Engineering Papers⌕ Search

SEARCH · Engineering Papers

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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Abstract We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Scalable computations for nonstationary Gaussian processes

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods can be very slow to converge when estimating many spatially varying parameters. In this paper, we present a computational framework which couples an algebraic block diagonal plus low-rank covariance matrix approximation with stochastic trace estimation to facilitate the efficient use of second-order solvers for maximum likelihood estimation of Gaussian process models with many parameters. We demonstrate the effectiveness of these methods by simultaneously fitting 192 parameters in the popular nonstationary model of Paciorek and Schervish using 107,600 sea surface temperature anomaly measurements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Reconstructing porous media using generative flow networks

One area of intense scientific interest for the study of sandstones, carbonates, and shale at the pore scale is the use of limited image and petrophysical data to generate multiple realizations of a rock’s pore structure. Such images aid efforts to quantify uncertainty in petrophysical properties, including porosity–permeability transforms. We develop and evaluate a deep learning-based method to synthesize porous media volumes using a so-called generative flow model trained on x-ray microscope images of rock texture and pore structure. These models are optimized on a log-likelihood objective and they synthesize large and realistic three-dimensional images. Further, we demonstrate the rapid generation of sandstone image volumes that display realism as gauged by quantitative comparison of topological features using Minkowski functionals of porosity, specific surface area, and the Euler–Poincaré characteristic (i.e., pore connectivity). We also evaluate the single-phase permeability using Navier–Stokes and lattice Boltzmann methods and show that transport properties of the generated samples match measured trends.

58 GEOSCIENCES↗
DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Normal stability of slow manifolds in nearly periodic Hamiltonian systems

Kruskal [J. Math. Phys. 3, 806 (1962)] showed that each nearly periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly invariant manifolds of each order, near which rapid oscillations are suppressed. We study the nonlinear normal stability of these slow manifolds for nearly periodic Hamiltonian systems on barely symplectic manifolds—manifolds equipped with closed, non-degenerate 2-forms that may be degenerate to leading order. In particular, we establish a sufficient condition for long-term normal stability based on second derivatives of the well-known adiabatic invariant. We use these results to investigate the problem of embedding guiding center dynamics of a magnetized charged particle as a slow manifold in a nearly periodic system. Here, we prove that one previous embedding and two new embeddings enjoy long-term normal stability and thereby strengthen the theoretical justification for these models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Local Noether theorem for quantum lattice systems and topological invariants of gapped states

Here, we study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fréchet–Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics

We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Shortcomings of meta-GGA functionals when describing magnetism

Several recent studies have shown that SCAN, a functional belonging to the meta-generalized gradient approximation (MGGA) family, leads to significantly overestimated magnetic moments in itinerant ferromagnetic metals. However, this behavior is not inherent to the MGGA level of approximation since TPSS, for instance, does not lead to such severe overestimations. In order to provide a broader view of the accuracy of MGGAfunctionals for magnetism, we extend the assessment to more functionals but also to antiferromagnetic solids. The results show that to describe magnetism there is overall no real advantage in using a MGGA functional compared to GGAs. For both types of approximation, an improvement in ferromagnetic metals is necessarily accompanied by a deterioration (underestimation) in antiferromagnetic insulators, and vice versa. Furthermore, we also provide some analysis in order to understand in more detail the relation between the mathematical form of the functionals and the results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

System Identification of a DC-DC Buck Converter Based on Two-Channel Relay Method

This work presents a system identification approach based on a two-channel relay applied to a DC-DC buck converter operating in closed-loop with a PI controller to regulate its output voltage. The implemented two-relay method allows system identification while the system is running online. Moreover, the algorithm works in a closed-loop configuration while introducing a minimal perturbation in the converter's operation. The presented algorithm was used to identify the frequency response of the converter with no-prior knowledge about the system structure. Furthermore, the identified transfer function parameters has a good agreement with the mathematical model of the converter. Simulation results of the comparison between the switching model, mathematical model and the identified model are provided to validate the theoretical analysis.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

A software package for modeling and simulating fault graphs

This report describes a novel fault graph modeling language and a simulation tool for executing models specified in the language. The modeling language has three primary features that distinguish it from similar reliability analysis tools. These are (1) a random variable modeling several distinct outcomes of a single fault; (2) chains of faults in which one fault triggers another; and (3) time to fail sampled from probability distributions including positive normal, exponential, Weibull with a minimum, or immediate. These features are motivated by their use in a historical analysis of centrifuge reliability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

W-4 W88 Systems Engineering Summer 2023 Project [Slides]

The purpose is to create a simple, streamlined process to produce reports on out of tolerance conditions with CMM data. The methods are to develop the code or process within MATLAB to import the data (import tool can be used) and to develop the code to be able to plot the data of interest. The end states are to use MATLAB to analyze CMM data from the PA and document the process for a user with some knowledge of MATLAB and an engineering background.

42 ENGINEERING↗
DOE OSTI2024

Shorter function summaries for finite state machine-based high consequence systems using logic synthesis and tautologies (Final Report LDRD 24-1302)

Computer programs are often viewed as collections of functions – each function has parameters (inputs) and computes a return value, and each has potential side effects that modify program state (outputs). In this research, a Sandia symbolic execution tool designed to support “human-in-the-loop” analysis was modified to automatically create “function summaries,” and a new tool, “diaboolical,” was created to support enhancing readability of the summary using a novel approach to bit-vector simplification that leverages logic synthesis and tautologies. For this effort, students at Auburn University created several finite state machines (FSMs) to serve as exemplars for high-consequence systems. Function summaries for each of the machines were obtained, and then portions of the summaries were simplified using both diaboolical and the simplification procedure of a popular SMT solver. A comparison of the results shows that diaboolical can often produce smaller function summaries, with expression length improvements over the unsimplified function summaries ranging from 0% to 90% for diaboolical and 0% to 65% for the SMT solver, though diaboolical had a significantly greater cost in time. Diaboolical was evaluated against a collection of “arbitrary” C-code as well as FSM exemplars, and for both datasets it achieved an approximately 10% improvement in expression length compared to simplifications that could be obtained using existing techniques. Function summaries can assist assurance efforts that evaluate existing systems and their executable code. A smaller function summary is likely easier for humans to understand and could thus increase the ability and efficacy of assurance practices centered around the analysis of executable artifacts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Enhancing Cloud Cybersecurity: Prescriptive Controls for Operational Technology

This whitepaper provides strategic insights and recommendations into security cloud-based solutions for electric utilities, encompassing operational technology (OT), virtual power plants (VPP), distributed energy resources (DERs), applications, networks, and data storage as they transition to and leverage cloud infrastructure through managed service providers (MSPs) and cloud service providers (CSPs). Principles derived from established frameworks serve as a foundation for best practices across cybersecurity projects and remove the constraints of settling on a single framework. For organizations that prefer not to integrate a specific framework altogether, elements of the proposed approach could be adopted or tailored to best fit defined requirements and expected functionalities. The Cirrus assessment, a utility cloud feasibility tool, and the roadmap it provides serve as a precursor to this paper, which seeks to be a valuable resource for defining next steps following cloud technology integration feasibility appraisal. With its comprehensive approach to adoption, the Cirrus framework offers strategic guidance on responsibly preparing for or deploying a utility cloud solution. The previously published whitepaper, “Use Case-Informed Framework for Utility Cloud Migration,” details the guiding strategy, research, and deployment of cloud solutions within electric and interconnected grid systems. Before implementing the controls suggested in this document, it is recommended that stakeholders complete Cirrus's cloud integration assessment and pair the results with their unique cybersecurity controls to form a comprehensive cloud-based utility cybersecurity plan. The Cirrus outcome will consider a series of future architectures for the grid before and after the energy transition and evaluate the arguments for and against cloud applications for each electric and interconnected grid layer. This document is a companion to the original whitepaper, "Use Case-Informed Framework for Utility Cloud Migration" to further identify and recommend security controls based on Cirrus’s cloud integration assessment output. The following whitepaper outlines the cybersecurity controls that secure cloud-service models pertinent to the electric sector using the predefined categories identify, protect, detect, and respond and recover. The objective is to outline prescriptive security controls based on the type of architecture and data stored in the cloud. The focus includes dissecting the shared responsibility model and elucidating what on-premises Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS) entail. A pivotal consideration in this context is allocating responsibility for foundational cybersecurity aspects—having used Cirrus for the cloud integration assessment. The ensuing controls detailed herein also represent a checklist of controls necessary for a secure cloud transition, equipping utilities with the knowledge to navigate this digital transformation with confidence and strategic foresight in a safe and responsible manner.

42 ENGINEERING↗
DOE OSTI2024

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Conquering Data Chaos: Research Data Management with Kubernetes

Managing massive volumes of data and effectively making it accessible to researchers poses significant challenges and is a barrier to scientific discovery. In many cases, critical data is locked up in unwieldy file formats or one-off databases and is too large to effectively process on a single machine. This talk explores the role of Kubernetes, an open-source container orchestration platform, in addressing research data management challenges. I will discuss how we are using a set of publicly available open-source and home-grown tools in the National Renewable Energy Lab (NREL) Data, Analysis, and Visualization (DAV) group to help researchers overcome data-related bottlenecks. The talk will begin by providing an overview of the data challenges faced in research data management, including data storage, processing, and analysis. I will highlight Kubernetes' ability to handle large-scale data by leveraging containerization and distributed computing, including distributed storage. Kubernetes allows researchers to encapsulate data processing infrastructure and workflows into portable containers, enabling reproducibility and ease of deployment. Kubernetes can then schedule and manage the resource allocation of these containers to enable efficient utilization of limited computing resources, leading to more efficient data processing and analysis. I will discuss some limitations of traditional, siloed approaches to dealing with data and emphasize the need for solutions which foster collaboration. I will highlight how we are using Kubernetes at NREL to facilitate data sharing and cooperation among research teams. Kubernetes' flexible architecture enables the deployment of shared computing environments, such as Apache Superset, where researchers can seamlessly access and analyze shared datasets. Providing the ability to have one research team easily consume data generated by another, utilizing Kubernetes' as a central data platform, is one of the major wins we've encountered by adopting the platform. Finally, I will showcase real-world use cases from NREL where we have used Kubernetes to solve some persistent data challenges involving large volumes of sensor and monitoring data. I will discuss the challenges we encountered when creating our cluster and making it available as a production-ready resource. I will also discuss the specific suite of tools, including Postgres and Apache Druid for columnar and timeseries data, and Redpanda Kafka for streaming data we have deployed in our infrastructure, and the process that went into the selection of these tools.

collaborative environment↗