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 73 records · Page 4

Uncertainty Quantification for Smooth Functional Data with Application to Material Properties

This document outlines a method for processing functional output (i.e., curves) for the ultimate purpose of sampling curves under specified input conditions for use in modeling and simulation uncertainty quantification (UQ) studies. A set of benchmark curves sufficiently representative of the relevant scenario(s) being simulated are provided to the process and formatted as described in Section 1. Principal Component Analysis (PCA) is utilized to discover the components of uncertainty in the benchmark curves and is outlined in Section 2. Section 3 describes the application of uncertainty quantification to the PCA results for the purpose of sampling curves to be used in UQ analysis. Section 4 applies these techniques to an example benchmark dataset. Concluding remarks are provided in the final section.

36 MATERIALS SCIENCE

A Practical Solver for Scalar Data Topological Simplification

This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of “signal” persistence pairs to maintain, our approaches produces an output field g that is close to f and which optimizes (i) the cancellation of “non-signal” pairs, while (ii) preserving the “signal” pairs. In contrast to pre-existing simplification algorithms, our approach is not restricted to persistence pairs involving extrema and can thus address a larger class of topological features, in particular saddle pairs in three-dimensional scalar data. Our approach leverages recent generic persistence optimization frameworks and extends them with tailored accelerations specific to the problem of topological simplification. Extensive experiments report substantial accelerations over these frameworks, thereby making topological simplification optimization practical for real-life datasets. Our approach enables a direct visualization and analysis of the topologically simplified data, e.g., via isosurfaces of simplified topology (fewer components and handles). We apply our approach to the extraction of prominent filament structures in three-dimensional data. Specifically, we show that our pre-simplification of the data leads to practical improvements over standard topological techniques for removing filament loops. Here, we also show how our approach can be used to repair genus defects in surface processing. Finally, we provide a C++ implementation for reproducibility purposes.

97 MATHEMATICS AND COMPUTING

FRAM v.7.1

Fixed-energy Response-function Analysis with Multiple efficiency (FRAM) is a software code designed primarily for plutonium and uranium isotopic analysis. It is widely used in both the domestic and international safeguards community. FRAM can quickly and accurately determine the isotopic compositions of plutonium, uranium, and mixed oxides (MOX) when measuring with a high-purity germanium (HPGe), cadmium zinc telluride (CZT), or lanthanum bromide (LaBr3) detector. The capabilities of FRAM have been enhanced to analyze the data of the pixelated CZT detector (made by H3D) and to measure the mass of plutonium, uranium, and MOX. Both the isotopic composition and mass of the item can be quickly determined with one measurement using a gamma detector with FRAM v.7.1.

07 ISOTOPE AND RADIATION SOURCES

Overlapping Schwarz Methods Are Not Anisotropy‐Robust Multigrid Smoothers

We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, it is well known that the smoothing properties of point-wise smoothers, such as Gauss Seidel, rapidly deteriorate as the strength of anisotropy increases. On the other hand, global smoothers based on line smoothing are known to generally provide good smoothing for diffusion problems, independent of the anisotropy strength. Here, a natural question is whether global methods are really necessary to achieve good smoothing in such problems, or whether it can be obtained with locally overlapping block smoothers using sufficiently large blocks and overlap. Through local Fourier analysis and careful numerical experimentation, we show that global methods are indeed necessary to achieve anisotropy-robust smoothing. Specifically, for any fixed block size bounded sufficiently far away from the global domain size, we find that the smoothing properties of overlapping multiplicative Schwarz rapidly deteriorate with increasing anisotropy, irrespective of the amount of overlap between blocks. Moreover, our results indicate that anisotropy-robust smoothing requires blocks of diameter 𝒪⁡(𝜖 −1/2 ) for anisotropy ratio 𝜖 ∈(0,1] .

97 MATHEMATICS AND COMPUTING

Low-Temperature Geothermal Play Fairway Analysis for the Denver Basin

This project is part of a national initiative to showcase the benefits of incorporating low-temperature geothermal resource assessment into the deployment of geothermal heating, combined heat and power (CHP), and geothermal direct-use (GDU) technologies. The initiative was established to accelerate the country's decarbonization efforts by identifying potential for low-temperature geothermal resource utilization (<150 degrees C, e.g., CHP and GDU) in selected sedimentary basins with numerous population centers. The play fairway analysis (PFA) methodologies in this study were adapted from previous PFA investigations of sedimentary basin geothermal play types (SBGPTs) that evaluated the potential for low-temperature resources (<150 degrees C). Workflows, relevant datasets, a new Python library, and common and composite geological criteria maps are utilized to develop low-temperature geothermal resource favorability maps for the Denver Basin, a sedimentary basin spanning Colorado, Nebraska, and Wyoming. The replication of these methodologies in other SBGPTs can evaluate potential for low-temperature resources. To facilitate future assessment of low-temperature geothermal resources in SBGPTs, this project provides PFA workflows, data, tools, and favorability maps that will ultimately support the utilization of low-temperature geothermal resources in sedimentary basins.

combined heat and power

Integrating PCTRAN with AI-Driven Host-Intrusion Detection and Secured Container Systems for Advanced Malware Analysis (Summer Internship Report)

This study presents a solution for enhancing the security of the Personal Computer Transient Analyzer (PCTRAN) PC-based Nuclear Power Plant Simulator by integrating the software with an artificial intelligence (AI)-driven host-intrusion detection system (HIDS), in addition to a secured container system, for malware analysis. PCTRAN is a Windows XP-based software package that has the ability to simulate a variety of accident and transient conditions for nuclear power plants (NPPs). It offers a high-resolution replica of the Nuclear Steam Supply System (NSSS) and displays the status of important parameters allowing for operator interaction. By including AI-driven HIDS for the NSSS, the framework can identify security threats in real-time, ensuring the integrity of the nuclear simulation environment. Additionally, the secured container system offers the ability to isolate and analyze malware, preventing potential threats from affecting core systems. The integration process involves extensive testing and validation in order to ensure accuracy, reliability, and compliance with security policies. This framework sets a new precedent for secure simulation and training in NPP operations, and offers insight for future advancements in cybersecurity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Emerging Per- and Polyfluoroalkyl Substances in Tap Water from the American Healthy Homes Survey II

Humans experience widespread exposure to anthropogenic per- and polyfluoroalkyl substances (PFAS) through various media, which can lead to a wide range of negative health impacts. Tap water is an important source of exposure in communities with any degree of contamination but routine or large-scale PFAS monitoring often depends on targeted analytical methods limited to measuring specific PFAS. We analyzed 680 tap water samples from the American Healthy Homes Survey II for PFAS using non-targeted analysis (NTA) to expand the range of detectable PFAS. Based on detection frequency and relative abundance, about half of the identified PFAS were found only by NTA. We identified (with varying degrees of confidence) 75 distinct PFAS, including 57 exclusively detected by NTA. The identified PFAS are members of seven structural subclasses differentiated by their head groups and degree of fluorination. Clustering analysis categorized the PFAS into four coabundance groups dominated by specific PFAS subclasses. One group uniquely identified by NTA contains zwitterionic PFAS and other PFAS transformation products which are likely associated with aqueous firefighting foam contaminants in a small number of spatially correlated samples. These results help further characterize the scope of exposure to emerging PFAS experienced by the U.S. population via tap water and augment nationwide targeted-PFAS monitoring programs.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN

Do We Really Need All That Data: From Data to Agency in Automated Microscopy

Microscopy is entering an era of automated laboratories and AI-enabled instruments, often justified by a simple narrative of automating experiments to collect more data and train better models. In this work, we argue that, for microscopy, this framing is incomplete and can be counterproductive.

97 MATHEMATICS AND COMPUTING

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

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