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Theoretical study of various nonlinear phenomena in plasma systems and scaling of magneto-inertial-fusion targets

Plasma physics is an exciting field of study with a wide variety of nonlinear processes that come into play. Examples of such processes include the interaction of small-scale turbulence with large-scale plasma structures and the nonlinear saturation of plasma instabilities, for example those of magneto-hydrodynamical nature. During this Truman LDRD project, I studied a collection of nonlinear problems that are of interest to the field of plasma physics. This LDRD report summarizes four main research accomplishments. First, a new statistical model for describing inhomogeneous drift-wave turbulence inter- acting with zonal flows was developed. This new model includes the effects of nonlinear wave-wave collisions, which are expected to change the spectrum of the underlying DW turbulence and therefore the generation of zonal flows. Second, a new mathematical formalism was proposed to systematically apply the non- linear WKB approximation to general field theories, including those often used in fluid dynamics. This formalism represents an interesting tool for studying physical systems that show an explicit scale separation. Third, a weakly nonlinear model was developed to describe the magneto-Rayleigh-Taylor instability. This instability is of paramount importance to understand as it can reduce the performance of magnetic-inertial-fusion (MIF) platforms. The developed models captures the effects of harmonic generation and saturation of the linear growth of the instability. Finally, a framework was proposed for scaling magneto-inertial fusion (MIF) targets to larger pulsed-power drivers. From this framework, a set of scaling rules were derived that conserve the physical regimes of MIF systems when scaling up in peak current. By doing so, deleterious nonlinear processes that affect MIF performance may be kept at bay.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Metalorganic chemical vapor deposition of ZnGeN 2 films on GaN: effects of cation stoichiometry on surface morphology and crystallinity

Novel optoelectronic device designs based on the heterostructures of III-N and II-IV-N 2 are promising to advance device performance significantly. For example, by utilizing InGaN-ZnGeN 2 quantum well (QW) structures instead of pure InGaN, the band structure engineering in the QW active region can lead to improved electron-hole wavefunction overlap, and thus enhance the radiative efficiency for photon generation. These novel heterostructures have great potential to address the current challenge of low quantum efficiency in InGaN QW based light emitting diodes emitting in green and beyond. The materials development of ZnGeN 2 is still at an early stage as compared to the much matured GaN material system. In an ideal octet rule preserving ordered structure of ZnGeN 2 , every N atom is coordinated by exactly two Zn and two Ge atoms. However, local violation of octet rule can be caused by non-ideal coordination of N by the cations. The disordered structure is thermodynamically less favorable but can still be achieved, for example, in kinetics-limited growth regime. The ordered ZnGeN 2 has a bandgap very close to that of GaN (~3.4 eV) and a lattice mismatch of <0.1% with GaN. Interestingly, the valence band of ZnGeN 2 has been predicted to be ~1 eV above that of GaN, which has inspired novel designs for high efficiency light emitters. In this work, we investigated the metalorganic chemical vapor deposition (MOCVD) of ZnGeN 2 films on GaN/c-sapphire templates. Diethylzinc (DEZn), germane (GeH4) and ammonia were used as the precursors for Zn, Ge and N, respectively. A systematic study was conducted to investigate the cation stoichiometry as a function of growth temperature (TG), total reactor pressure (P) and DEZn/GeH 4 molar flow rate ratio (RII/IV). Under the investigated growth window, the Zn/(Zn+Ge) composition in the films, determined from energy dispersive X-ray spectroscopy, decreased monotonically with increase in TG but increased with increase in P and RII/IV. Atom probe tomography data did not indicate the presence of any secondary phases such as Zn 3 N 2 or Ge 3 N 4 . The surface morphology and crystallinity of the grown films had strong correlation with the Zn/(Zn+Ge) composition. The scanning electron microscopy images showed that the near-stoichiometric films have planar surfaces whereas Zn-rich films had crystallites on their surface and the Zn-poor films had faceted surface. Scanning transmission electron microscopy (STEM) imaging revealed that the Zn-rich and Zn-poor films have columnar and filament-like morphology, respectively, whereas the near-stoichiometric films have continuous film-like cross-sectional morphology. TEM nano-diffraction patterns as well as X-ray diffraction 2θ-ω scan profiles indicate that the near stoichiometric films are single crystalline. Nano-diffraction pattern of the stoichiometric films resembled that of a disordered ZnGeN 2 structure. Room temperature Raman spectra of near-stoichiometric films showed only the phonon density of states like features of a cation disordered ZnGeN 2 . Cathodoluminescence and photoluminescence spectra measured at different temperatures had similar features with peak emission wavelength at ~ 2 eV. In conclusion, the stoichiometry of ZnGeN 2 films can be widely tuned by tuning the MOCVD growth parameters. The surface morphology and the crystallinity of the films were found to have strong correlation with the Zn/(Zn+Ge) composition. The stoichiometric ZnGeN 2 films grown on GaN were demonstrated with uniform surface morphology and high crystalline quality. The results from this work will provide pathway to implement ZnGeN 2 in device structures.

Karim, Md Rezaul↗

TChem v2.0 - A Software Toolkit for the Analysis of Complex Kinetic Models

TChem is an open source software library for solving complex computational chemistry problems and analyzing detailed chemical kinetic models. The software provides support for: complex kinetic models for gas-phase and surface chemistry; thermodynamic properties based on NASA polynomials; species production/consumption rates; stable time integrator for solving stiff time ordinary differential equations; and, reactor models such as homogenous gas-phase ignition (with analytical Jacobian matrices), continuously stirred tank reactor, plug-flow reactor. This toolkit builds upon earlier versions that were written in C and featured tools for gas-phase chemistry only. The current version of the software was completely refactored in C++, uses an object-oriented programming model, and adopts Kokkos as its portability layer to make it ready for the next generation computing architectures i.e., multi/many core computing platforms with GPU accelerators. We have expanded the range of kinetic models to include surface chemistry and have added examples pertaining to Continuously Stirred Tank Reactors (CSTR) and Plug Flow Reactor (PFR) models to complement the homogenous ignition examples present in the earlier versions. To exploit the massive parallelism available from modern computing platforms, the current software interface is designed to evaluate samples in parallel, which enables large scale parametric studies, e.g. for sensitivity analysis and model calibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗

Vendor-Independent Design Requirements for a Boiling Water Reactor Safety System Upgrade

This Vendor-Independent License Amendment Request (LAR) Framework Document is a research product developed for the Idaho National Laboratory Light Water Reactor Sustainability (LWRS) Program. It was developed by MPR Associates, Inc. with technical input from LWRS and Exelon Generation personnel. To accomplish the purpose of this research, an operating plant (Limerick Generating Station [LGS]) was used as a reference to provide a concrete example and to present a "top-down" view of design concepts consistent with functional requirements baseline documents (references X and Y) also developed for this research. While this document is written in a framework to support a complete LAR submittal, its purpose is to communicate research concepts and provide an example of how to present digital information necessary to address expectations with regard to leveraging the Alternate Review Process as provided in Digital Instrumentation and Controls Interim Staff Guidance #06, Revision 2, Licensing Process. To leverage that process, this research document presupposes that a utility would select a vendor platform which has been prequalified for safety-related by the United States Nuclear Regulatory Commission. While this document is written using the Exelon Generation Limerick Generating Station (LGS) Units 1 and 2 as a baseline, this document is a research product. This document contains no commitments and makes no binding design decisions for Exelon Generation. Exelon Generation is leveraging this research to support their in-progress LGS Plant Protection System (PPS) upgrade efforts and plans to leverage it for their Redundant Reactor Control System (RRCS) replacement. The LWRS Program appreciates the research support provided by Exelon Generation in the generation of this document.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Data-Driven Learning of Non-Autonomous Systems

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗

Predicting Compliance in an Epidemiological Model: Constructs from Psychological Theory and Research

Vaccination and the alternative behavior, vaccine refusal, are a classic example of manifesting behaviors driven by social norms and norm violations. Establishing how norms emerge, and under what circumstances people choose to violate them are key issues to understand in modeling epidemics. Interactions between individuals can lead to large-scale patterning of behavior (emergent phenomena). As norm violations are revealed through human behavior, drawing on psychological theory and principles to predict those violations is a viable approach for more human-constrained epidemiological models. As an example of the implications at scale, vaccine refusal is correlated with the spread of mis/disinformation about vaccine side-effects. Considering the complexities of network dynamics, the downstream effects means that if even a small group within a population are persuaded against vaccination, there is a reservoir from which disease and disease outbreaks can propagate. This work will attempt to identify those psychological indicators, to define circumstances that predict health behaviors, and identify potentially modifiable antecedents of health behavior, and factors that influence changes toward health protective behaviors.

59 BASIC BIOLOGICAL SCIENCES↗

In situ monitoring of the stopped muon flux at Mu2e

The specific object of Mu2e search is the neutrino-less coherent $\mu^-\rightarrow e^-$ conversion in the field of an aluminum nucleus and the signal is a monoenergetic electron of energy $ \approx 104.97$ MeV. This process is forbidden in the Standard Model but allowed in many of its extensions: with minimal changes to include neutrino masses and oscillation, the Branching Ratio of this process, or the similarly interesting $\mu\rightarrow e \gamma$ decay, is expected to be of the order of $\mathcal{O}(10^{-54})$. Values like these are below any currently achievable experimental sensitivity, and the observation of a signal would be unambiguous evidence of New Physics. The upper limit on the muon conversion was set by SINDRUM II at $7\times10^{-13}$ (90\% C.L.) and the goal of the Mu2e collaboration is an improvement of 4 order of magnitudes.\\ The Mu2e experiment can be conceptually divided into three stages: interaction of the primary proton pulse with the tungsten target a nd production of $\pi$ and $\mu$; collection and transport of the produced particles down to the aluminum stopping target; interaction with the stopping target and measurement of the output particles. The measurement of the stopped muon flux is of cardinal importance for the normalization of the Mu2e results. The baseline design includes two detectors developed to measure this flux, counting $\gamma$ emitted by the muonic atoms: HPGe and LaBr$_3$(Ce). The studies performed by the Mu2e Collaboration show that these two systems can be reliably used to determine the overall normalization.\\ The number of stopped muons is proportional to the number of protons on target, which itself depends on the extraction system for the proton beam. The Mu2e beam delivery system will use a resonant extraction to create the proton pulses and this method is characterized by intensity fluctuations on the time scale of milliseconds. These fluctuations, aside from the proportional fluctuation of t he number of muons, have a non-trivial impact on the overall! performance of the apparatus. For example, higher intensity proton bunches translate into higher veto rates by the Cosmic Rays Veto system, which is triggered by secondary particles generated by the proton interaction. Another example is the effect of the instantaneous luminosity on the reconstruction efficiency: higher intensity translates into higher detector occupancy, which in turn reduces the reconstruction efficiency.\\ The two cited detectors encounter limitations when trying to monitor the flux at the millisecond timescales: HPGe is by construction a slow detector while the rate of emission of the $\gamma (1809\textrm{ keV})$ the LaBr$_3$(Ce) will measure is too low. As of today, no system allows to monitor these fluctuations and the goal of this Thesis is to try filling this gap. The method we developed to monitor the fluctuations of the stopped muon flux, and by extension, the fluctuation in the proton pulses intensity is based on counting the number of muons capt ured in the stopping target by counting the number of protons produced in the process of the nuclear muon capture. This is one of the possible processes a stopped muon can undergo and it can lead to the ejection of charged particles.\\ The reconstruction algorithms were developed by the Mu2e collaboration with the explicit (and sometimes implicit) aim to reconstruct tracks of electrons in an energy range of a conversion electron. The protons we are interested in behave quite differently from these electrons and the cardinal task of this study has been to tailor the reconstruction routines to these particles. This has been done by analyzing simulated events consisting of a single proton to optimize the procedure and understand the features of these tracks. A major difference with respect to the electrons is the non-relativistic nature of $100\div300$ MeV$/c$ protons: accounting for the low velocity is both a challenge and a unique signature of the tracks.\\ The use of a pulse d beam and the need to allow produced $\pi$ to decay and $\m! u$ to int! eract in the stopping target forces the definition of a Mu2e \textit{event}: an event is comprised by everything which happens in a $1.7\ \mu$s window between the incidence two consecutive proton pulses. This means that the reconstruction will be performed in an environment crowded by many different particles. The next step of this study has been to estimate the performance of the method in a fully-fledged Mu2e simulated event and to study what kind of selections would improve it.\\ Our results are satisfactory since the number of reconstructed protons is significant (few per event), and show that a monitor on the timescale of milliseconds is indeed possible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Competitiveness Metrics for Electricity System Technologies

The relative economic competitiveness of power generation technologies is a topic of much interest to diverse electric industry participants. However, assessing competitiveness can be challenging as it requires considering both total costs and total system value of each technology, which are complicated by the (1) numerous and diverse grid services needed to operate a reliable power system; (2) variations in the economic value of the grid services with system state and location, and over multiple timescales, due to the challenges of transporting and storing electricity; and (3) the unique characteristics of different electric system assets. Ideally, metrics designed or used to convey technology competitiveness must consider these complexities, but existing metrics often fall short. For example, the levelized cost of energy does not consider the system economic value of the various technologies nor does it consider services beyond electricity production. Various other metrics have been designed with the purpose of more-accurately communicating the economic viability of electric system technologies. In this report, we summarize the primary sources and components of costs and value and review the known competitiveness metrics by presenting their definitions, applications, advantages, and disadvantages. We also introduce a new set of competitiveness metrics, which we refer to as System Profitability metrics, that more-directly applies the economic principles of return-on-investment to electric system technologies. We use conceptual examples to show how the System Profitability metrics better reflect economic viability and relative technology competitiveness compared with existing metrics. We also describe how competitiveness metrics can be quantified using optimization-based models and demonstrate this capability using a U.S. electric sector capacity expansion model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Transfer Learning using Denoising Auto-Encoders for Cellular-Level Annotation of Tumor in Pathology Slides

Adversarial examples can produce altered classifications using only seemingly innocuous, imperceptible perturbations to the original image. The imperceptibility of adversarial perturbations suggests that the corresponding classifiers use decision criteria different than those of a human. In a medical setting, inexplicable decision criteria confound a pathologist’s willingness to trust machine-generated annotations. Here, we analyze denoising tumor detection models to see if they are robust to imperceptible adversarial perturbations. Moreover, to be more fully trusted by pathologists, we require tumor detectors that generate interpretable annotations which segment pathology slides into tumorous and normal regions at the cellular level. We therefore compare transfer learning based on two different autoencoder architectures, one derived from a deep denoising bottleneck autoencoder and one from an over-complete sparse autoencoder. Both autoencoders were first trained in an unsupervised manner on a set of pathology slides drawn from the Camelyon16 dataset. The latent representations produced by each autoencoder were then passed to separate neural networks that were trained in a supervised manner on binary tumor-normal masks generated by pathologists at cellular resolution. Both tumor detectors supported better than 90% AUC PR as measured by the area under the precision/recall curve on a held-out pathology slide. To assess the underlying decision criteria used by both tumor detectors, we constructed imperceptible adversarial examples which reduced the AUC PR of both models to less than 70%. Random noise of the same amplitude had almost no effect on the AUC PR of either model. Additionally, each tumor detector was resistant to adversarial “transfer” attacks targeting the other. The adversarial perturbations showed strong characteristic differences: the deep denoising models perturbations were a very diffuse, seemingly unrecognizable pattern while the sparse coding models perturbations showed traces of tissue cells.

47 OTHER INSTRUMENTATION↗

The Virtual Blast Furnace - An Integrated High Performance Computing Modeling, Simulation, and Visualization Capability for Steel Manufacturing (Final Report)

Many manufacturing industries require substantial capital and utilize energy intensive processes that involve complex phenomena. One example of such an industry is the steel industry, which is the fourth largest energy consuming industry in the U.S. By harnessing the power of High-Performance Computing (HPC) to enhance current simulation and visualization methods in the steel industry, it should be possible to increase resolution and/or decrease time of these methods by a factor of 1000. In this way, information can be obtained in a time frame that is useful for making business and engineering decisions, optimizing manufacturing processes and, ultimately, improving the completeness of U.S. industries. For example, if coke usage in blast furnaces were optimized such that the average coke rate was reduced from 797 lb/net tonne of hot metal (NTHM) to 604 lb/NTHM, costs could be reduced by $894 million/year. Additionally, members of the steel industry need the flexibility to efficiently operate blast furnaces at a range of production rates in order to meet fluctuating market demands. Large scale parameter studies can be utilized to discover workable operating parameters at a range of production rates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

SCEPTRE 2.2 Quick Start Guide

This report provides a summary of notes for building and running the Sandia Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) code. SCEPTRE is a general- purpose C++ code for solving the li near Boltzmann transport equation in serial or parallel using unstructured spatial finite elements, multigroup energy treatment, and a variety of angular treatments including discrete ordinates and spherical harmonics. Either the first-order form of the Boltzmann equation or one of the second-order forms may be solved. SCEPTRE requires a small number of open-source Third Part y Libraries (TPL) to be available, and example scripts for building these TPLs are provided. The TPLs needed by SCEPTRE are Trilinos, boost, and netcdf. SCEPTRE uses an autotools build system , and a sample configure script is provided. Running the SCEPTRE code requires that the user provide a spatial finite-elements mesh in Exodus format and a cross section library in a format that will be described. SCEPTRE uses an xml-based input, and several examples will be provided.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

An Introduction to Word Embeddings and Language Models

Language models have advanced at a phenomenal pace over the past decade. This document provides a short introduction to terminology, word embeddings (aka low-dimensional representations), and popular large-scale language models (LMs). Word embeddings are used to represent words as numerical vectors and are context-independent, meaning a word can only have a single representation (e.g., club can only be club sandwich, not golf club ). Language models can determine the probability of a given sequence of words occurring in a sentence and can provide context to distinguish between words and phrases that sound similar. LMs are context-dependent (e.g., club can be club sandwich or golf club ) and largely fall in two main classes – autoregressive and autoencoding models. Autoregressive models are pretrained on the classic language modeling task: guess the next token having read all the previous ones. Those models can be fine-tuned and achieve great results on many tasks, the most natural application is text generation. A typical example of such models is GPT, but others include GPT-2, GPT-3, CTLR, TRANSFORMER-XL, REFORMER, XLNET. Autoencoding models are pretrained by corrupting the input tokens in some way and trying to reconstruct the original sentence. They can be fine-tuned and achieve great results on many tasks such as text generation, but their most natural application is sentence classification or token classification. A typical example of such models is BERT, but others include ROBERTA, ALBERT, XML, XML-ROBERTA, FLAUBERT AND LONGFORMER.

97 MATHEMATICS AND COMPUTING↗

Modeling the Fission Meter [Slides]

This presentation includes an overview of the process, example inputs, and example results for the Fission Meter and its response.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Embodied carbon in the U.S. manufacturing and trade

On average, one quarter of the global carbon footprint is embodied in traded goods. These emissions are a growing issue for global efforts to decarbonize the world economy. Embodied emissions in trade are not accounted for by existing greenhouse gas accounting systems. For example, countries only report their domestic carbon emissions (also known as production-based or territorial accounting) to the Intergovernmental Panel on Climate Change (IPCC). If the embodied carbon in trade were accounted for and reported, the promising climate trends depicted by many countries would be negated or reversed. For example, many achievements of reducing emissions by developed countries under the Kyoto Protocol would actually appear as emissions outsourced to developing countries. Like many other developed countries, the United States is a net importer of embodied greenhouse gas (GHG) emissions in trade. The goal of this study was to calculate the carbon footprint of various sectors of the U.S. economy using the latest available data and based on that, estimate the embodied carbon in certain manufacturing sector products imported and exported by the U.S. First, we conducted an input-output analysis to calculate the carbon footprint of 401 aggregate level sectors of the U.S. economy. After that, for a selected number of manufacturing subsectors /products(hereafter referred to as products),we collected their trade(import/export) data and combined that with their computed carbon footprint to estimate the embodied carbon in import and export of these products for the U.S. While we conducted the carbon footprint analysis for sectors covering the entire U.S. economy (401 sectors), we only conducted the embodied carbon in trade analysis for a few products within specific aggregate level manufacturing sectors,such as computer and electronic product manufacturing (NAICS 334), transport equipment manufacturing (NAICS 336), machinery manufacturing (NAICS 333), and chemical manufacturing (NAICS 325). It is possible to do the detailed embodied carbon analysis for all other products within the various aggregate level manufacturing sectors of the U.S. economy, but given the scope of this study and space constraint of this report, we only present the results for a few products. The results of our analysis for the selected products show the embodied carbon in trade for each product by country and also show the rankings of countries in terms of top importers and exporters of embodied carbon in trade with the U.S. Our results show that in majority of cases, the U.S. is a net importer of embodied carbon in trade. Unless consumption-based accounting is used, the U.S. and other net embodied carbon importing countries may continue to outsource their emissions to meet their climate change mitigation targets under the Paris Agreement, as observed previously with the Kyoto Protocol. Some countries reported reductions that exceeded their Kyoto targets, however, the changes in emissions embodied in imports were comparable to or larger than changes in domestic emissions. Traded emissions undermined emissions reductions in the Kyoto Protocol, and threaten to continue to do so for the Paris Agreement. New climate policies such as California’s Buy Clean act, EU’s proposed border carbon tax adjustment, as well as efforts in the private sector can help address the embodied carbon in traded products.

54 ENVIRONMENTAL SCIENCES↗

Data Assimilation Methods for Dynamical Systems [Slides]

Models are not perfect. Observations are not perfect. Data assimilation combines these sources of imperfect information to provide better information. The outline for this presentation is as follows: Introduction to Data Assimilation Variational Methods 3 Kalman Filter Methods Lorenz 96 EnKF Example Data Assimilation Examples

97 MATHEMATICS AND COMPUTING↗

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗

Application of Point Precipitation Frequency Estimates to Watersheds

This report documents work sponsored by the U.S. Nuclear Regulatory Commission (NRC) at the Oak Ridge National Laboratory (ORNL) as part of the RES project, “Application of Point Precipitation Frequency Estimates to Watersheds.” This project was implemented as part of the Probabilistic Flood Hazard Assessment (PFHA) Research Program. The objective of the PFHA Research Program is to develop tools and guidance on the use of PFHA methods to risk-inform NRC’s licensing of new facilities as well as licensing and oversight of currently operating facilities as they relate to flooding hazards. Many nuclear power plants (NPPs) are located on or near rivers so riverine flooding hazards need to be considered in their design and operation. Probabilistic riverine flood models are important tools for realistic assessment of flooding risks. However, these models require areal estimates of the depth, duration, and frequency of rainfall distributed over the watershed, which are not often available. Point precipitation frequency estimates are more widely available. For example, the National Oceanic and Atmospheric Administration (NOAA) has published NOAA Atlas 14, which provides point precipitation frequency estimates for 5-minute through 60-day durations at average recurrence intervals of 1-year through 1,000-year. The research documented in this report addresses areal reduction factors (ARFs), which can be used to convert the widely available point precipitation frequency estimates, to estimates of areal precipitation frequency over a watershed. The most widely used ARF source is Technical Paper 29 (TP-29) published by the then U.S. Weather Bureau in 1958. However, both the methods and the underlying precipitation data used to produce TP-29 are seriously out of date. For example, due to the small gauge network available at the time of TP-29’s compilation, ARF estimates developed are only for watersheds smaller than about 400 square miles. Due to the relatively short record lengths of precipitation data available, frequency considerations could not be accurately determined. Other factors such as regional climate and seasonality were not addressed. Several newer methods have been published since TP-29 was developed and both the type and quantity of precipitation data have increased significantly, along with computational resources and analytical tools such as geographic information systems. This report reviewed and assessed the available precipitation products and methods for conducting ARF analysis. The work applied up-to-date precipitation data products and analysis methods with a novel watershed-based approach to investigate how ARF estimates vary across different methods, data sources, geographical locations, return periods, and seasons. The overall findings reported here regarding basic ARF trends are in line with other recent studies showing that ARFs decrease with increasing area, increase with increasing duration, and decrease with increasing return period. This study found significant differences among the available ARF methods. This work also found a strong geographical variability across different US hydrologic regions, suggesting that the ARF are specific to regional climate patterns and geographical characteristics and should not be applied arbitrarily to other locations. The results also reveal the importance of data record length, especially for high return level ARFs. The work reported in NUREG/CR-7271 will assist NRC staff in assessing different classes of ARF methods in conjunction with available rainfall data sets. It will also support the development of guidance for application of point precipitation data in PFHAs. It should be noted that the ARF values presented in this report for any location or region were developed for the purposes of comparing methods and investigating the factors that influence ARFs. They should not be considered official and should not be used in leu of a site-specific analysis.

54 ENVIRONMENTAL SCIENCES↗