Search NASASearch

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 91 records · Page 5

Assessment of Accelerated Stress Testing Data for Silicon Photovoltaics Using Tensor Decomposition Methods

In this work, we examine the use of high-order tensor decompositions to analyze degradation pathways emerging from accelerated stress testing of silicon photovoltaic (PV) modules. Matrix-based decompositions are powerful tools for studying two-dimensional data arrays and form the foundation of a host of classical data analysis techniques. Tensors are high-order extrapolations of matrices that are able to account for more parameter dimensions, and a variety of tensor decomposition methods have been developed that similarly seek to extend insights from matrix decompositions to higher dimensions. Applying and interpreting tensor decomposition methods to sequences of PV module image data, we seek to uncover and isolate different degradation modes occurring from accelerated stress testing procedures. Further, we consider the contributions of different modes to PV module performance degradations.

data analysis

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6

A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

65M75, 70H05, 70G65

Physics and Components syntax to enable a systems-based approach to multiphysics

Simulations in MOOSE have traditionally used kernel and boundary condition classes to describe the equations. Downstream applications leveraged a system called Actions to define a pre-packaged discretization of the equations they solve. Unfortunately, the Action base class was very limited, and most applications implemented the same concepts in their Actions. This led to an increased maintenance burden and a reduction in coupling opportunities, save for the use of MultiApps which renders each input mostly independent. With the introduction of multi-system capabilities in MOOSE, there is growing interest in defining entire simulations of complex multiphysics systems in a single input file. By introducing a new Physics system, with its dedicated syntax and a new base class providing wide-ranging capabilities, we are now able to define multiple equations in a single input file in a compact and user-friendly way. With new interactions between Physics and the Component system, these equations can be defined on each component of a complex system. In this talk, we will present the capabilities of these new systems, their interactions, and how to define complex systems multiphysics simulations with Physics and Components.

22 - GENERAL STUDIES OF NUCLEAR REACTORS

MOOSE Thermal-Hydraulics Module - MOOSE workshop

The MOOSE Thermal Hydraulics Module (THM) is designed to facilitate the development of thermal hydraulic system models. It provides the capability to assemble networks of coupled components such as pipes, junctions, valves, turbomachinery, and heat exchangers. Its library of components supports a single-phase, compressible flow model based on a variable-area formulation of the Euler equations of gas dynamics and discretized using a finite volume scheme. THM offers a flexible system for specifying closures such as friction factors or heat transfer coefficients, allowing the user to choose from built-in correlations or define their own in the input file. A control logic system can be used to control input parameters, necessary for implementing transient scenarios and mirroring real control systems in thermal hydraulic systems. THM can be coupled with other MOOSE-based applications for multiphysics calculations. This training will give an introduction to the capabilities of THM and provide some examples of its usage and validation.

97 - MATHEMATICS AND COMPUTING

A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications

Our work on the DOE-sponsored project “A Contextually-Aware Sensitivity Analysis to Guide the Design of Randomized Least Squares Solvers in Applications,” was an effort to address critical challenges in nu merical computing and its applications to optimization. The increasing demand for robust and scalable solutions to large-scale linear algebra problems has highlighted the limitations of traditional approaches, particularly in heterogeneous and extreme-scale computing environments. Randomized Numerical Linear Algebra (RandNLA) offers a promising framework to address these challenges, and this proposal builds on this foundation by introducing innovations in sensitivity analysis and computational adaptability.

97 MATHEMATICS AND COMPUTING

AI/ML Expo Boosting Job Performance with AI: Innovative Approaches and Success Stories

Our technology leverages artificial intelligence (AI) to enhance the user experience in High Performance Computing (HPC) environments. By analyzing user behavior and providing personalized recommendations, our AI system helps HPC users optimize their workflows and improve productivity. Additionally, we offer an advanced image similarity search feature, which utilizes AI algorithms to identify and retrieve visually similar images, saving users valuable time and effort in their research and analysis.

97 - MATHEMATICS AND COMPUTING

Generic and ML Workloads in an HPC Datacenter: Node Energy, Job Failures, and Node-Job Analysis

HPC datacenters offer a backbone to the modern digital society. Increasingly, they run Machine Learning (ML) jobs next to generic, compute-intensive workloads, supporting science, business, and other decision-making processes. However, understanding how ML jobs impact the operation of HPC datacenters, relative to generic jobs, remains desirable but understudied. In this work, we leverage long-term operational data, collected from a national-scale production HPC datacenter, and statistically compare how ML and generic jobs can impact the performance, failures, resource utilization, and energy consumption of HPC datacenters. Our study provides key insights, e.g., ML-related power usage causes GPU nodes to run into temperature limitations, median/mean runtime and failure rates are higher for ML jobs than for generic jobs, both ML and generic jobs exhibit highly variable arrival processes and resource demands, significant amounts of energy are spent on unsuccessfully terminating jobs, and concurrent jobs tend to terminate in the same state. We open-source our cleaned-up data traces on Zenodo (https://doi. org/10.5281/zenodo.13685426), and provide our analysis toolkit as software hosted on GitHub (https://github.com/atlarge-research/2024-icpads-hpc-workload-characterization). This study offers multiple benefits for data center administrators, who can improve operational efficiency, and for researchers, who can further improve system designs, scheduling techniques, etc.

crossanalysis

Spatial modeling algorithms for reactions and transport in biological cells

Biological cells rely on precise spatiotemporal coordination of biochemical reactions to control their functions. Such cell signaling networks have been a common focus for mathematical models, but they remain challenging to simulate, particularly in realistic cell geometries. Here we present Spatial Modeling Algorithms for Reactions and Transport (SMART), a software package that takes in high-level user specifications about cell signaling networks and then assembles and solves the associated mathematical systems. SMART uses state-of-the-art finite element analysis, via the FEniCS Project software, to efficiently and accurately resolve cell signaling events over discretized cellular and subcellular geometries. We demonstrate its application to several different biological systems, including yes-associated protein (YAP)/PDZ-binding motif (TAZ) mechanotransduction, calcium signaling in neurons and cardiomyocytes, and ATP generation in mitochondria. Throughout, we utilize experimentally derived realistic cellular geometries represented by well-conditioned tetrahedral meshes. These scenarios demonstrate the applicability, flexibility, accuracy and efficiency of SMART across a range of temporal and spatial scales.

59 BASIC BIOLOGICAL SCIENCES

Mathematical modelling of the concave front in the adjacent high explosive detonation problem

This study presents an analysis of the transition-zone in adjacent high explosive (HE) detonation problems which uses a $D, 𝜅, \dot{D}$ relationship, where $D$ is the detonation front-normal velocity, 𝜅 is the detonation front curvature and $\dot{D}$ is the time derivative of detonation front-normal velocity. Our approach extends the traditional $(D, 𝜅)$ model to accurately predict the behaviour of both diverging and converging detonation shock fronts. Our findings affirm that a hyperbolic type of front evolution equation, enhanced with wave acceleration, provides a robust framework for modelling complex shock front dynamics in HE materials. This approach not only captures the natural effects of straightness and boundary slope jumps in the transition-zone but also bridges the gap between mathematical predictions and experimental observations, offering insights into the behaviour of both diverging and converging detonation propagations in a homogeneous HE.

acceleration

Enhancing ZFP: A Statistical Approach to Understanding and Reducing Error Bias in a Lossy Floating-Point Compression Algorithm

The amount of data generated and gathered in scientific simulations and data collection applications is continuously growing, putting mounting pressure on storage and bandwidth concerns. A means of reducing such issues is data compression; but, lossless data compression is typically ineffective when applied to floating-point data. Thus, users tend to apply a lossy data compressor, which allows for small deviations from the original data. It is essential to understand how the error from lossy compression impacts the accuracy of the data analytics. Thus, we must analyze not only the compression properties but the error as well. In this paper, we provide a statistical analysis of the error caused by ZFP compression, a state-of-the-art, lossy compression algorithm explicitly designed for floating-point data. We show that the error is indeed biased and propose simple modifications to the algorithm to neutralize the bias and further reduce the resulting error.

97 MATHEMATICS AND COMPUTING

Analyzing School Bus Electrification in Richmond, Virginia

School buses are an essential component of the transportation infrastructure, serving as a lifeline for students across the globe. However, the widespread use of diesel school buses has raised concerns about the health impact on millions of students exposed to harmful emissions daily. Recognizing this issue, school districts worldwide are urgently seeking cleaner energy alternatives. Electric school buses emerge as an environmentally friendly and sustainable option, fostering a healthier environment for both students and communities. However, school bus electrification faces the challenges of high upfront cost, cumbersome charging management, and constraints from power grids. To help school bus operators address those challenges, this study presents a data-driven analysis for school bus electrification. This study considered a real-world school bus system in Richmond, VA, and developed a mathematical programming model to analyze the system design, charging strategies, and charging load profiles for the electrification scenario. The study evaluated different charging strategies based on model outcomes, aiming to optimize efficiency and effectiveness. Ultimately, this research generated electric school bus charging demand profiles under various scenarios, shedding light on the feasibility and implications of transitioning to electric-powered school buses.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Landscaper v1

Understanding the inner workings of machine learning models through their loss landscapes offers crucial insights into model properties, optimization dynamics, and generalizability. However, accessing these insights has traditionally required specialized mathematical expertise, limiting broader adoption. Landscaper is an open-source Python package designed to bridge this gap. Landscaper seamlessly integrates a suite of multi-dimensional loss landscape analyses with cutting-edge topological data analysis (TDA) methods. This powerful combination makes both fundamental loss landscape analysis and advanced TDA techniques accessible to the broader scientific ML community, without requiring deep pre-existing mathematical knowledge. Landscaper offers three key functionalities: * Construction: Builds detailed loss landscape representations through versatile low and high-dimensional sampling techniques. * Quantification: Applies advanced metrics, including a novel topological data analysis (TDA) based smoothness metric, enabling new perspectives on model behavior. * Visualization: Offers intuitive tools to visualize and interpret loss landscapes, providing actionable insights beyond traditional performance metrics.

Weber, Gunther [Lawrence Berkeley National Laborat

Impacts of PV Module Connector Failures on Cost and Performance of Utility Scale Photovoltaic Systems

The reliability, cost and performance of electrical connectors are a concern in all types of electrical systems, and demands on connectors used on photovoltaic (PV) systems include that connectors maintain electrical conductivity and physical strength, endure ultraviolet sunlight and high ambient temperature, and resist moisture and chemical intrusion over a very long (>25 year) performance period. Connector failures increase operation and maintenance (O&M) costs and reduce plant production, but connector failure can also cause safety and liability problems, which are of greater concern. This work results from a three-year collaboration between Sandia National Laboratories (SNL), the Electric Power Research Institute (EPRI), and the National Renewable Energy Laboratory (NREL) and funded by the U.S. Department of Energy (DOE) Solar Energy Technology Office (SETO) under Agreements #39035 and #38531 "Connector Reliability Across the US Solar Sector." a multi-pronged investigation of PV connector health across the US (see https://energy.sandia.gov/pvconnectors/). This report presents derivation of a Techno-Economic Analysis (TEA) that models failure modes and frequencies (how often failure occurs), estimates O&M costs and lost production associated with connector failures, and then calculates the effect that PV module connectors can have on Levelized Cost of Energy (LCOE). The model is informed with initial data from quantitative assessment of failure rates, root causes and mechanisms, in-situ diagnostics and data collection, lab-based forensics, and interviews with PV connector manufacturers and plant operators. SNL conducted site inspections at multiple utility-scale sites in different climates and subjected field samples of new, used, and degraded connectors to visual and electrical characterization. EPRI conducted metallurgical analysis of the pin and sleeve conductors to study failure-induced morphological and compositional changes. There is in general a shortage of statistically valid data, but data from PVROM database maintained by SNL was sufficient to ascertain failure rates and lost production as well as provide qualitative insight in its curated maintenance records. This report details the structure of the mathematical model but the sources of data to inform the model will continue to evolve. Analysis of a 100 MW PV plant is provided as an example of the use of the model, with results indicating that connectors are responsible for Annualized O&M Costs of $\$$71,933/year; Annualized Unit O&M Costs of $\$$0.72/kW/year; that a Reserve Account of $\$$187,220 should be available to fund repairs related to connectors; that connectors add $\$$1,494,004 to the Net Present Value of the O&M Costs (project life); and that O&M related to connectors adds about $\$$0.00088/kWh to the Levelized Cost of Energy. The impact of this model is to provide a tool to make the US solar sector more robust by quantifying and monetizing the reliability risks to utility-scale PV systems posed by poorly installed, mismatched and/or poorly designed and manufactured connectors. The TEA provides a model incorporating failure statistics, O&M cost data, and lost production into a single figure of merit, informing decisions and enabling practitioners to optimize cost and performance trade-offs. Stakeholders include connector manufacturers, system designers and equipment specifiers, standards bodies, installers and O&M providers, investors and insurance underwriters. This report supports continued growth of PV predicated on assurances that properly installed and maintained PV system connectors are safe and reliable. The project team is proposing future work including accelerated testing of connectors and expanding the approach taken here to other PV system components, such as TEA for rapid shut-down devices.

14 SOLAR ENERGY

Demonstration of TOFFEE: A Response Uncertainty Quantification Tool

A key characteristic in neutron transport is nuclear data. Cross-section uncertainty is not used in MCNP6.3 to propagate response uncertainty without external analysis. Here, the TOol For Fast Error Estimation (TOFFEE) is a Python-based code developed to automate the propagation of cross-section uncertainty for MCNP evaluations. TOFFEE implements the sandwich rule to calculate the uncertainty from cross sections with sensitivity coefficients from MCNP6.3 and ENDF/B covariance data. In this paper, TOFFEE has been tested with benchmark experiments, and it has been compared to the uncertainty quantification capabilities of Sampler and TSUNAMI, within SCALE, to verify the application’s capabilities.

97 MATHEMATICS AND COMPUTING

Multitiered computational methodology for extracting three-dimensional rotational diffusion coefficients from x-ray photon correlation spectroscopy data without structural information

X-ray photon correlation spectroscopy (XPCS) is a powerful technique for analyzing particle systems by investigating their dynamics in suspensions across a broad range of temporal and spatial scales. This is done by illuminating samples with coherent x-ray beams and calculating the correlation function of the obtained x-ray scattering images. XPCS is uniquely suited for studying Brownian dynamics, consisting of translational and rotational diffusion. While traditional XPCS image analysis techniques can extract translational diffusion components, they are unable to estimate rotational diffusion coefficients. Here, we introduce a methodology that combines the angular-temporal cross-correlation analysis and a algorithmic framework called Multi-Tiered Estimation for Correlation Spectroscopy in 3D for estimating three-dimensional rotational diffusion coefficients from XPCS images of three-dimensional particle systems. We demonstrate our methodology for extracting rotational diffusion coefficients from XPCS data by applying it to simulated noisy x-ray images of systems of crossing nanotubes and proteins that evolve under translational and rotational Brownian motion for different diffusion rates. Furthermore, our results show that our approach determines rotational diffusion coefficients within a few percent error.

97 MATHEMATICS AND COMPUTING