Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Z Line VISAR Analysis with the LineVISAR SMASH Class

The Z line VISAR system (ZLV) is a spatially-resolved velocimeter that measures surface velocities in high-energy density experiments on the Z Pulsed Power Facility to facilitate the investigation of fusion, power flow, and dynamic material physics. The data measured in these experiments are analyzed with the LineVISAR SMASH class, a MATLAB software suite that provides tools for data importation, streak image correction, spatiotemporal registration, wrapped phase computation, phase unwrapping, shock handling, and velocity calculation. This report overviews the LineVISAR class, discusses its use, provides example implementations, and supplies analysis specifics not typically recorded in journal publications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improvement and Verification of Online Cross Section Generation Capability of Griffin for TRISO-fueled Reactors

Griffin, a MOOSE-based reactor multiphysics code jointly developed by Idaho National Laboratory and Argonne National Laboratory under the DOE Office of Nuclear Energy’s NEAMS program, has pursued the development of an online multigroup cross section generation capability for a few years to enable high-fidelity, problem-dependent neutronics analyses of advanced thermal reactors. Recent advancements in Griffin’s online multigroup cross section generation capability have significantly improved the accuracy, robustness, and efficiency of self-shielding calculations for both prismatic and pebble-bed TRISO-fueled reactor applications. Key developments include a unified fuel self-shielding method applicable to both TRISO and annular compact/spherical shell fuel zone geometries; an advanced Dancoff Category-based Equivalence Theory using a bell function for non-fuel resonance treatment, achieving more than an order-of-magnitude speedup compared to the Tone method; an on-the-fly multigroup equivalence approach to mitigate group condensation errors; and a streaming correction method for pebble-bed homogenization. A proof-of-concept demonstration of on-the-fly group condensation with consistent P0 transport correction was also achieved. The method reproduced direct fine-group solutions with excellent accuracy (eigenvalue errors within 10 pcm and pin-power differences within 0.5%), but due to performance limitations of the current fixed-source solver, improvements to solver efficiency will be addressed in future work. Verification tests were performed on graphite-moderated TRISO-fueled two-dimensional core benchmark problems representing gas-cooled microreactors, heat pipe-cooled microreactors, gas-cooled pebble-bed reactors, and fluoride salt-cooled high-temperature reactors. Across all cases, Griffin showed excellent agreement with Serpent2 continuous energy Monte Carlo solutions: eigenvalue errors within 200 pcm, pin-power root-mean-square errors within 2%, and control rod and drum worth errors less than 2%. It should be noted that, for the benchmark problem, cross section generation contributed less than 3% of the total simulation times. These results demonstrate that Griffin’s online cross section generation capability delivers accurate and efficient reactor physics solutions across a wide spectrum of TRISO-fueled advanced reactor designs. With further improvements to the fine-group fixed-source solver and planned extensions to depletion, transients, and coupled neutron–gamma transport, Griffin will be well-positioned to become a powerful and comprehensive tool for advanced reactor analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Statistical Estimation of EV Driver Charging Behavior and Influential Factors

INL received data collected via telematics from battery electric vehicles (BEVs), and these vehicles were owned by retail customers who had entered into a telematics user agreement. The goal of analyzing these data was to develop mathematical models to characterize how different sets of BEV drivers use charging infrastructure at home and away from home (i.e., public charging) and quantify how various factors influence BEV drivers’ decision to charge and use available infrastructure. The data used in this analysis are unique because they provide real world BEV driving and charging behavior at the individual driving and parking event level. In this study we seek to leverage this data to quantify BEV charging and driving metrics to help inform models that predict quantities like the specific times when loads are imposed on the electrical grid due to BEV charging. Most models that have been developed to predict electrical grid load due to BEV charging, use simulations of BEV driving events and rely on assumptions such as every vehicle charges every night. Using a statistical modelling framework, we seek to investigate BEV charging behavior and quantitatively assess these common assumptions of BEV charging behavior.

33 - ADVANCED PROPULSION SYSTEMS↗

Machine Learning for Well Log Analysis in Uranium Mining

This project explores the use of Artificial Intelligence (AI) and Machine Learning (ML) techniques to automate well log analysis for uranium mining. Geophysical log data—spontaneous potential, resistivity, and gamma ray—were used to classify lithology, correlate well logs and identify roll front zonation patterns, which are critical for locating uranium ore bodies. Supervised ML algorithms such as eXtreme Gradient Boosting (XGBoost), Categorical Boosting (CatBoost), and Random Forest were trained to classify lithology with high accuracy. Gradient Boosting Machines (GBM), XGBoost, Random Forest, and Neural Networks were also used for role front zone identification. Moreover, a Fast Dynamic Time Warping (FastDTW) algorithm was employed for well log correlation. Additionally, sample lag was addressed using dynamic programming. Results demonstrate the potential of AI and ML to streamline well log analysis and enhance uranium exploration workflows.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Techno-Economic Analysis of Recycling Strategies for Catalyst and Acid During Catalytic Graphitization

With the aim of meeting the urgent demand for active anode materials (AAM) in energy storage systems, bio-based graphite (biographite) emerges as an affordable solution to de-risk the turbulent supply chain of critical minerals. Anode grade biographite requires high crystallinity and purity, which can be achieved by catalytic graphitization with iron, followed by acid washing. Therefore, a well-conceived process integration that recycles catalyst can be the starting point to commercialization. This study evaluates closed-loop catalyst recovery, and byproducts valorization scenarios through a technoeconomic framework to help understand the scale-up potential of biographite. For the acid washing, three reactors in series meet the required biographite purity at 99.95%. Iron and acid recovery can reduce material consumption and waste generation by ~95%, albeit at the expense of ~80% increase in capital costs. Recovery scenarios present similar capital and operational expenses, yielding minimum selling prices (MSP) near $6 kg-1 of biographite. Monte Carlo methodology reveals that feedstock price accounts for ~60% of MSP variance, followed by plant capacity ~20%. The likelihood of reaching a competitive profit margin of 30% in the U.S. AAM market sits at 85% average for recovery scenarios, and 103% when iron oxide is sold as byproduct. Additionally, an IRR >= 15% can be achieved for half of Monte Carlo simulations, representing promising early-stage results. Biographite production offers a strategic pathway to stabilize the anode market beyond China by integrating established technologies for a scalable, economically viable, and sustainable process. The role of catalyst recovery and byproducts utilization is critical for advancing the biomaterials industry.

97 MATHEMATICS AND COMPUTING↗

Steam Generator Model Design Parameter Sensitivity Study Using Advanced Optimization Tools

This study focuses on design parameter sensitivity studies pertaining to a steam generator (SG) model, using both Python and machine-learning tools. The SG model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor (PWR)-type small modular reactor (SMR) system. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system (e.g., heat transfer coefficient [HTC], Nusselt number, heat transfer performance). Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in input parameters. By using machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), detailed design parametric sensitivity studies and model optimization were performed. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (±1% relative changes). The analysis results give valuable insights into SG system performance and optimization, and provide justification for researching optimized sensor placement to effectively monitor and obtain experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Steam Generator Model Design Parameter Sensitivity Study Using Advanced Optimization Tools

This study focuses on design parameter sensitivity studies pertaining to a steam generator (SG) model, using both Python and machine-learning tools. The SG model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor (PWR)-type small modular reactor (SMR) system. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system (e.g., heat transfer coefficient [HTC], Nusselt number, heat transfer performance). Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in input parameters. By using machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), detailed design parametric sensitivity studies and model optimization were performed. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (±1% relative changes). The analysis results give valuable insights into SG system performance and optimization, and provide justification for researching optimized sensor placement to effectively monitor and obtain experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Accurate and Data‐Efficient Micro X‐ray Diffraction Phase Identification Using Multitask Learning: Application to Hydrothermal Fluids

Traditional analysis of highly distorted micro X‐ray diffraction (μ‐XRD) patterns from hydrothermal fluid environments is a time‐consuming process, often requiring substantial data preprocessing and labeled experimental data. Herein, the potential of deep learning with a multitask learning (MTL) architecture to overcome these limitations is demonstrated. MTL models are trained to identify phase information in μ‐XRD patterns, minimizing the need for labeled experimental data and masking preprocessing steps. Notably, MTL models show superior accuracy compared to binary classification convolutional neural networks. Additionally, introducing a tailored cross‐entropy loss function improves MTL model performance. Most significantly, MTL models tuned to analyze raw and unmasked XRD patterns achieve close performance to models analyzing preprocessed data, with minimal accuracy differences. This work indicates that advanced deep learning architectures like MTL can automate arduous data handling tasks, streamline the analysis of distorted XRD patterns, and reduce the reliance on labor‐intensive experimental datasets.

97 MATHEMATICS AND COMPUTING↗

W2VPCA: A Machine Learning Method for Measuring Attitudes With Natural Language

Company strategy influences many decisions in freight transportation. Behavioral models of company decision-making therefore could benefit from including strategy variables. However, strategy is difficult to observe and quantify. Attitudinal surveys of company executives can be used to collect measurements of latent strategy to use in quantitative models. However, surveys are costly and burdensome. Text mining methods to collect measurements overcome these issues somewhat, but typically require manual intervention and ignore the context of words, which can be problematic. This study introduces a new machine learning method to generate strategy measurement data from existing big text data. The new method, called W2VPCA, combines Natural Language Processing and Principal Components Analysis. W2VPCA produces measurement data that serve as quantitative indicators of latent strategy in behavioral models. W2VPCA is unsupervised, data-driven, and uses information on word context. We apply W2VPCA to generate measurements of latent strategies using readily available, large-scale text data: annual company reports. The empirical measurements are used successfully to associate two latent strategies, one focusing on distribution and the other on products, with truck fleet and distribution center outsourcing decisions. The main empirical outcome is that the W2VPCA measurements outperform Bag-of-Words measurements in a psychometric analysis of latent firm strategies. While this study focuses on freight behavioral models, W2VPCA may also have applications in behavioral modeling in other domains.

97 MATHEMATICS AND COMPUTING↗

Cyber-Informed Engineering (CIE) Benefits Quantification: Recommendations for Consideration

Cyber-Informed Engineering (CIE) integrates engineering principles into the design, development, and operation of cyber-physical systems (CPS) to mitigate or eliminate the impact of cyber-enabled attacks. In July 2024, Idaho National Laboratory (INL) engaged MITRE researchers to investigate methods for systematically measuring the benefits of CIE implementation. This included evaluating the success and outcomes of CIE, identifying and quantifying the value of early adoption, and determining the business justification for its implementation, especially in existing infrastructure. MITRE reviewed existing methods in engineering and cybersecurity to understand how organizations prioritize security investments, considering their strengths, weaknesses, and relevance to CIE stakeholders. Based on this analysis, MITRE proposed potential approaches for quantifying CIE benefits and provided recommendations for INL's consideration.

42 ENGINEERING↗

Mathematical methods for optimal polynomial recovery of high-dimensional systems from noisy data

The goal of our Early Career Research Project (ECRP) is to establish a modern mathematical foundation that will enable next-generation computational methods for polynomial approximation of high-dimensional systems, having a certain set of constraints, from a limited amount of noisy data. Such a foundation is critical to realizing the future potential of the DOE user facilities, and will ultimately empower scientists to address a fundamental question, namely, “how many realizations of a nonlinear manifold are required to recover the entire high-dimensional solution map, with optimal approximation guarantees and minimal computational cost?” The central theme of this effort aims to conquer this challenge by pioneering the development of extraordinarily innovative theoretical analysis and transformational non-intrusive computational methodologies. Such approaches will enable the reconstruction of the entire high-dimensional solution map, with accuracy comparable to the best approximation, while utilizing an optimal number of samples. During this reporting period we have made significant progress on four thrusts.

97 MATHEMATICS AND COMPUTING↗

Polynomial Chaos Surrogate Construction for Random Fields with Parametric Uncertainty

Engineering and applied science rely on computational experiments to rigorously study physical systems. The mathematical models used to probe these systems are highly complex, and sampling-intensive studies often require prohibitively many simulations for acceptable accuracy. Surrogate models provide a means of circumventing the high computational expense of sampling such complex models. In particular, polynomial chaos expansions (PCEs) have been successfully used for uncertainty quantification studies of deterministic models where the dominant source of uncertainty is parametric. We discuss an extension to conventional PCE surrogate modeling to enable surrogate construction for stochastic computational models that have intrinsic noise in addition to parametric uncertainty. We develop a PCE surrogate on a joint space of intrinsic and parametric uncertainty, enabled by Rosenblatt transformations, which are evaluated via kernel density estimation of the associated conditional cumulative distributions. Furthermore, we extend the construction to random field data via the Karhunen–Loève expansion. We then take advantage of closed-form solutions for computing PCE Sobol indices to perform a global sensitivity analysis of the model which quantifies the intrinsic noise contribution to the overall model output variance. Additionally, the resulting joint PCE is generative in the sense that it allows generating random realizations at any input parameter setting that are statistically approximately equivalent to realizations from the underlying stochastic model. The method is demonstrated on a chemical catalysis example model and a synthetic example controlled by a parameter that enables a switch from unimodal to bimodal response distributions.

97 MATHEMATICS AND COMPUTING↗

A convergent genus expansion for the plateau

We conjecture a formula for the spectral form factor of a double-scaled matrix integral in the limit of large time, large density of states, and fixed temperature. The formula has a genus expansion with a nonzero radius of convergence. To understand the origin of this series, we compare to the semiclassical theory of “encounters” in periodic orbits. In Jackiw-Teitelboim (JT) gravity, encounters correspond to portions of the moduli space integral that mutually cancel (in the orientable case) but individually grow at low energies. At genus one we show how the full moduli space integral resolves the low energy region and gives a finite nonzero answer.

2D Gravity↗

A unifying equation for fermentation sustainability across the titer-rate-yield landscape

Industrial fermentation is central to the sustainable production of fuels and chemicals, yet commercial viability of emerging technologies hinges on improving fermentation titer, rate, and yield (TRY). How these metrics shape system cost remains difficult to generalize due to complex interactions among feedstocks, fermentation, separations, catalytic upgrading, waste management, and facility design. Here, we systematically map theoretical fermentation performance spaces (formed by all potential TRY combinations) for 32 representative biomanufacturing facilities—spanning distinct choices for feedstocks, fermentation regimes and products, separations, and catalytic upgrading—by simulating and evaluating them (via techno-economic analysis, TEA) under uncertainty (600,000 Monte Carlo simulations) and across TRY combinations (7500 TRY combinations for each of 32 configurations). Across this wide design and thermodynamic simulation space, we find the relationship between fermentation TRY and system cost is captured by a simple, generalizable mathematical equation (R 2 of 0.992 − 1.000 across our simulations; 0.954 − 1.000 when validated against prior studies that used different tools). We use this equation to elucidate key drivers that shape cost sensitivity to fermentation performance, generating widely applicable insights. By demonstrating a unifying relationship governs the impact of fermentation on biomanufacturing economics, this work establishes a foundation for agile, holistically predictive, resource-efficient strategies to prioritize fermentation research and development needs and accelerate commercialization of emerging biomanufacturing technologies.

applied mathematics↗