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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Beyond Expected Values Evolving Metrics for Resource Adequacy Assessment

Resource adequacy analysis quantifies the likelihood of capacity shortfall on a power system in a probabilistic manner. Using a combination of statistical techniques and power system fundamentals, the analysis typically evaluates hundreds or thousands of stochastic random samples (replications) of varying load, generator outages, variable renewable energy availability, and other aspects of power system uncertainty. In this range of uncertainty, there are - at times - periods where the power system's available resources are insufficient to meet system demand, referred to as a shortfall event. Today's power systems' rapidly evolving generation mix is changing the types of data needed by system planners and regulators, which can often render traditional resource adequacy metrics insufficient for ensuring resource adequacy for tomorrow's grid. In this paper we provide a critical assessment of traditional measures of shortfall risk in power systems, discussing their shortcomings and how they compare to metrics used in other domains. From this analysis we propose four steps forward for improving power system resource adequacy risk metrics in the future.

ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRSDate not supplied

Validation of a Probabilistic Continuity Assessment Method for Earth Observation Portfolios

With the increased reliance on spaceborne Earth observation data among the Earth science community and other end users, it is important that efforts are made to promote data continuity for a range of parameters of interest. Continuity gaps may occur between missions measuring like parameters due to mission development delays or early termination and introduce the potential of increased uncertainty for retrieved parameters. To inform portfolio-level decisions for Earth observing missions, Ivanco et al. developed a method that enables the assessment of the probability of continuity gaps for multi-mission architectures and provides a framework to assess this probability in the context of multiple scenarios that represent possible future states of the architecture [Ivanco et al., “A Scenario-Based Approach to Assess Continuity Gaps in Earth Observations,” IEEE Aerospace Conf., 2024]. While this method was previously applied to assess continuity gaps for a specific multi-mission architecture, it had not yet been validated with historical data. This paper outlines the process of validating the probabilistic gap assessment method by utilizing data obtained from past NASA Earth Science mission formulation documents and provides a discussion of the results and takeaways from the validation. Future areas of improvement pertaining to both the modeling and simulation methodologies and underlying assumptions are identified and discussed.

Katharine Burn↗
DOE OSTI2015

Branch-and-Bound algorithm applied to uncertainty quantification of a Boiling Water Reactor Station Blackout

Evaluation of the impacts of uncertainty and sensitivity in modeling presents a significant set of challenges in particular to high fidelity modeling. Computational costs and validation of models creates a need for cost effective decision making with regards to experiment design. Experiments designed to validate computation models can be used to reduce uncertainty in the physical model. In some cases, large uncertainty in a particular aspect of the model may or may not have a large impact on the final results. For example, modeling of a relief valve may result in large uncertainty, however, the actual effects on final peak clad temperature in a reactor transient may be small and the large uncertainty with respect to valve modeling may be considered acceptable. Additionally, the ability to determine the adequacy of a model and the validation supporting it should be considered within a risk informed framework. Low fidelity modeling with large uncertainty may be considered adequate if the uncertainty is considered acceptable with respect to risk. In other words, models that are used to evaluate the probability of failure should be evaluated more rigorously with the intent of increasing safety margin. Probabilistic risk assessment (PRA) techniques have traditionally been used to identify accident conditions and transients. Traditional classical event tree methods utilize analysts’ knowledge and experience to identify the important timing of events in coordination with thermal-hydraulic modeling. These methods lack the capability to evaluate complex dynamic systems. In these systems, time and energy scales associated with transient events may vary as a function of transition times and energies to arrive at a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. Unfortunately DPRA methods introduce issues associated with combinatorial explosion of states. This study presents a methodology to address combinatorial explosion using a Branch-and-Bound algorithm applied to Dynamic Event Trees (DET), which utilize LENDIT (L – Length, E – Energy, N – Number, D – Distribution, I – Information, and T – Time) as well as a set theory to describe system, state, resource, and response (S2R2) sets to create bounding functions for the DET. The optimization of the DET in identifying high probability failure branches is extended to create a Phenomenological Identification and Ranking Table (PIRT) methodology to evaluate modeling parameters important to safety of those failure branches that have a high probability of failure. The PIRT can then be used as a tool to identify and evaluate the need for experimental validation of models that have the potential to reduce risk. Finally, in order to demonstrate this methodology, a Boiling Water Reactor (BWR) Station Blackout (SBO) case study is presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

EFIT-Prime: Probabilistic and physics-constrained reduced-order neural network model for equilibrium reconstruction in DIII-D

We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Forecasting seasonal influenza with a state-space SIR model

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

60 APPLIED LIFE SCIENCES↗
NASA NTRSDate not supplied

A Machine Learning Approach to Improve Air Traffic Management Initiatives

Collaborating closely with commercial air carriers and related organizations, the Federal Aviation Administration(FAA) regulates air traffic and ensures the safety and efficiency of air operations. Air traffic controllers make strategic decisions, such as delaying, rerouting, or canceling flights, partly based on guidance provided by the FAA’s Air TrafficControl System Command Center (ATCSCC). The guidance includes, among other things, control measures known asTraffic Management Initiatives (TMIs) designed to enhance safety and improve operational efficiency. TMIs play a crucial role in managing the demand and capacity within the U.S. National Airspace System (NAS). Two major TMIs that are routinely used (primarily to mitigate the adverse effects of bad weather) are Ground Delay Programs (GDPs) andGround Stops (GSs). In a GDP, flights destined for airports facing thunderstorm activity experience delays at their origin airports. This proactive approach minimizes the risk of routing aircraft through hazardous weather conditions and also replaces (fuel burning) airborne delays with ground delays. In a GS, a temporary restriction is imposed on the departure or arrival of aircraft at a specific airport or within a designated airspace. Although other TMIs (e.g., miles-in-trail) are also implemented as part of (air) traffic flow management in the NAS, the focus of this work is on GDPs and GSs. Since TMIs, by design, lead to flight delays or cancellations, it is crucial to put in place the right set of parameters(e.g., scope and duration of the GDP). For example, when the end time of a GDP extends beyond what is necessary, it imposes unnecessary delays on departing flights. This situation could occur as a result of inaccurate prediction of the(required) duration of the GDP based on the weather forecast. On the other hand, if a GDP ends prematurely before the underlying capacity constraints are resolved at the destination airport, it may result in airborne holding. The delicate balance lies in matching the termination of the GDP precisely with the resolution of capacity constraints, avoiding both the imposition of unnecessary ground delays and the need for airborne holding due to premature program termination.Failing to specify the right parameters for TMIs also leads to flight delays, creating a significant obstacle in managing the increasing traffic volumes causing increased work load for the controllers. To address this issue, we propose the integration of Machine Learning (ML) models in the traffic flow management(TFM) pipeline. In current operations, decisions are made by human experts based on extensive training, historical patterns, available traffic and weather data. Since we have an abundance of data from past events that tell us the likely impact of various TMIs, by ingesting historical data, properly trained ML models can offer valuable insights and aid human decision-making. With the FAA increasingly exploring advanced analytics, ML emerges as a focal point for enhancing TFM within the National Airspace System (NAS). As a first step, this study aims to provide traffic controllers with decision-making support for the issuance and adjustment of TMIs. Data analytics and machine learning have been previously employed to address some of the challenges associated with TMIs. Numerous studies have concentrated on various facets of TMI issuance, exploring factors influencing TMI parameters, including arrival rate, airport capacity, and delay prediction. For example, using weather forecasts, several statistical methods were used to produce probabilistic capacity profiles which in conjunction with deterministic models provided insights into the GDP planning process [1–4]. The downside of using deterministic models is that they rely on fixed inputs and predetermined rules, which lack the ability to account for the inherent uncertainty and variability present in real-world scenarios. In a separate series of studies, researchers aimed to predict the occurrences of GDPs and GSs. The majority of these studies utilized various supervised learning methods, including Decision Trees, Naive Bayes, Support VectorMachines, and Random Forests to analyze the influence of weather conditions and arrival demand on TMI incidents[5–8]. However, these studies primarily focused on predicting the incidence of TMIs without explicitly addressing the scope of TMIs, including their duration and their geographical coverage. Furthermore, the emphasis of these studies was largely on GDPs, given their higher frequency and longer duration when compared to GSs. A limited number of studies focused on predicting the parameters of TMIs, specifically addressing their duration and extent. In one such study focusing on optimizing the TMI parameters at San Francisco International Airport (SFO),the authors utilized a probabilistic forecast of fog [9]. They simulated various capacity scenarios based on the (fog)burn-off forecasts, selecting GDP parameters that minimized airborne and overall ground delays. However, this approach exclusively emphasizes stratus (fog) burn-off as the primary determinant of GDP and GS, neglecting other influential factors like severe weather events, runway closures, lower capacity than traffic demand, and other important variables. Given the complexity of predicting the TMI and determining its scope, we seek a more holistic approach. We aim to consider all significant factors that could impact TMIs and their parameters. What sets this research apart is the fusion of all data sources relevant to the issuance and adjustment of TMIs and it represents the first comprehensive attempt to optimize TMIs in this manner. Since this comprehensive solution involves various aspects, we break down the problem into smaller components and input all parameters into a unified model called the “TMI Adjuster”. Figure 1 shows the overall framework and the list of datasets used in each model. The objective of the TMI Adjuster module is to deliver reliable, consistent and expedited recommendations for the progression, adjustment, and termination of TMIs. The ML solution entails developing a pipeline capable of predicting the necessity of a TMI (e.g., GS or GDP) along with its various parameters. For example, in the case of a GS, this includes the scope of the GS either in terms of distance from the destination airport or based on pre-defined airspace sectors. Here, scope refers to those regions and departing airports that are subject to the GS. In this paper, we concentrate on the issuance of GSs in the three major airports in the New York area — LaGuardia(LGA), John F. Kennedy International (JFK), and Newark Liberty International (EWR). We fuse traffic, weather and other relevant aviation data from years 2017 to 2019 to train and validate the ML models. In particular, we use the following datasets: •Terminal Aerodrome Forecast (TAF): meteorological forecasts specific to each airport, issued four times a day, covering predefined time periods. •TMI data: includes all GSs and GDPs along with their respective parameters. •Aviation System Performance Metrics (ASPM): includes traffic related data such as aircraft delays, arrival, and departure rates. •Notices to Airmen (NOTAMs): utilized to extract runway closure data and manage interdependencies between terminals in close proximity. •Flight cancellation data •Airspace Flow Programs (AFP): includes information on flight airborne holdings caused by TMIs. The data preprocessing entails transforming ASPM, TMI, AFP, NOTAMs, and weather data into an hourly format and consolidating all datasets by merging them based on date and time as the primary key. The TMI Adjuster framework comprises two parallel models: one dedicated to GS and a second model focused on GDP. As previously mentioned, our specific focus is on the GS model as a multi-classification problem. In this framework, each data point of the GS model input summarizes ten hours of data. Specifically, the data loader for the GS model generates the input and output of the model as follows: at a given time step, the input includes the actual traffic, weather, and TMI data from the two-hour window before the time step, alongside the weather forecast and scheduled traffic for the next 8 hours starting from the time step. Based on this information, the output of the GS model for each time interval consists of three dimensions. The first dimension represents a binary decision on whether there should be a GS in place for the next hour or not. The second dimension is related to the scope of the GS in the United States, and the third dimension is related to the scope of the GS in Canada (i.e., to determine if the GS impacts airports in Canada).One of the challenges with TMI modeling is the sparsity of TMI events, particularly regarding its scope. To address this challenge in the scope of the GS model output, we implement grouping. The GS scope for the US region is defined based on a list of centers that should be included when the GS is in place. With 20 centers in the US, we utilized historical data to group them into 4 categories. In particular, we summarized our historical data in a graph format where nodes represent centers, and link weights are defined based on the co-occurrence of centers in the scope parameter ofTMIs. By identified strongly connected components in this graph, we were able to partition the centers into four groups. We consider two model structures for the GS Model. Firstly, a hierarchical classification model [10], where the human decision-making for a GS is of hierarchical nature. The decision-maker first decides whether there is a need fora GS, and if the answer is yes, determines the scope. A hierarchical classification model organizes the problem into a class hierarchy, typically a tree or a Directed Acyclic Graph (DAG) structure, and considers the dependency of the decision in the previous step to the next component [10]. Here, we employ the local classifier per level approach, which involves training one multi-class classifier for each level of the class hierarchy. The second structure is the independent structure. In this setting, as the name suggests, we do not consider the dependency of the decisions in the different dimensions of the output of the model. Instead, for each dimension, we train a multi-class classifier independently. Table 1 summarizes GS model statistics for training, validation and testing. The table documents the effect of limiting data to the time steps when there was actually a TMI in place or when a TMI had just terminated. This resulted in a more balanced distribution of the GS class(GS positive class)versus “No GS”(GS negative class), which might help the training process. While JFK and LGA follow very similar distributions, with 40% and 42% GS positive class respectively, EWR has proportionally fewer GS incidents at 28%. Our subsequent phase involves evaluating the performance of both hierarchical structure and independent structure using different state-of-the-art multi-class classifier models such as Random Forest, Decision Trees, K-nearest Neighbors, and Logistic Regression and forecast the duration and scope of the GSs.

Farzan Masrour Shalmani↗
DOE OSTI2015

Simplified predictive models for CO 2 sequestration performance assessment

CO2 sequestration in deep saline formations is increasingly being considered as a viable strategy for the mitigation of greenhouse gas emissions from anthropogenic sources. In this context, detailed numerical simulation based models are routinely used to understand key processes and parameters affecting pressure propagation and buoyant plume migration following CO2 injection into the subsurface. As these models are data and computation intensive, the development of computationally-efficient alternatives to conventional numerical simulators has become an active area of research. Such simplified models can be valuable assets during preliminary CO2 injection project screening, serve as a key element of probabilistic system assessment modeling tools, and assist regulators in quickly evaluating geological storage projects. We present three strategies for the development and validation of simplified modeling approaches for CO2 sequestration in deep saline formations: (1) simplified physics-based modeling, (2) statisticallearning based modeling, and (3) reduced-order method based modeling. In the first category, a set of full-physics compositional simulations is used to develop correlations for dimensionless injectivity as a function of the slope of the CO2 fractional-flow curve, variance of layer permeability values, and the nature of vertical permeability arrangement. The same variables, along with a modified gravity number, can be used to develop a correlation for the total storage efficiency within the CO2 plume footprint. Furthermore, the dimensionless average pressure buildup after the onset of boundary effects can be correlated to dimensionless time, CO2 plume footprint, and storativity contrast between the reservoir and caprock. In the second category, statistical “proxy models” are developed using the simulation domain described previously with two approaches: (a) classical Box-Behnken experimental design with a quadratic response surface, and (b) maximin Latin Hypercube sampling (LHS) based design with a multidimensional kriging metamodel fit. For roughly the same number of simulations, the LHS-based metamodel yields a more robust predictive model, as verified by a k-fold cross-validation approach (with data split into training and test sets) as well by validation with an independent dataset. In the third category, a reduced-order modeling procedure is utilized that combines proper orthogonal decomposition (POD) for reducing problem dimensionality with trajectory-piecewise linearization (TPWL) in order to represent system response at new control settings from a limited number of training runs. Significant savings in computational time are observed with reasonable accuracy from the PODTPWL reduced-order model for both vertical and horizontal well problems – which could be important in the context of history matching, uncertainty quantification and optimization problems. The simplified physics and statistical learning based models are also validated using an uncertainty analysis framework. Reference cumulative distribution functions of key model outcomes (i.e., plume radius and reservoir pressure buildup) generated using a 97-run full-physics simulation are successfully validated against the CDF from 10,000 sample probabilistic simulations using the simplified models. The main contribution of this research project is the development and validation of a portfolio of simplified modeling approaches that will enable rapid feasibility and risk assessment for CO2 sequestration in deep saline formations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Characterization of Extremes and Compound Impacts: Applications of Machine Learning and Interpretable Neural Networks

Focal Area: This white paper responds to Focal area III by exploring data fusion, learning and explainable AI methods in characterizing hydrological extremes and interconnections. It also addresses Focal area II by using probabilistic AI and ensemble ML for predicting extremes and compound extremes. Science Challenge: A key question associated with the integrated water (or hydrological) cycle grand challenge in the Earth and Environmental Systems Sciences Division (EESSD) strategic plan, is how the frequency and intensity of hydrological events will change. Prediction of the tail behavior (extremes) of the hydrological cycle is especially challenging, because of their stochasticity and low probability. These extreme events and their compound impacts have significant societal and economic consequences. It is anticipated for the next-generation Earth System models (ESMs), that model predictability of the water cycle will improve with increased resolution (e.g., regionally refined E3SM), advanced software and computational architectures, and improved model physics based on the data from ARM measurements and high-fidelity models. However, the challenges for predictability of low-probability high-impact extreme events will unlikely be alleviated with conventional modeling and data-driven approaches, as ESMs are calibrated largely for capturing the high-frequency mean climate states. Recent AI and ML applications have shown great potential in quantifying well-defined climate extremes (e.g., supervised learning of tropical cyclones/atmospheric rivers by ClimateNet1) but few efforts are dedicated to compound events, extreme drivers and uncertainty estimation. We envision the opportunity to develop and apply ML and interpretable AI methods extended on the existing efforts, specifically, for: (1) identification of compound extremes, (2) diagnosing drivers of extremes, (3) bias correction in extreme predictions and (4) probabilistic modeling of extremes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Past and present cosmic structure in the SDSS DR7 main sample

We present a chrono-cosmography project, aiming at the inference of the four dimensional formation history of the observed large scale structure from its origin to the present epoch. To do so, we perform a full-scale Bayesian analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS) Data Release 7 main galaxy sample, relying on a fully probabilistic, physical model of the non-linearly evolved density field. Besides inferring initial conditions from observations, our methodology naturally and accurately reconstructs non-linear features at the present epoch, such as walls and filaments, corresponding to high-order correlation functions generated by late-time structure formation. Our inference framework self-consistently accounts for typical observational systematic and statistical uncertainties such as noise, survey geometry and selection effects. We further account for luminosity dependent galaxy biases and automatic noise calibration within a fully Bayesian approach. As a result, this analysis provides highly-detailed and accurate reconstructions of the present density field on scales larger than ∼ 3 Mpc/h, constrained by SDSS observations. This approach also leads to the first quantitative inference of plausible formation histories of the dynamic large scale structure underlying the observed galaxy distribution. The results described in this work constitute the first full Bayesian non-linear analysis of the cosmic large scale structure with the demonstrated capability of uncertainty quantification. Some of these results will be made publicly available along with this work. The level of detail of inferred results and the high degree of control on observational uncertainties pave the path towards high precision chrono-cosmography, the subject of simultaneously studying the dynamics and the morphology of the inhomogeneous Universe.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2003

Self-Directed Cooperative Planetary Rovers

The project is concerned with the development of decision-theoretic techniques to optimize the scientific return of planetary rovers. Planetary rovers are small unmanned vehicles equipped with cameras and a variety of sensors used for scientific experiments. They must operate under tight constraints over such resources as operation time, power, storage capacity, and communication bandwidth. Moreover, the limited computational resources of the rover limit the complexity of on-line planning and scheduling. We have developed a comprehensive solution to this problem that involves high-level tools to describe a mission; a compiler that maps a mission description and additional probabilistic models of the components of the rover into a Markov decision problem; and algorithms for solving the rover control problem that are sensitive to the limited computational resources and high-level of uncertainty in this domain.

Zilberstein, Shlomo↗
DOE OSTI2013

THE PANCHROMATIC HUBBLE ANDROMEDA TREASURY. IV. A PROBABILISTIC APPROACH TO INFERRING THE HIGH-MASS STELLAR INITIAL MASS FUNCTION AND OTHER POWER-LAW FUNCTIONS

We present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M {approx}> 1 M {sub Sun }). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that {approx}3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield ({alpha}) = 2.46, with a 1{sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the initial mass function, beyond the lower bound of the most massive star actually observed. We show that avoiding substantial biases in the MF slope requires (1) including the MF as a prior when deriving individual stellar mass estimates, (2) modeling the uncertainties in the individual stellar masses, and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. The precision on MF slope recovery in this paper are lower limits, as we do not explicitly consider all possible sources of uncertainty, including dynamical effects (e.g., mass segregation), unresolved binaries, and non-coeval populations. We briefly discuss how each of these effects can be incorporated into extensions of the present framework. Finally, we emphasize that the technique and lessons learned are applicable to more general problems involving power-law fitting.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A probabilistic analysis of cumulative carbon emissions and long-term planetary warming

Efforts to mitigate and adapt to long-term climate change could benefit greatly from probabilistic estimates of cumulative carbon emissions due to fossil fuel burning and resulting CO 2 -induced planetary warming. Here we demonstrate the use of a reduced-form model to project these variables. We performed simulations using a large-ensemble framework with parametric uncertainty sampled to produce distributions of future cumulative emissions and consequent planetary warming. A hind-cast ensemble of simulations captured 1980–2012 historical CO 2 emissions trends and an ensemble of future projection simulations generated a distribution of emission scenarios that qualitatively resembled the suite of Representative and Extended Concentration Pathways. The resulting cumulative carbon emission and temperature change distributions are characterized by 5–95th percentile ranges of 0.96–4.9 teratonnes C (Tt C) and 1.4 °C–8.5 °C, respectively, with 50th percentiles at 3.1 Tt C and 4.7 °C. Within the wide range of policy-related parameter combinations that produced these distributions, we found that low-emission simulations were characterized by both high carbon prices and low costs of non-fossil fuel energy sources, suggesting the importance of these two policy levers in particular for avoiding dangerous levels of climate warming. With this analysis we demonstrate a probabilistic approach to the challenge of identifying strategies for limiting cumulative carbon emissions and assessing likelihoods of surpassing dangerous temperature thresholds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Probabilistic Inference of Low-Surface-Brightness Galaxy Morphological Parameters Using Simulation-Based Inference

Low-surface-brightness galaxies (LSBGs) are diffuse, often dark-matter-dominated systems whose faintness makes their structural parameters difficult to measure reliably in wide-field imaging surveys. Robust parameter inference, including uncertainty quantification, is important for population studies and for comparisons with models of galaxy formation, as future surveys are expected to produce increasingly large samples of diffuse galaxies. In practice, LSBG profile modeling is sensitive to sky- background errors, masking choices, contaminating background sources, and the computational cost of obtaining posterior-level uncertainties for large samples. Motivated by these questions, we develop a simulation-based inference (SBI) framework for estimating posterior distributions of LSBG morphological parameters from simulated galaxy images. Using PyImfit, we generate DES-like single-Sersic profile LSBG images with known position angle, ellipticity, Sersic index, effective surface brightness, and effective radius. We then train a normalizing-flow-based neural posterior estimator using the sbi package to infer these parameters from the simulated images. For isolated simulated galaxies, the SBI posterior recovers the true input parameters, produces posterior predictive residuals consistent with the assumed noise model, and shows good empirical calibration in a DES-motivated test regime. We also compare SBI with PyImfit-based MCMC inference and find broadly comparable posterior constraints, while SBI enables substantially faster posterior sampling after training. Finally, we test robustness to compact background contaminants. A model trained only on isolated galaxies produces undercovered posteriors on contaminated images, whereas training on simulations with variable contaminant positions and fluxes improves calibration across contaminated test sets. These results demonstrate the promise of SBI for scalable, uncertainty-aware LSBG morphology inference, while emphasizing that posterior reliability strongly depends on whether training simulations include relevant observational complications.

Batbayar, Bilguun [U. Chicago (main)]↗
DOE OSTI2013

Decision Analysis Methods For the Analysis of Nuclear Terrorism Threats with Imperfect Information

Protection of commercial nuclear fuel cycles against adversary groups who may attempt to steal weapons-usable material is an issue of interest to the U.S. Department of Energy, Office of Nuclear Energy. The wide array of potential nuclear fuel cycle configurations and the security measures that could be deployed to protect them pose a daunting system design problem. In general, there are billions of potential design configurations. Moreover, the design choices are not independent – the effectiveness of one design feature or security measure can affect the desirability of other design choices. To explore this issue, we develop a mixed-integer optimization problem that solves a complex decision tree to allocate security resources across a commercial nuclear fuel cycle configuration. A nominal UREX+ reprocessing facility is used to demonstrate how the model allocates resources across a particular fuel cycle facility and shows how the problem can be scaled up to include other facilities and design features in the fuel cycle. In our model, the defender first chooses a set of safeguards to implement in order to mitigate the risk of a terrorist theft from various unit operations in the reprocessing facility. The attacker observes the defender’s strategy choice and executes an attack to acquire material, including the possibility of declining to attack at all. The model considers the terrorist as an intelligent adversary with a set of attack strategies known to the defender. The strategic choices made by both the defender and attacker affect the probability of a successful attack by the terrorist and in turn affect the distribution of consequences to the defender. We use a decision tree to illustrate the interactions among costs, decisions, correlated uncertainties, and outcomes, and then show how to formulate the problem as a mixed-integer program with an equivalent solution. The novel features of our formulation include the following. First, as discussed above, we use a sequential game-theoretic formulation (a Stackelberg game). This formulation assumes the attacker can observe the defender’s actions before the attack is executed. Many previous game-theoretic studies have assumed attacker and defender act simultaneously without knowledge of the other’s strategy choice. We believe the sequential game formulation is more applicable for knowledgeable insider adversaries, the focus of this study. Second, we build on our previous work that has developed a methodology to reflect the correlation among probability distributions represented as discrete chance nodes in a decision tree. We illustrate how this methodology can be applied to two chance nodes in a decision tree that relate the quality of the materials that might be stolen or diverted by an adversary with the yield of a weapon that might be constructed from that material. In a decision tree, the dependence of the yield on the quality of the material could be modeled with conditional probabilities of the weapon yield given the quality of the materials obtained. For three outcome discretizations, this would require the assessment of nine conditional probabilities from domain experts as part of the model building effort. In contrast, our methodology will allow this same representation of the tree based on the assessment of the correlation between these two chance nodes by the experts, which we believe is a much easier and more reliable assessment task. The advantage of this approach increases as the number of dependent chance nodes grows in a decision tree representation of this problem. Third, we extend this approach to the approximation of the dependence between discrete binary events such as success or failure represented by binary chance nodes in a decision tree or in the special case of a probabilistic risk analysis (PRA) based on an event tree. This extension is a novel application in this domain, and uses Monte Carlo simulation to determine the appropriate conditional probabilities on the binary chance nodes when the number of correlated uncertainties is more than two. Fourth, we show how these decision trees or probability trees can be formulated and solved as equivalent integer programming (IP) problems. The advantages of the IP representation include the opportunity to use the computing power associated with powerful optimization solver algorithms available on high speed computers to solve very large versions of these trees, and the ability to include several such models of different facilities into a much larger IP with connecting constraints that represent budget restrictions, number of available inspection opportunities in a given time window, or other dependencies among these facilities. Policy makers can use the resulting model to inform their decisions about how to assess terrorism risk and to safeguard the commercial nuclear fuel cycle.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

A probabilistic application of oil and gas data for exploration stage geothermal reservoir assessment in the Appalachian Basin

Geothermal energy is a renewable, widespread, baseload energy source that has the potential to supply a large portion of the world’s energy needs. High development risk, specifically high drilling costs combined with uncertainty in subsurface flow properties, have hampered growth of geothermal energy development. One option to reduce subsurface risk is to target locations where reservoir data are already available, including sedimentary basins where there has been extensive hydrocarbon production. Sedimentary basins are widespread and often have suitable geothermal gradients. This chapter presents a low-cost methodology that can be used at the pre-drilling exploration phase of a low-temperature geothermal project to predict the location of high-productivity and low-risk reservoirs, applied to a case study of the Appalachian Basin in the eastern United States. Because only averaged reservoir data were available for analysis, the technique uses a Monte Carlo simulation of the Reservoir Flow Capacity (RFC) and Reservoir Productivity Index (RPI) for over 1800 individual reservoirs, using liquid water or supercritical carbon dioxide (sCO 2 ) as the reservoir fluid. RFC is used as an initial screening tool to identify high-priority geologic formations and reservoirs. Here our results indicate that 99% of the reservoirs in the basin are of insufficient quality for geothermal heat production with water as the assumed fluid and without using stimulation technologies associated with Enhanced Geothermal Systems (EGS). RPI is also used as an alternative metric to identify high-productivity reservoirs. When comparing the RPI results to natural gas production volumes from several selected reservoirs, the predicted RPI proves to be a good estimate of flow potential for porous reservoirs, but overestimates flow by a factor of three for fractured or vuggy reservoirs. A greater uncertainty ought to be utilized when applying the RPI equation to non-porous media, therefore we recommend utilizing the RPI metric when higher resolution data are available for analysis. This methodology can be utilized in other basins that have experienced hydrocarbon exploration and production, to highlight low-risk reservoirs or geologic formations for further geothermal development.

15 GEOTHERMAL ENERGY↗
DOE OSTI2017

Development of robust pressure management strategies for geologic CO 2 sequestration

Injecting CO 2 into deep geologic formations for permanent storage can potentially lead to leakage or induced seismicity if the overpressures exceed the fracture gradient or fault re-activation pressure. Strategies that remove reservoir fluids before or after injection may reduce these risks. But, even extensively characterized reservoirs can have substantial gaps in characterization necessary for developing optimal deterministic or even probabilistic pressure management strategies. The characterization data may not provide well-defined bounds or distributions of reservoir parameters or conditions (permeability, fault locations, fracture gradient, fault reactivation pressure). To assess the impact of these uncertainties, we present an approach for evaluating alternative pressure management strategies based on their robustness of meeting project performance criteria. We quantify the robustness of alternative strategies against several criteria: (1) exceeding fault re-activation pressure, (2) failing to inject a desired quantity of CO 2 , (3) exceeding a maximum quantity of extracted brine, and (4) failing to reach a desired extraction efficiency. Our approach allows nuances of competing and complimentary criteria to be quantitatively evaluated in a manner and in a level of detail not possible with optimization approaches. We illustrate the fundamentals of the approach on a simple one-dimensional analytical example using the Thiem equation. Here, we demonstrate the approach using a numerical flow and transport model with uncertain heterogeneous permeabilities using data and site characteristics from the Rock Springs Uplift Carbon Storage Site in southwestern Wyoming.

58 GEOSCIENCES↗
DOE OSTI2019

Data-Consistent Solutions to Stochastic Inverse Problems Using a Probabilistic Multi-Fidelity Method Based on Conditional Densities

In this work, we build upon a recently developed approach for solving stochastic inverse problems based on a combination of measure-theoretic principles and Bayes' rule. We propose a multi-fidelity method to reduce the computational burden of performing uncertainty quantification using high-fidelity models. This approach is based on a Monte Carlo framework for uncertainty quantification that combines information from solvers of various fidelities to obtain statistics on the quantities of interest of the problem. In particular, our goal is to generate samples from a high-fidelity push-forward density at a fraction of the costs of standard Monte Carlo methods, while maintaining flexibility in the number of random model input parameters. Key to this methodology is the construction of a regression model to represent the stochastic mapping between the low- and high-fidelity models, such that most of the computations can be leveraged to the low-fidelity model. To that end, we employ Gaussian process regression and present extensions to multi-level-type hierarchies as well as to the case of multiple quantities of interest. Finally, we demonstrate the feasibility of the framework in several numerical examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

Comparison of Two Methods for Estimating the Sampling-Related Uncertainty of Satellite Rainfall Averages Based on a Large Radar Data Set

The uncertainty of rainfall estimated from averages of discrete samples collected by a satellite is assessed using a multi-year radar data set covering a large portion of the United States. The sampling-related uncertainty of rainfall estimates is evaluated for all combinations of 100 km, 200 km, and 500 km space domains, 1 day, 5 day, and 30 day rainfall accumulations, and regular sampling time intervals of 1 h, 3 h, 6 h, 8 h, and 12 h. These extensive analyses are combined to characterize the sampling uncertainty as a function of space and time domain, sampling frequency, and rainfall characteristics by means of a simple scaling law. Moreover, it is shown that both parametric and non-parametric statistical techniques of estimating the sampling uncertainty produce comparable results. Sampling uncertainty estimates, however, do depend on the choice of technique for obtaining them. They can also vary considerably from case to case, reflecting the great variability of natural rainfall, and should therefore be expressed in probabilistic terms. Rainfall calibration errors are shown to affect comparison of results obtained by studies based on data from different climate regions and/or observation platforms.

Lau, William K. M.↗