for large and stochastic, leaky systems such as geological reservoirs (by natural migration-seeps) and petroleum production from those reservoirs remain largely unknown, needed to address current approach limitations. The scale of many petroleum systems favors remote sensing, but the sensitivity of such systems often precludes detection of weak emissions. Consequently, an accurate evaluation requires that the relative contribution from the emission "tails" of small leaks also be quantified, which is best carried out using high-sensitivity in situ methods. Fusion of remote sensing and in situ approaches leverages complementary capabilities to address these limitations. We show results from mobile surface (AMOG) and airborne in situ (AJAX) and thermal-infrared (TIR) hyperspectral imaging spectroscopy (Mako) data applied to a producing oil field in the California Central Valley near Bakersfield. AMOG is an automobile-based mobile lab that measures 13 trace gases, aerosol size distributions and vertical profiles, 3D winds and other meteorology, and atmospheric column measurements by solar spectroscopy at highway speeds. AJAX measures 5 trace gases and 3D winds at ~140 m/s. Mako is a broad-area TIR imaging spectrometer that can discriminate multiple gases present in each pixel acquired. In situ-derived, total field emissions were 31±16 Gg/yr CH4. This was compared with Mako-derived emissions from all plumes identified across the study site. We found that super-emitters were not the dominant emissions mode and the spatial pattern of plume locations from production infrastructure was correlated to geological structures.

Leifer, Ira↗

NASA NTRS2019

Bayesian Inference and the Effects of Varying Uncertainty Models in Charring Ablator Calibration and Uncertainty Quantification Problems

The Mars Science Laboratory (MSL) vehicle utilized a heat shield constructed from NASA’s Phenolic-Impregnated Carbon Ablator (PICA) material to protect the main structure from the high enthalpy environment encountered during hypersonic atmospheric entry. During the vehicle’s descent through Martian atmosphere, multiple thermocouples embedded within the heat shield captured in-depth material temperature data that allow for studies to be conducted on current material response reconstruction tools. In the present work, material temperature data obtained from thermocouples within the MISP-4 plug (MEDLI (Mars Science Laboratory Entry, Descent, and Landing Instrument) Integrated Sensor Plug) are utilized in the calibration of Theoretical Ablative Composite for Open Testing (TACOT) model parameters in conjunction with NASA’s Porous material Analysis Toolbox (PATO) through Bayesian inference where uncertainty due to parametric, modeling, and experimental sources is simultaneously quantified. Prior to the study, a sensitivity analysis is performed through computation of the robust Sobol indices in an effort to study the relationship between input space and model response and to reduce the dimensionality of the statistical inverse problem. The Bayesian inference methodology necessitates an a-priori choice to be made for the uncertainty model for which numerous possibilities are available. Across most works, however, only basic additive or multiplicative models are utilized with pre-defined magnitudes of uncertainty based on a-priori knowledge or to-be-calibrated multipliers of static covariance matrix structures. The present effort explores the effects of informed uncertainty models, ones with temporal dependence that are simultaneously calibrated through Bayesian inference, on calibrated results for parameters that make up the uncertain input space.

Sensitivity Analysis↗

NASA NTRS2016

Uncertainty and Sensitivity Analysis of Afterbody Radiative Heating Predictions for Earth Entry

The objective of this work was to perform sensitivity analysis and uncertainty quantification for afterbody radiative heating predictions of Stardust capsule during Earth entry at peak afterbody radiation conditions. The radiation environment in the afterbody region poses significant challenges for accurate uncertainty quantification and sensitivity analysis due to the complexity of the flow physics, computational cost, and large number of un-certain variables. In this study, first a sparse collocation non-intrusive polynomial chaos approach along with global non-linear sensitivity analysis was used to identify the most significant uncertain variables and reduce the dimensions of the stochastic problem. Then, a total order stochastic expansion was constructed over only the important parameters for an efficient and accurate estimate of the uncertainty in radiation. Based on previous work, 388 uncertain parameters were considered in the radiation model, which came from the thermodynamics, flow field chemistry, and radiation modeling. The sensitivity analysis showed that only four of these variables contributed significantly to afterbody radiation uncertainty, accounting for almost 95% of the uncertainty. These included the electronic- impact excitation rate for N between level 2 and level 5 and rates of three chemical reactions in uencing N, N(+), O, and O(+) number densities in the flow field.

West, Thomas K., IV↗

NASA NTRS2017

A Probabilistic Asteroid Impact Risk Model

Asteroid threat assessment requires the quantification of both the impact likelihood and resulting consequence across the range of possible events. This paper presents a probabilistic asteroid impact risk (PAIR) assessment model developed for this purpose. The model incorporates published impact frequency rates with state-of-the-art consequence assessment tools, applied within a Monte Carlo framework that generates sets of impact scenarios from uncertain parameter distributions. Explicit treatment of atmospheric entry is included to produce energy deposition rates that account for the effects of thermal ablation and object fragmentation. These energy deposition rates are used to model the resulting ground damage, and affected populations are computed for the sampled impact locations. The results for each scenario are aggregated into a distribution of potential outcomes that reflect the range of uncertain impact parameters, population densities, and strike probabilities. As an illustration of the utility of the PAIR model, the results are used to address the question of what minimum size asteroid constitutes a threat to the population. To answer this question, complete distributions of results are combined with a hypothetical risk tolerance posture to provide the minimum size, given sets of initial assumptions. Model outputs demonstrate how such questions can be answered and provide a means for interpreting the effect that input assumptions and uncertainty can have on final risk-based decisions. Model results can be used to prioritize investments to gain knowledge in critical areas or, conversely, to identify areas where additional data has little effect on the metrics of interest.

Asteroid↗

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↗

NASA NTRS2007

NASA Langley's Approach to the Sandia's Structural Dynamics Challenge Problem

The objective of this challenge is to develop a data-based probabilistic model of uncertainty to predict the behavior of subsystems (payloads) by themselves and while coupled to a primary (target) system. Although this type of analysis is routinely performed and representative of issues faced in real-world system design and integration, there are still several key technical challenges that must be addressed when analyzing uncertain interconnected systems. For example, one key technical challenge is related to the fact that there is limited data on target configurations. Moreover, it is typical to have multiple data sets from experiments conducted at the subsystem level, but often samples sizes are not sufficient to compute high confidence statistics. In this challenge problem additional constraints are placed as ground rules for the participants. One such rule is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand. Also, participants are constrained to use these models and the multiple data sets to make predictions about the target system response under completely different input conditions. Our approach involved initially the screening of several different methods. Three of the ones considered are presented herein. The first one is based on the transformation of the modal data to an orthogonal space where the mean and covariance of the data are matched by the model. The other two approaches worked solutions in physical space where the uncertain parameter set is made of masses, stiffnesses and damping coefficients; one matches confidence intervals of low order moments of the statistics via optimization while the second one uses a Kernel density estimation approach. The paper will touch on all the approaches, lessons learned, validation 1 metrics and their comparison, data quantity restriction, and assumptions/limitations of each approach. Keywords: Probabilistic modeling, model validation, uncertainty quantification, kernel density

Horta, Lucas G.↗

NASA NTRS2012

Use of In Situ and Airborne Multiangle Data to Assess MODIS- and Landsat-based Estimates of Surface Albedo

The quantification of uncertainty of global surface albedo data and products is a critical part of producing complete, physically consistent, and decadal land property data records for studying ecosystem change. A current challenge in validating satellite retrievals of surface albedo is the ability to overcome the spatial scaling errors that can contribute on the order of 20% disagreement between satellite and field-measured values. Here, we present the results from an uncertain ty analysis of MODerate Resolution Imaging Spectroradiometer (MODIS) and Landsat albedo retrievals, based on collocated comparisons with tower and airborne multi-angular measurements collected at the Atmospheric Radiation Measurement Program s (ARM) Cloud and Radiation Testbed (CART) site during the 2007 Cloud and Land Surface Interaction Campaign (CLAS33 IC 07). Using standard error propagation techniques, airborne measurements obtained by NASA s Cloud Absorption Radiometer (CAR) were used to quantify the uncertainties associated with MODIS and Landsat albedos across a broad range of mixed vegetation and structural types. Initial focus was on evaluating inter-sensor consistency through assessments of temporal stability, as well as examining the overall performance of satellite-derived albedos obtained at all diurnal solar zenith angles. In general, the accuracy of the MODIS and Landsat albedos remained under a 10% margin of error in the SW(0.3 - 5.0 m) domain. However, results reveal a high degree of variability in the RMSE (root mean square error) and bias of albedos in both the visible (0.3 - 0.7 m) and near-infrared (0.3 - 5.0 m) broadband channels; where, in some cases, retrieval uncertainties were found to be in excess of 20%. For the period of CLASIC 07, the primary factors that contributed to uncertainties in the satellite-derived albedo values include: (1) the assumption of temporal stability in the retrieval of 500 m MODIS BRDF values over extended periods of cloud-contaminated observations; and (2) the assumption of spatial 45 and structural uniformity at the Landsat (30 m) pixel scale.

Roman, Miguel O.↗

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↗

NASA NTRS2019

Uncertainty Quantification for JPL Retrievals

We define the notions of verification, validation, and uncertainty quantification (VVUQ), and place them in the context of retrievals of Earth science data. Uncertainty quantification (UQ) is the process of characterizing the uncertainty of a measurement system relative to the true, physical quantity it measures. UQ is needed when measurements are used for scientific inference, assimilated into models with other data, and used for decision-making and risk analysis. Many measurements come with measures of standard error and bias, but these uncertainty measures are often inaccurate, due to the operational need to assume crisp values for parameters which are in fact uncertain, as well as the failure of technical assumptions needed by operational error-estimation approaches. UQ provides a way to study which assumptions fail to hold, and a tool to improve the measurement. We describe a particular, broadly-applicable UQ setup that has been successful for JPL retrievals including OCO-2, and provide recommendations for furthering the UQ state of the practice at JPL.

Turmon, Michael↗

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↗

NASA NTRS2017

Sensitivity Analysis and Uncertainty Quantification of a Mars Ascent Vehicle Concept

The design of a conceptual Mars ascent vehicle is a challenging problem. In order to aid the vehicle and mission concept design it is important to understand the driving design parameters and the expected performance in the presence of model errors and uncertainties. An existing six degree of freedom simulation model is analyzed on a statistical basis using the methods available in the Design Analysis Kit for Optimization and Terascale Applications toolkit. The methods utilized include conventional Monte Carlo techniques, metamodeling via polynomial chaos expansions, and global variance-based sensitivity analyses. Two additional analysis methods referred to as “Monte Carlo filtering” and ”Classification trees” are used to determine which uncertain parameters are driving the performance of the vehicle. Monte Carlo filtering provides a methodology to determine which parameters cause qualitatively different behavior while the classification trees use heuristics to partition the input space and assign probabilities to each partition. These methods serve as qualitative descriptors of model sensitivity while variance-based global sensitivity analysis seeks a quantitative mapping from total output variance to the variance of individual inputs. Application of these techniques to several outputs of a Mars ascent vehicle concept simulation indicates that only a select few input factors dominate their variance.

Noyes, Connor↗

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)↗

NASA NTRS2012

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Crespo, Luis G.↗

NASA NTRS2014

Exact and Approximate Probabilistic Symbolic Execution

Probabilistic software analysis seeks to quantify the likelihood of reaching a target event under uncertain environments. Recent approaches compute probabilities of execution paths using symbolic execution, but do not support nondeterminism. Nondeterminism arises naturally when no suitable probabilistic model can capture a program behavior, e.g., for multithreading or distributed systems. In this work, we propose a technique, based on symbolic execution, to synthesize schedulers that resolve nondeterminism to maximize the probability of reaching a target event. To scale to large systems, we also introduce approximate algorithms to search for good schedulers, speeding up established random sampling and reinforcement learning results through the quantification of path probabilities based on symbolic execution. We implemented the techniques in Symbolic PathFinder and evaluated them on nondeterministic Java programs. We show that our algorithms significantly improve upon a state-of- the-art statistical model checking algorithm, originally developed for Markov Decision Processes.

Symbolic Execution↗