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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

The ReSWARM microgravity flight experiments: Planning, control, and model estimation for on‐orbit close proximity operations

Abstract On‐orbit close proximity operations involve robotic spacecraft maneuvering and making decisions for a growing number of mission scenarios demanding autonomy, including on‐orbit assembly, repair, and astronaut assistance. Of these scenarios, on‐orbit assembly is an enabling technology that will allow large space structures to be built in situ, using smaller building block modules. However, like many of these scenarios, robotic on‐orbit assembly involves several technical hurdles, such as changing system models. For instance, grappled modules moved by a free‐flying “assembler” robot can cause significant changes in the combined system inertia, which have cascading impacts on motion planning and control portions of the autonomy stack. Further, on‐orbit assembly and other scenarios require collision‐avoiding motion planning, particularly when operating in a “construction site” scenario of multiple assembler robots and structures. Multiple key technologies that address these complicating factors for autonomous microgravity close proximity operations are detailed in this work, in particular: (1) application of global long‐horizon planning, accomplished using offline and online sampling‐based planner options that consider the system dynamics; (2) adaptation of the recently proposed RATTLE information‐aware planning framework for on‐orbit reconfiguration model learning; and (3) connection with robust control tools to provide low‐level control robustness using current system knowledge. These approaches were demonstrated for an autonomous on‐orbit assembly use case by the RElative Satellite sWarming and Robotic Maneuvering (ReSWARM) experiments using NASA's Astrobee robots on the International Space Station. Results of the ReSWARM experiments are provided along with significant operational and implementation detail discussing the practicalities of hardware implementation and unique aspects of working with the Astrobee free‐flyer robots in microgravity. ReSWARM provides a base set of planning and control tools for robotic close proximity operations, demonstrates them in microgravity, and outlines some of the important hardware aspects that future autonomous free‐flyers will need to consider.

Robotics↗

A Sustainable Wind–Biogas Hybrid System for Remote Areas in Jordan: A Case Study of Mobile Hospital for a Zaatari Syrian Refugee Camp

Access to reliable and sustainable energy in remote areas remains a pressing global challenge, significantly affecting economic development and the quality of life. This study focuses on the implementation of fully off-grid wind–biogas hybrid power systems to address this issue, with a focus on remote healthcare camp facilities. This paper investigates the performance of a hybrid renewable energy system within the context of one of Jordan’s northern remote areas, the Zaatari Syrian Refugee Camp, assessing its efficiency and environmental impact by taking the Zaatari hospital as the case study. Simulations were conducted to evaluate system components, including wind turbines, biogas generators, and diesel generators. A comprehensive evaluation was conducted, encompassing both the operational efficiency of the system and its impact on the environment. This study also considered various scenarios (SC#), including grid availability and autonomy levels, to optimize system configurations. The techno-economic assessment employed the levelized cost of energy (LCOE) as a key performance indicator, and sensitivity analyses explored the impact of diesel costs and wind power fluctuations on the system. Additionally, environmental assessment was conducted to evaluate the environmental effects of hybrid systems, with a specific focus on reducing greenhouse gas emissions. This investigation involved an examination of emissions in three different scenarios. The results indicate that the lowest LCOE that could be achieved was 0.0734 USD/kWh in SC#1 with 72.42% autonomy, whereas achieving 100% autonomy increased the LCOE to 0.1756 USD/kWh. Additionally, the results reveal that in scenarios SC#2 and SC#3, which have a higher proportion of diesel generator usage, there were elevated levels of NO x and CO 2 emissions. Conversely, in SC#1, which lacks diesel generators, emissions were notably lower. The proposed hybrid system demonstrates its potential to provide a reliable energy supply to healthcare facilities in remote regions, emphasizing both economic feasibility and environmental benefits. These findings contribute to informed decision making for sustainable energy solutions in similar contexts, promoting healthcare accessibility and environmental sustainability.

09 BIOMASS FUELS↗

Highway Eco-Driving of an Electric Vehicle Based on Minimum Principle

The digital map in the on-board navigation system on passenger vehicles nowadays gives controllers access to detailed information of a planned route. Connected automated vehicles equipped with high computing power, are able to process data and leverage high control freedom available through automation. This paper proposes a fast optimization algorithm for eco-driving of electric vehicles in highway cruising scenarios. The algorithm is based on optimal control theory and takes into account road grades as well as state constraints imposed by speed limits and safe headway to the preceding car. Using Autonomie, the proposed algorithm is evaluated by simulating two example scenarios. The first result demonstrates an energy saving potential of 4.4%.

connected automated vehicle↗

Approaches for Synthesis and Deployment of Controller Models on Automated Vehicles for Car-following in Mixed Autonomy

This paper describes the software design patterns and vehicle interfaces that were employed to transition vehicle controllers from simulation environments to open-road field experiments. The approach relies on a life cycle that utilizes model-based design and code generation, along with agile software development, and both software and hardware-in-the-loop testing, with additional safety margins. Autonomous designs should consider the dynamics of mixed autonomy in traffic to safely operate among humans. The software that provides a vehicle’s behavior intelligence is often developed through simulation, which may have a mismatch between dynamics, or as a result of a reinforcement learning workflow, which may be a black box with challenges to analyze. In each of these cases, it is important to have research interfaces that provide strongly typed data streams accessible to researchers who are not software experts while continuing to satisfy safety and liveness constraints. This paper describes how we design the hardware platform interfaces and software design process for a mixed autonomy traffic experiment with a leader-follower scenario. Controller synthesis for these vehicles requires clearly articulated vehicle interfaces and software design patterns for successful onboard deployment. Testing strategies for such controllers are also described before algorithms are transitioned to full-scale field experiments with safety operators for the vehicles. Testing strategies include software-in-the-loop simulation testing, hardware-in-the-loop simulation, ghost-car testing, and read-only testing in live traffic. With our approach, we were not only able to validate our controller synthesized in scripts and simulation, but also able to scale deployment to multiple vehicles.

Bhadani, Rahul↗

Energy Prediction of the Chicago Metropolitan Area Using Distributed Transportation MBSE Framework

Energy consumption impact of vehicle powertrain is traditionally assessed using standard and regulatory drive cycles. In this paper, energy consumption is determined by studying all the trips occurring in the Chicago Metropolitan Area in a 24 hour period. The data is generated by combining Polaris, an agent based traffic flow model with SVTrip, a stochastic model that generates 1 Hz vehicle speed profiles and Autonomie, a detailed vehicle level modeling tool used to predict fuel consumption. Different scenarios are constructed to define trips for different timeframes and assumptions. Vehicle fleet distribution, vehicle technologies and automation levels are applied to represent an appropriate vehicle fleet for each scenario. Analysis of energy consumption is then discussed with a particular emphasis on the impact of powertrain technology and vehicle types.

Autonomie↗

Energy Consumption and Cost Reduction of Future Light-Duty Vehicles through Advanced Vehicle Technologies: A Modeling Simulation Study Through 2050

The U.S. Department of Energy’s (DOE’s) Vehicle Technologies Office (VTO) and Hydrogen and Fuel Cell Technologies Office (HFTO) aim to develop sustainable, affordable and efficient technologies for transportation of goods and people. Translating investments in advanced transportation component technologies and powertrains to estimate vehicle-level fuel savings potential is critical for understanding DOE’s impact. In this work, we simulated technologies funded by VTO and HFTO for light duty vehicles. The simulations were performed across: Multiple powertrain configurations (i.e., conventional, power-split, extended-range electric vehicle, battery electric drive, and fuel-cell vehicles), Vehicle classes (i.e., compact car, midsize car, small sport utility vehicle [SUV], midsize SUV, and pickup trucks); and Fuels (i.e., gasoline, diesel, hydrogen, and battery electricity). These various technologies are assessed for six different timeframes: laboratory years 2015, 2020, 2025, 2030, and 2045. A delay of 5 years is assumed between laboratory year and model year (year technology is introduced into production). Finally, uncertainties are included for both technology performance and cost aspects by considering two cases: Low case, aligned with DOE technology manager estimates of expected original equipment manufacturer (OEM) improvements based on regulations, business as usual; and High case, aligned with aggressive technology advancements based on R&D targets developed through support by VTO & HFTO. These scenarios are not intended as predictions of future performances. The energy and cost impact of different technologies were estimated using Autonomie (www.autonomie.net), Argonne vehicle system simulation tool. Autonomie is a state-of-the-art vehicle system simulation tool used to assess the energy consumption, performance and cost of multiple advanced vehicle technologies across classes (from light to heavy duty), powertrains (from conventional to HEVs, FCEVs, PHEVs and BEVs), components and control strategies. Autonomie is packaged with a complete set of vehicle models for a wide range of vehicle classes, powertrain configurations and component technologies, including vehicle level and component level controls. These controls were developed and calibrated using dynamometer test data. Autonomie has been used to support a wide range of studies including analyzing various component technologies, sizing powertrains components for different vehicle requirements, comparing the benefits of powertrain configurations, optimizing both heuristic and route based vehicle energy control and predicting transportation energy use when paired with a traffic modeling tool such as POLARIS. This report documents the assumptions and estimates the vehicle-level energy consumption benefits and associated technology costs for the various types of light duty vehicles. All details of vehicle assumptions and simulation results are available in the spreadsheets accompanying this report.

33 ADVANCED PROPULSION SYSTEMS↗

Detect the Unobservable: Abnormality Detection in mixed Autonomy for Lane Change Maneuver with Following Vehicles’ Trajectories Only

Highly Automated Vehicles (HAVs) and Advanced Driver-Assistance Systems (ADAS) are transforming modern transportation with enhanced mobility, safety, and efficiency. Despite their advantages, cybersecurity vulnerabilities in these systems can lead to abnormal behavior, posing significant risks to surrounding human-driven vehicles (HDVs) in mixed traffic environments. Here, this article addresses the challenge of detecting abnormal lateral movements of HAVs/ADAS vehicles using only trajectory profiles of following HDVs. Specifically, we propose a novel modeling approach that captures both normal and abnormal lateral behaviors through vehicle kinematics, integrated decision-making processes, vehicle control using symbolic regression for lane change vehicles. Additionally, we introduce an abnormality detection framework that relies on observable HDV data, even in occlusion scenarios. The framework evaluates the sensitivity of various car-following models to detect abnormal behaviors, providing insights into the interaction between HAVs/ADAS and HDVs in mixed autonomy systems.

Connected and Automated vehicles↗

Ocean Energy for Ocean Worlds

Energy systems generating power from ocean waves, currents, tides, and thermal and salinity gradients are being developed to power oceanographic instrumentation and autonomous vehicles in Earth’s oceans. Exploration missions enabled or extended with in-situ energy harvesting on Earth may be similar to those on extra-terrestrial ocean worlds including mapping, biogeochemical sampling, acoustic monitoring, search for building blocks of life, and physical oceanographic characterization. With the addition of ocean energy available at the point of observation, data can be collected on larger spatial and temporal scales, enabling more comprehensive missions on other worlds. Power resource characteristics (e.g. current speed, variability) will similarly need to be assessed. Earth and extra-terrestrial ocean missions share vast technical challenges including high expense, need for advanced autonomy, ability to survive in the harshest environments, and limited communications or opportunities for intervention. Marine energy systems may be the only option for in-situ generation in certain scenarios (e.g., under a thick layer of ice) or advantageous over onboard energy storage options that may interfere with the natural environment (e.g., radioisotope thermoelectric generators). This work provides an overview of existing marine energy technology pertaining to ocean observations, highlights emerging research and development and new funding and program initiatives, explores similarities in mission requirements between terrestrial and extra-terrestrial applications, and suggests innovation pathways towards enabling high-value ocean world exploration powered by ocean energy.

Cavagnaro, Robert J.↗

Interactions Between Climate Policy and Technology-influenced Travel Behavior: Mitigating Induced Demand from CACC

Advances in vehicle technology have influenced the development of automated vehicle systems, where vehicles that do not require human intervention are already deployed in the roadway networks. While these advances are proved to increase roadway safety and highway capacity, more research is needed to understand the long-term and regional-level impacts on mobility, land use, energy consumption, and emissions. This study proposes a multi-model approach to analyze the effect of vehicle automation and deep decarbonization policies over a period from 2020 to 2040 in Austin, Texas. We use the Global Change Analysis Model (GCAM) to develop internally the scenarios that are then passed to the SMART Mobility modeling workflow, a large-scale simulation framework combining the POLARIS activity-based travel demand model and mesoscopic traffic simulator with the Autonomie vehicle energy consumption model and the UrbanSim land use simulator. Results suggest that the introduction of vehicles with advanced automation could increase fuel consumption when no decarbonization policies are implemented. Also, advances in vehicle technology research and development could lead to a decline in energy use in the long-term. Energy pricing and vehicle electrification incentives could help reduce the impact of vehicle automation. Finally, our analysis indicates the relevance of introducing land use processes in longterm vehicle automation studies.

land use↗

Understanding Electric Vehicle Range and Charging Needs: Interactions Between Ambient Temperature, Commute Patterns, and State-of-Charge Usage

Electric vehicle (EV) performance can vary substantially under real-world operating conditions, particularly due to ambient temperature effects on energy consumption, battery behavior, and thermal management requirements. This study quantifies how weather conditions, daily driving patterns, and State-of-Charge (SOC) usage strategies jointly influence EV driving range, charging frequency, and overall energy efficiency. A detailed and experimentally validated Autonomie vehicle model is developed, integrating a powertrain, a mono-zonal cabin model, and a battery electro-thermal model. Three battery sizes (200-, 300-, and 400-mile homologated ranges) are assessed across five commute profiles (20–200 miles) and six ambient temperatures (−18 °C to 50 °C), including scenarios with and without preconditioning. Results show that extreme temperatures could significantly decrease the maximum achievable range by up to 55% in cold conditions (−18 °C) and 40% in hot conditions (50 °C), relative to moderate conditions. Larger battery packs retain a greater fraction of their nominal range under thermal stress, while smaller packs experience sharper relative penalties due to the higher contribution of thermal loads to total energy demand. The analysis further demonstrates that limiting operation to partial SOC windows (e.g., 80–20%), a common real-world practice, significantly reduces achievable range and increases charging frequency, particularly in cold weather. Thermal preconditioning while plugged in is shown to mitigate these effects for short trips, reducing energy consumption by up to 31% in hot conditions and 7% in cold conditions. The findings demonstrate how climate, SOC usage behavior, and thermal management jointly shape the practical driving capability of EVs, highlighting the importance of efficient thermal management and realistic user charging strategies for ensuring reliable EV operation across diverse climatic scenarios.

33 ADVANCED PROPULSION SYSTEMS↗

BEAM CORE: A Flexible Ecosystem for Freight, Demographics, and Vehicle Analysis

The Behavior, Energy, Autonomy, and Mobility Comprehensive Regional Evaluator (BEAM CORE) is an open-source, modular ecosystem of highly refined, agent-based modeling tools developed by Lawrence Berkeley National Laboratory and the National Laboratory of the Rockies. Organizations such as metropolitan planning organizations, agencies, and companies can use BEAM CORE to analyze freight movement and optimize logistics solutions, assess the impacts of emerging freight technologies or e-commerce trends, model dynamic population growth and evolution, and understand the drivers and impacts of electric vehicle adoption across households in a given region. Users can choose from a flexible suite of modeling modules according to their needs and priorities. The modules integrate with travel demand models to support enhanced analysis of diverse scenarios involving freight movement, vehicle technologies, and other key factors relevant to regional planning.

33 ADVANCED PROPULSION SYSTEMS↗

Distributed Coordination of Networked Microgrids for Voltage Support in Bulk Power Grids

The increasing deployment of distributed energy resources (DERs) and microgrids (MGs) in power distribution systems has enabled the adjustment of reactive power consumption as seen at the substation, which can be used to provide voltage support for the bulk power system (BPS). Leveraging this new capability will provide greater resiliency to the power system as a whole. Here, the goal of this paper is to develop and compare three different algorithms, namely distributed optimal power flow, distributed consensus algorithm, and fully decentralized collaborative autonomy for unbalanced distribution systems for microgrid coordination. These algorithms use networked MGs to support the BPS voltage when a contingency at the bulk grid results in abnormally low voltages, which may be a precursor to voltage collapse. Our comparative analysis includes both qualitative and quantitative assessments of the three algorithms and a discussion of the trade-offs between the decentralized and distributed methods in normal and disrupted conditions. Each algorithm was evaluated on the modified IEEE 13-bus system and a real power distribution system at Chattanooga, Tennessee, that encompasses more than 4500 buses. Each algorithms excels differently and may be suited for different scenarios depending on the condition, operations, and priorities of the power and communication systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Autonomous Restoration of Networked Microgrids Using Communication-Free Smart Sensing and Protection Units

Here this paper presents autonomous restoration of networked microgrids using distributed energy resources (DERs), inverter-based resources (IBRs) in general, and controllable assets of intelligence without communication to achieve a extremely resilient power system restoration. The main innovation of this work lies in use of real-time smart sensing and decision making that enable autonomous recombination of islanded microgrids, which are individually black-started by local grid-forming (GFM) inverter units. The smart circuit breakers (SCBs) designed and demonstrated here play critical roles in the restoration process to achieve autonomy; the autonomous restoration scheme is not pre-engineered and may be subject to encounter overloading, live or downed segments as the boundary of the microgrids dynamically expands without prior knowledge and only with local measurement. We demonstrate autonomous microgrid restoration both in simulation of a modified IEEE 13-bus system, and in a hardware testbed comprising 24 GFM-IBRs and 6-SCBs, depicting several scenarios to evaluate their functionalities and interoperability. This work validates high potential of extremely resilient microgrid using novel approaches for inverter-based bottom-up system restoration in a communication-free paradigm.

24 POWER TRANSMISSION AND DISTRIBUTION↗

RuralAI in Tomato Farming: Integrated Sensor System, Distributed Computing, and Hierarchical Federated Learning for Crop Health Monitoring

Precision horticulture is evolving due to scalable sensor deployment and machine learning (ML) integration. These advancements boost the operational efficiency of individual farms, balancing the benefits of analytics with autonomy requirements. However, given concerns that affect wide geographic regions (e.g., climate change), there is a need to apply models that span farms. Federated learning (FL) has emerged as a potential solution. FL enables decentralized ML across different farms without sharing private data. Traditional FL assumes simple two-tier network topologies and, thus, falls short of operating on more complex networks found in real-world agricultural scenarios. Networks vary across crops and farms and encompass various sensor data modes, extending across jurisdictions. New hierarchical FL (HFL) approaches are needed for more efficient and context-sensitive model sharing, accommodating regulations across multiple jurisdictions. Here, we present the RuralAI architecture deployment for tomato crop monitoring, featuring sensor field units for soil, crop, and weather data collection. HFL with personalization is used to offer localized and adaptive insights. Model management, aggregation, and transfers are facilitated via a flexible approach, enabling seamless communication between local devices, edge nodes, and the cloud.

60 APPLIED LIFE SCIENCES↗

Detailed Simulation Datasets Quantifying U.S. DOE VTO/HFTO R&D Benefits Across Light- to Heavy-Duty Vehicles

For more than 20 years, Argonne National Laboratory’s Vehicle & Mobility Systems Department has assessed how R&D investments by the U.S. Department of Energy’s Transportation Technologies Office and Alternative Fuels and Feedstocks Office affect vehicle energy use and cost. The analyses are performed using Autonomie, Argonne’s full-vehicle simulation tool for energy consumption, performance, and cost. The study covers five time frames ranging from present day through 2050, with more than 30 vehicle classes and applications (10 light duty and >20 medium and heavy duty), as well as six powertrain configurations (conventional, start-stop, hybrid electric vehicle, plug-in hybrid electric vehicle, battery-electric vehicle, and fuel cell electric vehicle) and five fuels (gasoline, diesel, natural gas, hydrogen, and electricity). Low and high technology uncertainty scenarios have been considered to capture a realistic range of outcomes. The resulting datasets include the assumptions used (i.e., efficiency, $/kWh), vehicle-level data (power, energy, weight, and cost), and outputs such as energy consumption, manufacturer’s suggested retail price, and total cost of ownership. These data are critical to stakeholders working in transportation, technology assessment, and long-term R&D planning.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Modeling Framework for Connectivity and Automation Co-simulation

This paper presents a unified modeling environment to simulate vehicle driving and powertrain operations within the context of the surrounding environment, including interactions between vehicles and between vehicles and the road. The goal of this framework is to facilitate the analysis of the energy impacts of vehicle connectivity and automation, as well as the development of eco-driving algorithms. Connectivity and automation indeed provide the potential to use information about the environment and future driving to minimize energy consumption. To achieve this goal, the designers of eco-driving control strategies need to simulate a wide range of driving situations, including the interactions with other vehicles and the infrastructure in a closed-loop fashion. The framework, called RoadRunner, extends the capability of Autonomie, a vehicle energy consumption and performance modeling platform, to simulate the longitudinal movements of one or more user-defined vehicles along a user-defined route. In the first part of the paper, we provide an overview of how the framework is organized. The route attributes (position of traffic lights, grade, etc.) can be automatically extracted from a digital map after origin and destination are provided. The user defines which vehicle models to simulate and in which order. The Simulink model is then automatically generated from the scenario description. In the second part of the paper, we present an example case of a scenario with an eco-approach, using traffic signals that provide their signal phase and timing information to the vehicle. A two-stage control algorithm inspired by the literature is implemented to adjust the vehicle’s velocity while traveling through a signalized corridor with the goal of minimizing fuel consumption. Finally, we present simulation results for speed patterns and powertrain operations in typical roads with multiple intersection, comparing the energy savings with traditional driving of unconnected vehicles.

Kim, Namdoo↗

Status Report on Regulatory Criteria Applicable to the Use of Artificial Intelligence (AI) and Machine Learning (ML)

Although the interest in the use of artificial intelligence (AI) and machine learning (ML) in nuclear energy is increasing rapidly, at present their implementation is limited. This rapid increase in interest is not surprising considering that implementing AI and ML technology would allow for continuous monitoring, facilitate the implementation of predictive maintenance with optimized staffing plans, enable automation and autonomy opportunities that could drastically reduce fixed operation and maintenance costs, and provide training for operations and maintenance. Other industries are using AI for construction, and in the nuclear arena AI could provide great benefit in decommissioning activities. The ability of AI and ML to operate in real time vastly increases their potential impact. Before AI can be used in design, operations, or as a regulatory tool, the specifics on the regulations applicable to the use of AI for nuclear power applications need to be established. The difficulty is that the specific use cases will dictate the applicability of regulations. For example, even within the application domain associated with operations, the regulations might vary if the AI is used to create a virtual reference for plant operations or is used for training, optimization of maintenance intervals, prioritization of maintenance activities, etc. Different still is if the AI is to be used for design or setting technical specifications, which will introduce additional requirements. US Nuclear Regulatory Commission (NRC) licensing reviews are based on an applicant’s design meeting its performance assessment based on (1) safety goals and objectives, (2) deterministic and/or probabilistic analysis of accident scenarios, and (3) quantitative assessment of design alternatives against the safety goals and objectives using accepted engineering tools, methodologies, and performance criteria. The current regulatory framework does not explicitly address AI or autonomous control. However, as implementing AI technology will require the use of a digital platform, it must meet the requirements of an instrumentation and control (I&C) system. The regulatory requirements for AI, which will be incorporated into the I&C system, will be very dependent on how it is used (i.e., its functionality, safety classification, etc.). The licensing process is primarily risk-based with the identification of components and systems as nonsafety, important to safety, or safety related. A risk-informed approach allows further gradation of components and systems based on risk metrics such as core damage frequency or large early release fractions. Thus, the use cases and the risk categorization of impacted systems and components will determine the regulatory requirements. Regardless of how AI is used it presents new opportunities for risk-informing operating, maintenance, and regulatory decisions. Trustworthiness, transparency, and the ability to validate and verify the results will be paramount in showing that the systems and plant still meet their performance requirements. This report describes the results of research to identify regulatory implications of AI technologies and their uses. Specifically, this report reviews current regulatory guidance relevant to the application of AI for design (including design changes or new designs including advanced reactors), construction, operations, training, maintenance, research, testing, and as a regulatory tool. AI can be automated at different levels from purely informative purposes to autonomous controls. The focus of this review included determination of constraints on the application of AI technology, identification of any regulatory gaps or uncertainties, and clarification of anticipated technical basis information likely to be important for regulatory acceptance of these technologies. Currently, any use of AI at nuclear power plants is focused on nonsafety-related applications. The NRC and other regulatory bodies are evaluating providing guidance to address gaps rather than create new regulations to address the use of AI and ML. This approach seems to be the best to encourage AI development without adding regulatory uncertainty.

97 MATHEMATICS AND COMPUTING↗