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DOE OSTI2021

Data-Driven Exploration of Climate Attractor Manifolds For Long-Term Predictability

Focal Area: This white paper responds to Focal Area 3. We seek to gain insight into decadal-scale climate predictability by applying novel manifold-finding probabilistic AI techniques to the complex data produced by Earth System models (ESMs) such as E3SM. The associated portfolio of research activities leverages DOE’s asset mix of HPC platforms, climate expertise, climate simulation codes, and AI expertise. Science Challenge: Climate and climate models are dynamical systems exhibiting properties that are interpretable through chaos theory. The theory contains an important concept that is relevant to multi-decade-scale climate prediction: a chaotic attractor. While the space containing all the possible states of the Earth’s atmosphere and ocean, the possible weather, is large, the realized states tend to stay near the smaller-dimensioned attractor. This behavior is responsible for the “order behind the irregularity” [1] of climate phenomena. Climate change can be thought of as a change in the properties of the attractor, and predicting the climate over years to decades is equivalent to predicting how those properties will change. To date, the attractor has been a useful conceptual tool, but has not been amenable to direct characterization. A new development is the advent of efficient high-dimensional manifold-finding probabilistic AI techniques, which permit a data-driven characterization of the ESM attractor and its probability distribution over weather states. Such a characterization would result in a natural dimensional reduction — a “non-linear Principal Components Analysis (PCA) adapted to climate simulation data” — leading to important advances in scenario-based long-term climate prediction, long-term prediction of water cycle extremes, ESM verification, inter-model comparison, and process model development.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Guidelines for Determining the Load Resistance of Thin-Glass Triple-Pane Insulating Glass Unit Configurations

This guideline is intended to provide information relevant to the specification of triple- pane insulating glass (IG) units where the thickness of lite number 2 (center lite) is less than or equal to the thickness of lite numbers 1 and 3. Procedures and charts are presented to determine the load resistance (LR) of common soda-lime glass thicknesses from 0.7 mm (3/128 in.) to 1.8 mm (9/128 in.) exposed to a uniform lateral load of short or long duration, for a 0.008 probability of breakage. Deflection under load, horizontal self-weight deflection, and natural frequency procedures and charts are also included to aide in the selection of glass thickness to meet manufacturing and/or loading criteria determined by the user.

42 ENGINEERING↗

DOE OSTI2024

A Review of Resilience and Long-Term Planning in Power and Water Systems in the United States

There is recognition among power and water utilities that the frequency and magnitude of high consequence and low probability events could increase as a result of climate change. The interconnected nature of energy-water systems raises the possibility of cascading failures, increasing complexity and risks. Resilience and long-term planning are important ways of weathering the effects of climate change. First, to understand more about resilience, we reviewed existing literature on resilience definitions, metrics, and modeling, focusing on integrated water-power systems. Second, to understand how resilience and planning are being applied in practice, we interviewed utilities and organized, curated, and synthesized the interview data to arrive at several key findings, which are presented here. We found that there is not a consistent definition for resilience, yet it is something that utilities regularly plan for, often with different names and varying methods/measures. However, there is a tangible shift in the industry towards defining and determining measurable resilience metrics. While the exact metrics are a work in progress, utilities are taking steps forward by (1) putting people and culture at the center of resilience, (2) recognizing their own interdependencies, and (3) pursuing better cross-sector collaboration.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Exceedance Probabilities and Recurrence Intervals for Extended Power Outages in the United States

Power outages cause significant economic and societal impacts. An increasing likelihood of extreme weather coupled with aging grid infrastructure is leading to a higher prevalence of extended power outages, which can leave customers without power for multiple days or even weeks. Planners at the facility, local, state, and federal levels are interested in resilience solutions to reduce the impacts of extended power outages. Resilience solutions—such as installing backup systems, integrating microgrid solutions, weatherizing buildings, and hardening distribution and transmission components—can reduce the consequences of extended power outages, but these solutions come with increased capital costs. Conducting cost-benefit analyses is important for determining which steps to take to mitigate the impact of power outages without investing in ineffective and cost-prohibitive resilience solutions. The expected benefits of resilience investments depend on the frequency of power outages of various durations, particularly extended outages lasting several hours, days, or weeks. A significant barrier to resilience planning is the lack of publicly available data on the frequency and duration of extended power outages. The absence of outage duration information severely limits the ability to conduct quantitative cost-benefit analyses of resilience investments. This report provides estimates of recurrence intervals and conditional exceedance probabilities for major power outages by U.S. region between 2015 and 2021. Additionally, we provide estimates for grid management, particularly outages caused by California’s public safety power shutoffs (PSPS), and for natural outages caused by major hurricanes. Outage recurrence intervals are the average number of years between outage events, and conditional exceedance probabilities are the likelihoods that a customer who experiences a major power outage will experience an outage exceeding a given duration. Major outage events are those that affect 10,000 or more customers, as defined by the U.S. Department of Energy’s (DOE’s) Electric Emergency Incident and Disturbance Report, called OE-417 (DOE 2020). These results can be applied to determine the likelihood of experiencing long-duration outages, which can be integrated into cost-benefit analyses of resilience solutions and broader energy resilience studies. We developed a methodology to estimate customer outage durations for extended outage events using publicly available data on customer outages. Shorter-duration power outages are relatively common, with customers experiencing on average more than one power outage each year lasting fewer than 12 hours. An outage event lasting between 1 day and 1 week is expected to occur between once every 16 years and once every 42 years, depending on the region, with an average recurrence rate of once every 32 years across the contiguous United States.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Exceedance Probabilities and Recurrence Intervals for Extended Power Outages in the United States

This report provides estimates of recurrence intervals and conditional exceedance probabilities for major power outages by U.S. region between 2015 and 2021. Additionally, we provide estimates for grid management, particularly outages caused by California’s public safety power shutoffs (PSPS), and for natural outages caused by major hurricanes. Outage recurrence intervals are the average number of years between outage events, and conditional exceedance probabilities are the likelihoods that a customer who experiences a major power outage will experience an outage exceeding a given duration. Major outage events are those that affect 10,000 or more customers, as defined by the U.S. Department of Energy’s (DOE’s) Electric Emergency Incident and Disturbance Report, called OE-417 (DOE 2020). These results can be applied to determine the likelihood of experiencing long-duration outages, which can be integrated into cost-benefit analyses of resilience solutions and broader energy resilience studies.

Ericson, Sean↗

DOE OSTI2020

An Uncertainty Management Framework for Integrated Gas-Electric Energy Systems

In many parts of the world, electric power systems have seen a significant shift toward generation from renewable energy and natural gas. Because of their ability to flexibly adjust power generation in real time, gas-fired power plants are frequently seen as the perfect partner for variable renewable generation. However, this reliance on gas generation increases interdependence and propagates uncertainty between power grids and gas pipelines and brings coordination and uncertainty management challenges. To address these issues, we propose an uncertainty management framework for uncertain, but bounded gas consumption by gas-fired power plants. The admissible ranges are computed based on a joint optimization problem for the combined gas and electricity networks, which involves chance-constrained scheduling for the electric grid and a novel robust optimization formulation for the natural-gas network. This formulation ensures feasibility of the integrated system with a high probability, while providing a tractable numerical formulation. A key advance with respect to existing methods is that our method is based on a physically accurate, validated model for transient gas pipeline flows. Our case study benchmarks our proposed formulation against methods that ignore how reserve activation impacts the fuel use of gas power plants and only consider predetermined gas consumption. Here, the results demonstrate the importance of considering uncertainty to avoid operating constraint violations and curtailment of gas to the generators.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Attribution of the role of climate change in the forest fires in Sweden 2018

In this study, we analyse the role of climate change in the forestfires that raged through large parts of Sweden in the summer of 2018 from ameteorological perspective. This is done by studying the Canadian FireWeather Index (FWI) based on sub-daily data, both in reanalysis data sets(ERA-Interim, ERA5, the Japanese 55 year Reanalysis, JRA-55, and Modern-Era Retrospective analysis for Research and Applications version 2, MERRA-2) and three large-ensemble climatemodels (EC-Earth, weather@home, W@H, and Community Earth System Model, CESM) simulations. The FWI, based on reanalysis, correlates well with the observed burnt area in summer (r=0.6 to 0.8). We find that the maximum FWI in July 2018 had return times of ~24 years (90 % CI, confidence interval, > 10 years) for southern and northern Sweden. Furthermore, we find a negative trend of the FWI for southern Sweden over the 1979 to 2017 time period in the reanalyses, yielding a non-significant reduced probability of such an event. However, the short observational record, large uncertainty between the reanalysis products and large natural variability of the FWI give a large confidence interval around this number that easily includes no change, so we cannot draw robust conclusions from reanalysis data. The three large-ensembles with climate models point to a roughly 1.1 (0.9 to 1.4) times increased probability (non-significant) for such events in the current climate relative to preindustrial climate. For a future climate (2 °C warming), we find a roughly 2 (1.5 to 3) times increased probability for such events relative to the preindustrial climate. The increased fire weather risk is mainly attributed to the increase intemperature. The other main factor, i.e. precipitation during summer months, isprojected to increase for northern Sweden and decrease for southern Sweden. We, however, do not find a clear change in prolonged dry periods in summer months that could explain the increased fire weather risk in the climate models. In summary, we find a (non-significant) reduced probability of such eventsbased on reanalyses, a small (non-significant) increased probability due to global warming up to now and a more robust (significant) increase in the risk for such events in the future based on the climate models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A VR-based volumetric medical image segmentation and visualization system with natural human interaction

Volume rendering produces informative two-dimensional (2D) images from a 3-dimensional (3D) volume. It highlights the region of interest and facilitates a good comprehension of the entire data set. However, volume rendering faces a few challenges. First, a high-dimensional transfer function is usually required to differentiate the target from its neighboring objects with subtle variance. Unfortunately, designing such a transfer function is a strenuously trial-and-error process. Second, manipulating/visualizing a 3D volume with a traditional 2D input/output device suffers dimensional limitations. To address all the challenges, we design NUI-VR 2 , a natural user interface-enabled volume rendering system in the virtual reality space. NUI-VR 2 marries volume rendering and interactive image segmentation. It transforms the original volume into a probability map with image segmentation. A simple linear transfer function will highlight the target well in the probability map. More importantly, we set the entire image segmentation and volume rendering pipeline in an immersive virtual reality environment with a natural user interface. NUI-VR 2 eliminates the dimensional limitations in manipulating and perceiving 3D volumes and dramatically improves the user experience.

42 ENGINEERING↗

DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The interesting properties of natural gas as well as the growing electric power demand worldwide have led to increasing attention to natural-gas-based distributed generation applications in electric distribution systems. This paper goes over the interdependency between a residential natural gas network and an electric distribution network that are coupled via fuel cells. The modeling of the gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the gas and electric distribution networks, subject to their model constraints. In addition to this, in order to capture the probabilistic nature of the optimization problem under study, the K-means clustering algorithm is applied to the gas and electricity demands to determine hourly load states and their corresponding probabilities. Furthermore, simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution feeder and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

How earthquakes organize stress

Stress is not uniform in the Earth. Therefore, we must use natural experiments to measure the distribution of stresses and related quantities, rather than single values. For instance, dynamic triggering shows that faults are uniformly distributed over their loading cycles in Southern California. The probability that a fault ruptures across a barrier measures the in situ energy distribution. Fault roughness reflects the distribution of strength. These natural experiments produce observable distributions that are surprisingly consistent and suggest some degree of self-organization in the Earth’s crust. Once established, the functional form of the distributions can be used to track changes in response to earthquakes as well as to distinguish fundamentally different fault systems. Transient fault locking before stress release in laboratory experiments can be interpreted as a consequence of self-organization of fault stress. The robust self-organization of multiple variables in earthquake systems suggests that the most consequential mechanical outcome of earthquakes may be the redistribution of stress and the strain energy associated with it. The low friction on a fault during seismic slip as inferred by temperature measurements of the Tohoku earthquake is consistent with dissipation playing a secondary role to this redistribution process. Through stress redistribution and interaction, subduction zone faults tend to synchronize, perhaps due to their geometric simplicity, while the continental system of Southern California cannot synchronize, perhaps due to the complexity of the fault network. Earthquakes organize stress in the crust and produce a suite of well-defined, consistent distributions.

earthquakes↗

DOE OSTI2023

Uniform-in-phase-space data selection with iterative normalizing flows

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗

DOE OSTI2024

Simulation-based inference for parameter estimation of complex watershed simulators

High-resolution, spatially distributed process-based (PB) simulators are widely employed in the study of complex catchment processes and their responses to a changing climate. However, calibrating these PB simulators using observed data remains a significant challenge due to several persistent issues, including the following: (1) intractability stemming from the computational demands and complex responses of simulators, which renders infeasible calculation of the conditional probability of parameters and data, and (2) uncertainty stemming from the choice of simplified representations of complex natural hydrologic processes. Here, we demonstrate how simulation-based inference (SBI) can help address both of these challenges with respect to parameter estimation. SBI uses a learned mapping between the parameter space and observed data to estimate parameters for the generation of calibrated simulations. To demonstrate the potential of SBI in hydrologic modeling, we conduct a set of synthetic experiments to infer two common physical parameters – Manning's coefficient and hydraulic conductivity – using a representation of a snowmelt-dominated catchment in Colorado, USA. We introduce novel deep-learning (DL) components to the SBI approach, including an “emulator” as a surrogate for the PB simulator to rapidly explore parameter responses. We also employ a density-based neural network to represent the joint probability of parameters and data without strong assumptions about its functional form. While addressing intractability, we also show that, if the simulator does not represent the system under study well enough, SBI can yield unreliable parameter estimates. Approaches to adopting the SBI framework for cases in which multiple simulator(s) may be adequate are introduced using a performance-weighting approach. The synthetic experiments presented here test the performance of SBI, using the relationship between the surrogate and PB simulators as a proxy for the real case.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Applying Quantum Tomography to Hadronic Interactions

A proper description of inclusive reactions is expressed with density matrices. Quantum tomography reconstructs density matrices from experimental observables. We review recent work that applies quantum tomography to practical experimental data analysis. Almost all field-theoretic formalism and modeling used in a traditional approach is circumvented with great efficiency. Tomographically-determined density matrices can express information about quantum systems which cannot in principle be expressed with distributions defined by classical probability. Topics such as entanglement and von Neumann entropy can be accessed using the same natural language where they are defined. A deep relation exists between separability, as defined in quantum information science, and factorization, as defined in high energy physics. Factorization acquires a non-perturbative definition when expressed in terms of a conditional form of separability. An example illustrates how to go from data for momentum 4-vectors to a density matrix while bypassing almost all the formalism of the Standard Model.

Martens, J. C.↗

DOE OSTI2022

Sensitivity analysis applied to SiC failure probability in TRISO modeled with BISON

Here, a sensitivity analysis on the failure probability of the Silicon Carbide (SiC) layer in tristructural isotropic (TRISO) nuclear fuel during transient conditions predicted by the BISON fuel performance code is performed. The principal goal of the analysis is to understand the most important parameters dictating SiC failure behavior in BISON during Reactivity Initiated Accidents (RIAs). SiC brittle fracture probability is modeled using Weibull statistics. A total of seven inputs related to SiC failure has been selected for the analysis, including the Weibull statistics parameters, elastic moduli for SiC and Pyrolitic Carbon (PyC) and SiC stress-free temperature. A 1D TRISO BISON model has been established for various reactivity insertions performed at the Nuclear Safety Research Reactor (NSRR). The principal advantage associated with the 1D TRISO model developed in this work is its computational efficiency. The Sobol variance decomposition method is used, and the sensitivity indices are presented for eight different values of the energy deposition. The results show that the two most important parameters impacting the predicted SiC failure probability are the Weibull modulus and the characteristic stress, and a co-variance amongst these parameters is obtained for low reactivity insertions. An additional new finding of this work is that the relative importance of Weibull parameters depends on the energy deposition, and thus reactivity, regime. For low energy depositions, two parameters are of influence on SiC failure probability, while for high energy depositions only one parameter impacts failure probability results. Moreover, optimization of the Weibull modulus and characteristic stress is performed by minimizing the RMSE between BISON failure probability predictions and experimental failure fractions for each energy deposition. This work also demonstrates the validity of the NSRR tests BISON simulations and of the respective sensitivity analysis results as conservative, yet indicative for slower transients characterized by lower deposited energies. Such verification is achieved through the partial extension of the analysis to a group Control Rod Withdrawal reproduced from a previous study. Another novel result of this analysis is that no single set of Weibull parameters can reproduce all reactivity insertion experimental failure results, which is related to the intrinsic nature of SiC failure properties, and a new range for the parameters is proposed to produce a failure probability envelope that encompasses the experimental fractions. Additionaly, this work proposes a new approach for future failure analysis with BISON, consisting in the use of Weibull parameters ranges, rather than fixed sets, along with failure envelopes generation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Fine-tuned vs. natural supersymmetry: what does the string landscape predict?

A vast array of (metastable) vacuum solutions arise from string compactifications, each leading to different 4-d laws of physics. The space of these solutions, known as the string landscape, allows for an environmental solution to the cosmological constant problem. We examine the possibility of an environmental solution to the gauge hierarchy problem. We argue that the landscape favors softly broken supersymmetric models over particle physics models containing quadratic divergences, such as the Standard Model. We present a scheme for computing relative probabilities for supersymmetric models to emerge from the landscape. The probabilities are related to the likelihood that the derived value of the weak scale lies within the Agrawal et al. (ABDS) allowed window of values leading to atoms as we know them. This then favors natural SUSY models over unnatural (SUSY and other) models via a computable probability measure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗