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At least 415 records · Page 23

AFIP6-MkII and RERTR-12 Porosity Data Collection and Analysis for Modeling and Simulation

Gathering data for the improvement of nuclear fuel modeling and simulation efforts is the primary driver for this work. Mechanistic models allow for a better understanding of the material on a micro- and macrostructural level while saving time and money over traditional experiment efforts. Historically, summarized data and correlations are the inputs for empirical material models and model validation. When improving these models for nuclear fuels with experimental results, there is a lack of reliable data readily available. Experiments - RERTR-12 and AFIP6-MkII - were conducted to understand the irradiation behavior of metallic U-10Mo monolithic fuels for use in extreme reactor environments such as research reactors like the Advanced Test Reactor (ATR) or the High Flux Isotope Reactor (HFIR). Microstructural characteristics of fission gas pores (FGP) in each experiment are collected using an automated image analysis technique developed at the University of Florida and presented here. A series of statistical tests are performed to explore the reliability of the results, as well as understand where the data is lacking and what future data collection is necessary to provide sufficient information to assist modeling efforts. The focus is on the porosity, pore size, and eccentricity of FGPs formed during irradiation in three AFIP6-MkII samples and one RERTR-12 sample. From the analysis, it is clear there are substantial impacts of fission density on the pore structure, but there also exist also underlying connections between each sample and the behavior observed in the pores. Further analyses of the pre- and post-irradiation microstructure are needed to improve the understanding of these connections. An early method for microstructural data analysis is presented within and is currently being expanded to include other microstructure data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of Weakly Informed Priors for FLEX Data

On behalf of the U. S. Nuclear Regulatory Commission (NRC), Idaho National Laboratory (INL) has reviewed the development and use of “weakly informed prior” (WIP) probability distributions to obtain industry-wide failure probability and rate distributions for portable “FLEX” equipment, as documented in the Pressurized Water Reactor Owner’s Group (PWROG) report, FLEX Equipment Data Collection and Analysis (PWROG 18043-P) by MM Degonish. The review includes a description of the methods used by the PWROG analysts. It also includes an implementation of those methods for comparison purposes and an implementation of two constrained-noninformative (CN) distributions for further WIP comparisons. The report documents several issues that the review identified in the development of the WIP distributions. They relate to the quality and representativeness of the current portable “FLEX” component data, the choice of informed distributions for related installed components, and the lack of verification for the factors chosen to weaken the information from the installed components. Two errors occurred in the computations: the posterior distribution of the WIP was used to modify the WIP itself, resulting in a lack of independence between the WIP and the data; and an error was made in the conversion of WIP mean and variance values to beta distributions. The INL reviewers think the WIP distributions presented in the report are untenable for use in risk assessments at the present time because of these issues.

99 GENERAL AND MISCELLANEOUS↗

Mechanical Behavior of Hybrids with Hyper-Connected Molecular Networks

Our research is focused on fundamental studies related to the molecular design, synthesis, characterization and modeling of molecular-reinforced hybrid glass films for superior mechanical and fracture properties. Molecular-reinforced hybrid glass films exhibit unique electro-optical properties while maintaining excellent thermal stability. They have important technological application for emerging nanoscience and energy technologies including anti-reflective and ultra-barrier layers in photovoltaics, display technologies, as well as quantum technologies. However, they are often inherently brittle in nature, do not adhere well to adjacent substrates, and exhibit poor mechanical properties. Furthermore, a robust understanding of the underlying mechanisms of deformation, fracture and fatigue has been lacking particularly given their mechanically fragile nature. The related lack of structure-property relationships between molecular structure, mechanical properties and processing represents a fundamental challenge to their integration into device technologies, compromises their thermomechanical reliability and has thwarted efforts to improve mechanical and, particularly, fracture properties.

36 MATERIALS SCIENCE↗

Requirements and Conceptual Design of Off-gas Systems for the Reprocessing of Metallic Fuels

An assessment has been conducted to determine how key regulations regarding volatile radionuclide emissions to the atmosphere may apply to the off-gas streams associated with electrochemical reprocessing. The scope of this assessment was based upon a generic electrochemical reprocessing scheme with a throughput rate of 200 MTIHM/y applied to metallic fuel discharged from a sodium fast reactor (SFR), but the findings are able to be translated to other advanced nuclear scenarios as merited. Air dispersion modeling was performed using the EPA CAP-88 model and evaluated the uncontrolled decontamination factors (DFs) that would be required to achieve regulatory compliance with the dose-based limits set forth by EPA regulation 40 CFR 190.10(a). These DFs were compared to those required by fuel cycle–based limits set forth by EPA regulation 40 CFR 190.10(b). Two theoretical sites with disparate climatological conditions were selected for air dispersion modeling (Idaho and Tennessee). The radionuclides modeled included 3 H, 85 Kr, 129 I, and selected alpha-emitting transuranic isotopes (referred to here as 239 Pu-TRU <1y ). It was found that the fuel cycle-based limits in 40 CFR 190.10(b) are most restrictive for 85 Kr and 239 Pu-TRU <1y , with DFs of 3 and 6.1E+09, respectively. The dose-based limit as derived from 40 CFR 190.10(a) could require mitigation of tritium in some scenarios, with an estimated DF of about 3 for the reference scenarios. The fuel cycle-based limit for 129 I resulted in a DF of about 240 for the reference scenario. The need for iodine mitigation based on dose to the public depended upon the physical form of iodine as either particulate or vapor-phase species. Emission of iodine from the facility as a vapor necessitated DFs of about 2 but emission as a particulate would require DFs >6,000 to meet thyroid dose-based limits. Effects of physical form on needed iodine mitigation are significant, but the understanding of speciation of iodine both during electrochemical reprocessing and after release to the atmosphere is limited. The electrochemical processing unit operations were evaluated to identify potential release points for the volatile radionuclides and to assess the potential for retention of the radionuclides within the process (thus decreasing the need for mitigation). Mitigation strategies for 3 H, 85 Kr, 129 I, and 239 Pu-TRU <1y were identified. In all cases, there are reasonably achievable pathways to regulatory compliance, although in some cases additional R&D is merited to verify the chemical speciation of these isotopes and to develop and demonstrate potential treatment technologies for this application. Whether or not additional off-gas controls (beyond common operations such as HEPA filtration and oxygen and moisture control) are needed for any of these regulated or volatile radionuclides depends on the (a) type of facility (NRC-regulated or DOE), (b) used fuel process rate, (c) used fuel burnup and composition, (d) speciation and retention of volatile radionuclides in the process and in the cell gas cleanup system, (e) site-specific parameters such as location, meteorology, stack height, and site boundaries, and (f) levels of conservatism and safety factors used in assessing compliance to air emissions regulations. Performance of this assessment revealed several areas where information is lacking or additional research is required in order to better determine if or what kinds of off-gas control might be needed. First, and most significantly, the understanding of the chemical speciation and physical form and partitioning of iodine during electrochemical processing operations is lacking and prevents the ability to accurately assess the potential iodine mitigation requirements. Future research in this area should be multifaceted and include thermodynamic modeling of iodine speciation in different process steps, experiments to quantify the kinetics of vapor-phase and melt-phase transitions, bench-scale experiments to determine the potential chemical and physical form of iodine emissions from the electrorefining process, and verification of iodine behavior with experiments utilizing operational facilities. Similarly, an improved understanding of iodine behavior in the environment after release from the facility stack will be required to refine dose estimations, as particulate and vapor-phase emissions result in significantly different doses to the MEI.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Grand Challenge "Uncertainty Project" to Accelerate Advances in Earth System Predictability: AI-Enabled Concepts and Applications

This proposal is emerging from GISS ModelE3 ESM development in the area of cloud physics, so we begin with an example of research needs/gaps from that work. Here, some of our greatest development concerns arise where we lack fundamental process-level understanding, as in ice formation. Namely, it is currently unclear what is the main process that is forming the majority of ice crystals in commonly occurring convection, apparently via secondary ice production at warm temperatures. We are keenly awaiting laboratory data for candidate mechanisms, which is not yet in hand to crucially establish their efficiency. Our progress is also hampered by a lack of uncertainty characterization in currently available measurements of ice crystal number size distributions. Furthermore, the same multiplication process may be responsible for a majority of ice crystals in many extratropical mixed-phase clouds, whose variable representation in CMIP6 ESMs may be a leading cause of differences in cloud phase feedback and ECS. Yet we have been required to deliver an ESM with the cloud physics knowledge at hand. The proposed grand challenge project is AI-enabled via application of machine learning (ML) to climate model and observational data streams (focal area 3), and applications include AI-guided observing system design and model/component/parameterization selection (areas 1 and 2). The project is structurally agnostic as to whether model or observing system components use AI approaches or not, but uncertainties must be estimated and propagatable in both.

58 GEOSCIENCES↗

How AI Predicts the Untrained and Unseen

Focus Area: Model predictability improvements (Primary); Data optimization (secondary); Data complexity insights (secondary). The Scientific Challenge: If we believe that a future under extreme conditions will look very differently from today, we can likely agree that ML/AI models trained on past and present datasets will not be adequate to make reliable predictions into the future. This is true for water cycling, as well as biogeochemistry and other Earth system components and behaviors. Additionally, ML/AI models are inherently non-physical. Despite the flourishing success of ML/AI in many applications, such as computer vision, natural language process, and gaming, even the most sophisticated AI models don’t understand the very basic physical laws. Therefore, a natural question is: Can we trust ML/AI based predictions of Earth system behaviors that are fundamentally driven by physical laws? So, are physics models with meticulous process representation a better choice? Not exactly. Physical models, when firmly rooted in first principles, work great at predicting behaviors of systems with a well-defined set of boundary conditions and variables. However, as a complex system, the number of parameters and the degree of complexity and dynamics in processes, coupling, and scale dependent emergent behaviors make the Earth system behaviors very challenging to predict with physical models composed of deterministic laws. In addition, due to the lack of fundamental understandings, physical models often implement empirical correlations derived from observations with biases from locality of data generation. Because correlation is not necessarily causation or comply with first principles, scaling of model predictions beyond locality is often invalid. Beyond the limitation of models, physics or AI, our knowledge of the Earth system is limited by the lack of observational technologies and resources. Insufficient data density, dimensionality and diversity only offer a sliced (or projected) view of the Earth system, e.g. Plato’s Cave analogy, limiting our capability to better understand and represent fundamental processes in models.

54 ENVIRONMENTAL SCIENCES↗

DOE Deep Energy Retrofit Cost Survey

A survey was conducted by the Lawrence Berkeley National Laboratory on deep energy retrofit (DER) market drivers, opportunities, and challenges. The survey was part a research study sponsored by the U.S. Department of Energy to gather information on the costs of DER from home performance contractors and stakeholders. Cost data was gathered from DER projects that use a comprehensive, whole-home approach to drastically reduce energy use and improve performance. DER projects often aim at reducing energy use by 50% or more. In addition, these projects can improve home comfort and potentially benefiting occupant health. Yet, market adoption of DER has been limited. Major limiting factors include complex projects, high costs, perceived risks, extensive disruption, and unfamiliar work scopes to some contractors. In order to better understand what motivates and deters DER projects in today’s market, a survey was conducted to gather this information, and to learn about promising approaches and technologies from the industry perspective. Past surveys on homeowners and home energy performance professionals have studied the motivations and barriers of energy efficiency retrofits. Two surveys of home energy performance professionals were conducted in recent years. The Resources for the Future (RFF) Home Energy Audit and Retrofit Survey was conducted in 2011 by recruiting energy auditors and retrofit installers through members of Efficiency First and Building Performance Institute (BPI) accredited contractors. The survey asked about the business and services that respondents provide, how often homeowners follow their recommendations to retrofit their homes, and the respondents’ opinion on barriers faced by the industry. The survey found that not enough homeowners know about energy audits, but more importantly, it is the high cost of retrofits compared to low energy prices that is responsible for few energy audits and retrofits being completed. The RESNET Deep Retrofit Industry Stakeholder Survey was conducted shortly after launching of the EnergySmart Home Performance Team program. The EnergySmart Team program involves a formal agreement among allied contractors who are engaged in high performance retrofits. Using this allied team approach, teams can pool their expertise and provide each other with customer referrals. The survey asked EnergySmart Team members and outside stakeholders on questions about market and technical barriers in performing home energy retrofits. Survey respondents identified lack of consumer awareness and lack of affordable financing for consumers as the leading market barriers to home energy retrofits. In their written comments, many survey respondents also echoed that the high costs of retrofit compared to low energy prices is a market barrier. Respondents found “certain housing characteristics that prevent effective retrofit” and “energy analysis software inaccuracy or limitations” are the two leading technical barriers. Their choices for technical barriers were reflective of the energy rater/auditor role played by the majority (78%) of the survey respondents. In comparison to past surveys, this work aimed to gather inputs from a broader segment of the home performance industry to identify the opportunities and barriers faced by DERs from all perspectives. The survey asks for project costs to help breakdown the high costs of DERs. This survey is also motivated by a need to better understand the role of DERs in reducing energy use by the residential sectors and meeting climate goals. The survey is designed towards obtaining more substantive inputs from survey respondents by encouraging written comments, rather than setting the goal to reach a large number of respondents. We took this approach because DER is currently still a niche market, so it is more valuable to gather in-depth inputs from individuals who are performing this work rather than getting to the masses.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

New High-Energy & Safe Battery Technology with Extreme Fast Charging Capability for Automotive Applications (Final Technical Report)

Being able to refill a cars gas tank when low on fuel is incredibly convenient and is a lacking feature for battery elective vehicles. New High-Energy & Safe Battery Technology with Extreme Fast Charging Capability for Automotive Applications was a research project designed to help correct this lacking feature by developing automotive sized Li-ion battery cells and demonstrating their ability to charge in under 10-minutes. To address the technical challenges Microvast, a cell manufacturer, was joined by Argonne National Labs, battery technology innovator, and BMW, a renown OEM, worked together to define and validate materials and cells for this project. By projects end, Microvast had successfully built and demonstrated a 240 Wh/kg, 35 Ah pouch cell that was capable of over 800 10-minute charge, full discharge cycles. From the outset of the project the plan was to use large amp-hour cells (ie automotive relevant sizes) to ensure the project findings and outcomes were most relevant for electric vehicle applications. The manufacture of cells was done using test manufacturing lines at Microvast and BMW that closely resemble the procedures of a Li-ion battery cell factory.

25 ENERGY STORAGE↗

Business Models for Coal Plant Decommissioning

Aging coal-fired power plants are retiring across the United States. Researchers at Pacific Northwest National Laboratory studied coal-fired power plant decommissioning business models to support program development for the Department of Energy’s Office of Energy Efficiency & Renewable Energy (EERE) to engage with communities affected by power plant retirement processes. Evaluating and reducing the impact on coal-dependent communities from phasing out coal production is a crucial piece of nationwide economic development and community-directed engagement in the clean energy future. This report describes the steps in the typical coal-fired power plant decommissioning process, including analysis of the following key factors: Drivers including policy and regulations, competition with other fuels, and corporate responsibility goals; Types of coal plant decommissioning including plant retirement without full decommissioning, repurposing with fuel switch, redeveloping to utilize existing transmission, and decommissioning and repurposing with other commercial activities; and, Costs of coal plant decommissioning, including variations across regulated and deregulated markets and the funding resources to support decommissioning activities. The details described in this report relied heavily on the availability of local news reports and communications regarding plant retirements, as the researchers identified a lack of formal literature surrounding business models for coal plant decommissioning and a need for a more robust source material collection. In addition, a lack of oversight entities responsible for decommissioning processes may have led to this shortfall of information. Future research regarding coal plant decommissioning can include quantitative studies on power plant retirement drivers, procedures, and costs, qualitative assessments on affects decommissioning has on surrounding communities, investors, and other stakeholders, and identifying best practices to engage community stakeholders in the decommissioning process.

01 COAL, LIGNITE, AND PEAT↗

Evaluation of Hands-On Cybersecurity Skills Development

Cybersecurity is a relatively new and quickly advancing industry, though there is a deficit in industry professionals throughout the world. This deficit is a result of the inability of education to keep up with the continuously changing cyber-threat landscape. A lack of effective, accessible, hands-on training platforms is a barrier for students and professionals who seek to gain the skills and abilities necessary to enter the workforce. Additionally, the lack of adequate training makes it difficult for industry experts to upskill or stay up to date on new advancements within the field of cybersecurity. The goal of this cohort is to discover what makes an effective or ineffective training platform, what platforms are currently available, and to determine the next steps for hands-on learning. Hands-on experience is necessary to create workforce ready professionals, yet it is underutilized by students and professionals of cybersecurity due to costs, availability, and ease of use. This cohort has uncovered hands-on training solutions, identified many effective training solutions, and explored potential improvement to cybersecurity training. These findings resulted in the cohort moving beyond research to test the resources that currently exist or are in development, and to apply that knowledge to discovering and developing engaging hands-on training.

97 MATHEMATICS AND COMPUTING↗

The False Dilemma: Rethinking AF Science and Technology Officer Talent Management

In 2019, Secretary of the Air Force (SECAF) Heather Wilson launched the 2030 Science and Technology (S&T) Strategy by stating, “The advantage will go to those who create the best technologies and who integrate and field them in creative operational ways that provide military advantages.” In 2021, 15% of Air Force general officers responsible for creating and integrating this technological edge had a science, technology, engineering, and math (STEM) graduate degree, and less than 1% of generals had a STEM doctorate. As one point of comparison, at least 32% and 13% of founding CEOs of Fortune 500 technology companies had a master’s and doctoral STEM degree, respectively. The gulf is larger when you consider that these CEOs used their technical degrees throughout their careers whereas most general officers do not. In large organizations, if the leader does not possess technical knowledge, it is difficult to drive innovation systems and connect ideas to reality. The evidence for this disconnect is abundant in acquisition challenges for high-tech systems, significant pushback to the “revolution in military affairs”, and failure of the “Third Offset” to take hold and deliver capabilities to offset Chinese and Russian capabilities. Indeed, when the former Air Force and Space Force Chief Software Officer, Nicolas M. Chaillan, offered his resignation, one of the main reasons for leaving was “the failure of OSD and the Joint Staff to deliver on their own alleged top ‘priority’, JADC2 – they couldn’t ‘walk the walk.’” Senior leaders have recognized this disconnect, and several inquiries and studies regarding STEM competency have been conducted. Many have posed a false dilemma: a large, STEM-cognizant or small, STEM-expert force. However, current and future STEM human capital needs are managed at the unit and functional area level. This leads to “silos” and the tactical “needs of the present” dominating the strategic “needs of the future”, highlighted by only two functional areas systematically tracking future STEM needs. Therefore, the decision on force structure appears to have been historically made by default through these and other perceived structural realities, and a vast majority of recommendations have focused on the small STEM community – an exercise in diminishing returns. In essence, the solution often boils down to finding unicorns – officers that have chartered the unforgiving pathway through the traditional “gates” to general officer while obtaining sufficient STEM proficiency along the way. Fortunately for the Air Force, these officers exist, albeit at a rate below what the evidence would suggest is necessary. However, this approach fundamentally limits the ability to develop a deep pool of officers with the ability to create and integrate technologies and ensures the Dunning-Kruger effect is prevalent. The Dunning-Kruger effect is a cognitive bias where those with limited knowledge in an area lack the expertise necessary to recognize their lack of expertise and consequently are prone to overestimate their knowledge and performance. In short, we need less leaders overestimating their STEM knowledge and more with hard-earned STEM competency required to “walk the walk” to create and integrate technologies for military advantage. This will not be accomplished by restricting the emphasis to the traditional scientists and engineering (S&E) career fields – the pool, only 10% of line officers, and general officer progression is just too small. Fortunately, the recent SECAF’s Management Initiatives and Chief of Staff’s (CSAF) Action Orders, both containing emphasis on organic expertise to “accrue advantage in military-technological competition,” present an opportunity to truly develop a framework for the force of the future.

99 GENERAL AND MISCELLANEOUS↗

A High-Throughput Computing Infrastructure to Generate Custom, Open Community Geothermal Datasets

The most significant challenge facing geothermal research, development, and deployment is a lack of comprehensive datasets describing the geological and economical properties of North America. Automated knowledge base construction, the process of designing algorithms to analyze text and images to programmatically build new datasets, is one possible solution to this problem. The xDD library of full-text scientific articles (https://xdd.wisc.edu) is one of the largest collections of open and controlled-access scientific documents available for knowledge base construction in the world, but it has been underutilized by experts in geothermal research. The xDD development team attributed the lack of engagement by software developers and geothermal researchers to two perceived shortcomings of the system. First, the workflow for obtaining data from xDD for local development and testing of data mining applications was unnecessarily abstruse and required significant manual intervention by xDD systems administrators. Second, although xDD already held articles from a broad cross-section of scientific literature with an emphasis on the geosciences, it did not have an explicit set of geothermal research documents that could serve as the nucleus of a geothermal data mining application. To address these issues, the Automated Data Extraction PlaTform (ADEPT) was proposed to extend the data distribution capabilities of the xDD system. The ADEPT extension added the following four key features to xDD: 1) integration of National Geothermal Data System (NGDS) documents into the xDD library to provide an explicitly geothermally-themed collection; 2) improved RESTful (i.e., https-protocol driven) web services for external partners to access xDD data for machine learning application development; 3) a web platform for end-users and xDD administrators to coordinate the development of data mining applications from the initial step of browsing available documents to the final stage of deploying a production-quality machine learning application on high-throughput computing infrastructure; and 4) the development of demonstration data mining applications to illustrate the new workflow to potential collaborators. A total of 21,674 geothermal documents from NGDS were fully ingested into the xDD library and the associated metadata is publicly available through the xDD web services; furthermore, the ADEPT web platform is now publicly accessible and fully live at https://xdd.wisc.edu/adept/.

15 GEOTHERMAL ENERGY↗

Porosity Determination and Classification of Laser Powder Bed Fusion AlSi10Mg Dogbones Using Machine Learning [Slides]

Angular pores (lack of fusion) pores are more detrimental to the health of the part due to induced stress concentrations. Three types of porosity found in AM parts: keyhole porosity, gas porosity, and lack of fusion porosity. In this research, we address the question, "Which machine learning and/or machine vision techniques work best to segment porosity and determine the type of porosity observed in the sample?"

42 ENGINEERING↗

Advanced Power Systems Measurements: A Literature Review

In 2020, a literature survey was performed as part of a project aimed at producing guidance for the Department of Energy in the form of a Roadmap. The topic of the Roadmap was measurement. That was viewed as being generally underrepresented in consideration of sensing and measurement or instrumentation and measurement. Sensing is just the beginning of a process, and the instrument is just the container for the process. Measurement, the experimental process, has acquired a considerable body of theory over the last few decades, theory that is not widely taught and disseminated. The results of the survey can be said broadly to reflect that lack of appreciation. Specifically, the review found that there is support for the development of a more “capable” PMU. New algorithms and new documentary standards will be needed. Some of the findings are: (1) Point-on-wave technology adds new capability to the existing suite of measurements, and could allow for improved operation and protection (2) Power quality analysis has historically been concerned with assessment of how non-sinusoidal the delivered voltage shows promise in signature recognition, a departure from the modeling that has historically characterized power system measurements. (3) The PMU is assed as being a remarkable measurement system, but its performance is held back by the lack of understanding of the measurement theory underpinning its operation. (4) The PMU is being considered for application in the distribution system. There is a danger that it will be seen only in the light of the successful PMU implementation in transmission, and the two have different requirements. These various expansions of measurements will no doubt benefit from a better appreciation of the theoretical aspects of measurement. In this, and other, regards, our survey of the literature has identified gaps as well as possibilities.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

US Fallout Shelter

Being indoors (sheltering) reduces radiation exposures resulting from nuclear fallout or a power-plant accident. However, most US building types, particularly non-residential buildings, lack quantitative estimates. We provide here a high-level modeling analysis of modern US building protection based on a novel radiation protection building attribute taxonomy, a new building protection model, compilation of prior experimental results, and nationally representative building survey data. This approach provides a consistent, quantitative understanding of US building protection and, when combined with the distribution of people among different buildings, can assist in selecting emergency response strategies. We find that indoor radiation protection varies by orders of magnitude. Most people in non-residential buildings are adequately protected, particularly below ground or in the building center. Residential buildings are less protective and those with lighter weight walls lack adequate, above ground protection. This work also highlights key areas where further investigation will improve the current results. These include the improving the understanding of residential basement protection, additional experimental data on non-residential buildings (particularly schools and industrial buildings), and the frequency of brick veneer and stucco exterior residential buildings.

61 RADIATION PROTECTION AND DOSIMETRY↗

Model-Form Epistemic Uncertainty Quantification for Modeling with Differential Equations: Application to Epidemiology

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

97 MATHEMATICS AND COMPUTING↗

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗