Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical Modeling”

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 271 records · Page 15

A Combined Computational and Mathematical Analysis of Interconnect Fatigue Potential in Photovoltaic Modules

A finite element model of a 60-cell monocrystalline silicon glass-polymer photovoltaic module was simulated with ±1.0 kPa and ±2.4 kPa loads applied to the glass to calculate the deformation under load. Cell-to-cell displacements were used to approximate interconnect strain and stress. A mathematical fatigue cycle life relation was fitted to data for the interconnect material (copper), to generate a life prediction at each interconnect location based on the local stress means, reversal extents, and amplitudes. Interconnect stress was found to be significantly asymmetric about zero despite symmetric positive and negative module loads due to laminate thickness offsets about the neutral plane and the effects of module framing. Cycle life results indicated that interconnect fatigue failure was unlikely to occur over a 30-year lifetime of conservative wind and snow load cycles since the typical cell design feature of leaving some unconstrained length between the cell edge and first solder pad increases the effective gauge length and decreases the stress levels below the material endurance limit. Follow-up analyses found that 3.6 mm and 6.4 mm were the minimum unconstrained lengths required to survive the assumed lifetime of wind and snow cycles, respectively, confirming that typical industrial module constructions with 8–15 mm unconstrained lengths should survive conservatively. Notably, large magnitude, low-cycle snow loading was consistently the limiting factor requiring a longer unconstrained interconnect length. Finally, insights and workflows from this study inform module interconnection design limits for survival against mechanical fatigue in deployment environments.

14 SOLAR ENERGY↗

Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs

Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DRDMannTurb: A Python package for scalable, data-driven synthetic turbulence

Synthetic turbulence models (STMs) are used in wind engineering to generate realistic flow fields and are employed as inputs to industrial wind simulations. Examples include prescribing inlet conditions in large eddy simulations that model loads on wind turbines and tall buildings. We are interested in STMs capable of generating fluctuations based on prescribed second-moment statistics since such models can simulate environmental conditions that closely resemble on-site observations. To this end, the widely used Mann model (see Mann, 1994, 1998) is the inspiration for DRDMannTurb. The Mann model is described by three physical parameters: a magnitude parameter influencing the global variance of the wind field and corresponding to the Kolmogorov constant multiplied by the rate of viscous dissipation of the turbulent kinetic energy to the two-thirds, αϵ 2/3 , a turbulence length scale parameter L, and a nondimensional parameter Γ related to the lifetime of the eddies. A number of studies, as well as international standards (e.g., those by the International Electrotechnical Commission (IEC)), include recommended values for these three parameters with the goal of standardizing wind simulations according to observed energy spectra. Yet, having only three parameters, the Mann model faces limitations in accurately representing the diversity of observable spectra. This Python package enables users to extend the Mann model and more accurately fit field measurements through flexible neural network models of the eddy lifetime function. Following Keith et al. (2021), we refer to this class of models as Deep Rapid Distortion (DRD) models. DRDMannTurb also includes a general module implementing an efficient method for synthetic turbulence generation based on a domain decomposition technique. This technique is also described in Keith et al. (2021).

17 WIND ENERGY↗

Uncertainty quantification for neural network potential foundation models

Abstract For neural network potentials (NNPs) to gain widespread use, researchers must be able to trust model outputs. However, the blackbox nature of neural networks and their inherent stochasticity are often deterrents, especially for foundation models trained over broad swaths of chemical space. Uncertainty information provided at the time of prediction can help reduce aversion to NNPs. In this work, we detail two uncertainty quantification (UQ) methods. Readout ensembling, by finetuning the readout layers of an ensemble of foundation models, provides information about model uncertainty, while quantile regression, by replacing point predictions with distributional predictions, provides information about uncertainty within the underlying training data. We demonstrate our approach with the MACE-MP-0 model, applying UQ to the foundation model and a series of finetuned models. The uncertainties produced by the readout ensemble and quantile methods are demonstrated to be distinct measures by which the quality of the NNP output can be judged.

36 MATERIALS SCIENCE↗

Formal Definitions and Performance Comparison of Consistency Models for Parallel File Systems

The semantics of HPC storage systems are defined by the consistency models to which they abide. Storage consistency models have been less studied than their counterparts in memory systems, with the exception of the POSIX standard and its strict consistency model. The use of POSIX consistency imposes a performance penalty that becomes more significant as the scale of parallel file systems increases and the access time to storage devices, such as node-local solid storage devices, decreases. While some efforts have been made to adopt relaxed storage consistency models, these models are often defined informally and ambiguously as by-products of a particular implementation. Here in this work, we establish a connection between memory consistency models and storage consistency models and revisit the key design choices of storage consistency models from a high-level perspective. Further, we propose a formal and unified framework for defining storage consistency models and a layered implementation that can be used to easily evaluate their relative performance for different I/O workloads. Finally, we conduct a comprehensive performance comparison of two relaxed consistency models on a range of commonly seen parallel I/O workloads, such as checkpoint/restart of scientific applications and random reads of deep learning applications. We demonstrate that for certain I/O scenarios, a weaker consistency model can significantly improve the I/O performance. For instance, in small random reads that are typically found in deep learning applications, session consistency achieved a 5x improvement in I/O bandwidth compared to commit consistency, even at small scales.

97 MATHEMATICS AND COMPUTING↗

PSA 2025 DPRA for Cyber Optimization

Cyberattacks can have many different attack paths, durations, and goals. There are also many different mitigation options involving hardware, software, and/or humans. Evaluating defense options should include quantitative evaluation of overall effectiveness to make cost and risk-informed decisions. Typical cyberattack modeling methods only provide a qualitative evaluation and have difficulty with time dependent scenarios. The main areas of cybersecurity are confidentiality, integrity, and availability. For companies with cyber-physical systems such as advanced nuclear reactors, cyber-related integrity is a requirement set by the U.S. Nuclear Regulatory Commission. But companies are also concerned about availability or reliability as a business case. As cyber threats are evolving to a business-for-hire structure, more attacks focus on disrupting business success and reliability, causing financial and economic stability risk. Companies want reliability analysis while optimizing cost, which requires more than safety modeling methods. Dynamic-state-based and Markov-based modeling provides a method for better cyber scenario modeling with timing and conditional features not found in other numerical evaluation methods. EMRALD (Event Modeling Risk Assessment using Lined Diagrams) is a dynamic risk analysis modeling and simulation tool and has features that reduce modeling issues such as state-base explosion found in Markov-based tools. It has been used to model different time-dependent events including plant behavior and operator procedures. As a general modeling tool, EMRALD can also be used to model cyberattack scenarios with varying mitigation options and quantify effectiveness, producing numerical data for risk-informed decisions. This paper uses EMRALD to demonstrate that dynamic risk analysis can be used for cyber threat modeling to provide insights for design decision-making and optimize defense strategies.

97 - MATHEMATICS AND COMPUTING↗

Impacts of Biomass Feedstock Pre-Processing on Heat and Mass Transfer During Pyrolysis Using X-Ray Computed Tomography and Multiscale Modeling

Knowledge of the transport properties of biomass particles such as porosity, tortuosity, and permeability is paramount for high-fidelity modeling of biomass pyrolysis due to the heat and mass transfer limitations imposed by particle microstructure. X-ray computed tomography (XCT) is a non-destructive imaging method that enables full 3D reconstructions of the biomass particle microstructure with high resolution, permitting direct calculation of porosity, tortuosity, and permeability from real particle geometries. In this study, XCT imaging revealed the 3D microstructures of particles and chars from pyrolytic conversion of cylindrically cut or milled/pelletized loblolly pine samples. The porosity, tortuosity, and permeability were calculated directly from the XCT geometries via open-source microstructural analysis tool MATBOX+TauFactor (https://github.com/NREL/MATBOX_Microstructure_analysis_toolbox) and computational fluid dynamics (CFD) simulations using our solver, Mesoflow (https://github.com/NREL/mesoflow). These properties were used in a reactor scale model developed in COMSOL of the single particle reactor at NREL to investigate the impact of feedstock pre-processing on biomass conversion during pyrolysis with rigorous experimental validation.

biomass↗

Simulators for quantum network modeling: A comprehensive review

Quantum network research is exploring new networking protocols, physics-based hardware and novel experiments to demonstrate how quantum distribution will work over large distances. Current work explores much of these concepts in simulations, that are developed to understand how quantum networking will be set up and researchers can experiment virtually. Exposing flaws in network designs, like unsustainable topologies, or develop protocols that efficiently utilize network resources, simulators can also help assess whether workloads are balanced across virtual machines in the network. However, much of these simulation models come without reliable verification methods, for testing performance in real deployments. Here, in this paper, we present a review of, to the best of our knowledge, currently used toolkits for modeling quantum networks. With these toolkits and standardized validation techniques, we can lay down the foundations for more accurate and reliable quantum network simulators.

97 MATHEMATICS AND COMPUTING↗

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗

Added value of site load measurements in probabilistic lifetime extension: a Lillgrund case study

Site-specific fatigue estimation is an essential part of wind turbine lifetime extension, with various methods depending on data availability. The present study compares probabilistic lifetime extension assessment results for rotor blades with and without load measurements. It also addresses two key questions in such assessments: the applicability of the Frandsen model for estimating waked turbulence under complex and mixed wake conditions and the extrapolation of mid-term data over longer time periods. The case study wind turbine is SWT-2.3-93, located at the edge of the Lillgrund wind farm, situated in the Øresund Strait between Denmark and Sweden. The turbine is extensively instrumented, with 5 years of data available from its supervisory control and data acquisition (SCADA) system. Although the Frandsen turbulence estimates deviate in a different manner from measurements at below- and above-rated mean wind speeds, the model remains a conservative approach for fatigue load prediction and reliability. In the current case study, the site-specific assessment using strain gauge measurements yields a 33 % higher annual fatigue reliability index after 35 years compared to a scenario based on the Frandsen estimation combined with ambient environmental data and a generic aeroelastic model. The results also demonstrate that the sensitivity of fatigue reliability to load uncertainty is negligible when load measurements are used directly but relatively high when relying on the Frandsen model in combination with a generic aeroelastic model. Overall, the high variability of the lifetime extension in different scenarios of data availability and accuracy shows the importance and added value of high-quality measurements combined with wind-farm-level SCADA and a model updated in real time (digital twins).

17 WIND ENERGY↗

Developing a Nuclear Quality Assurance Compliant Design Methodology for Neutronic Analysis of Xe-100 Design

The primary objective of this work is to develop a design methodology compliant with nuclear quality assurance standards for the Xe-100 neutronic design verification studies. To achieve this, a Monte Carlo model of the Xe-100 reactor was constructed using the exclusion principle, transformation technique, and universe-based level specification following Idaho National Laboratory (INL) NQA level-1 compliant standards and an NQA-1 compliant version of MCNP6. The model encompasses the entire reactor core structures, including the upper plenum, core region, and lower plenum sections, along with all sub-components. The active core section was represented using the spectral regions, each comprising a particular fuel composition and temperature averaged over the considered zone, calculated by X-energy using Very Superior Old Programs (VSOP). Additionally, a component-wise temperature map was implemented into the model, not only for the core region but also for the structural components. Temperature-dependent cross-section libraries, along with thermal scattering law libraries, generated using INL NQA-1 compliant version of NJOY21, were utilized for each isotope in the burnt fuel and the structural materials. Furthermore, the volume of each modeled component was estimated using a stochastic approach with the ray tracing method in MCNP and criticality calculations were performed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

97 MATHEMATICS AND COMPUTING↗

Floating Wind Array Ontology and Modeling Framework

While there are many tools for designing and modeling a single floating turbine, array level design and modeling has much more to consider. Designing floating wind arrays requires a coupled approach considering many variables, from bathymetry to installation and maintenance to failure and risk analysis. With all of these considerations, an array-level modeling tool is needed to quickly evaluate array designs. The Floating Array Model (FAModel) tool developed at the National Renewable Energy Laboratory was created to fill this gap in low-fidelity array modeling. FAModel is a python framework created to streamline holistic low-fidelity floating wind modeling for array-level analysis. FAModel integrates site data and models with a variety of open-source modeling tools developed by NREL, including FLORIS, RAFT, MoorPy, and anchor capacity models. The integration of these tools allows users to quickly and holistically design an array by considering forces, area analysis, visualization, annual energy production, failure modeling, and component costs.

17 WIND ENERGY↗

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. Furthermore, the comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

97 MATHEMATICS AND COMPUTING↗