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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

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

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Mathematical methods for neutrino cross-section extraction

Precise modeling of neutrino-nucleus scattering is becoming increasingly important as accelerator-based oscillation experiments seek definitive answers to open questions about neutrino properties. To guide the needed model refinements, a growing number of experimental collaborations are pursuing a wide-ranging program of neutrino interaction measurements at GeV energies. A key step in most such analyses is cross-section extraction, in which measured event counts are corrected for background contamination and imperfect detector performance to yield cross-section results that are directly comparable to theoretical predictions. In this paper, I review the major approaches to cross-section extraction in the literature using representative examples from the MINERvA, MicroBooNE, and T2K experiments. I then present two mathematical techniques, blockwise unfolding and the conditional covariance background constraint, which overcome some limitations of typical cross-section extraction procedures.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Final report of activities for the LDRD-express project #223796 titled: “Fluid models of charged species transport: numerical methods with mathematically guaranteed properties”, PI: Ignacio Tomas, Co-PI: John Shadid

This report summarizes the findings and outcomes of the LDRD-express project with title “Fluid models of charged species transport: numerical methods with mathematically guaranteed properties”. The primary motivation of this project was the computational/mathematical exploration of the ideas advanced aiming to improve the state-of-the-art on numerical methods for the one-fluid Euler-Poisson models and gain some understanding on the Euler-Maxwell model. Euler-Poisson and Euler-Maxwell, by themselves are not the most technically relevant PDE plasma-models. However, both of them are elementary building blocks of PDE-models used in actual technical applications and include most (if not all) of their mathematical difficulties. Outside the classical ideal MHD models, rigorous mathematical and numerical understanding of one-fluid models is still a quite undeveloped research area, and the treatment/understanding of boundary conditions is minimal (borderline non-existent) at this point in time. This report focuses primarily on bulk-behaviour of Euler-Poisson’s model, touching boundary conditions only tangentially.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

For many problems in computational science and engineering, the so-called forward problem—solution of the underlying mathematical model to yield output quantities of interest, given input parameters—is difficult enough for frontier complex models, which are often characterized by coupled multiphysics and possibly stochastic behavior over a wide range of length and time scales. However, we face the need to move beyond the forward problem, to address what is often the ultimate goal of CS&E: decision making. This requires us to tackle a spectrum of mathematical problems that subsume, and are thus even more difficult than, the forward problem. First, given experimental data, we wish to estimate unknown parameters characterizing a model of a natural or engineered system by solving an inverse problem. Second, we seek the optimal configuration of the system (or experiments) by solving an optimal design problem. Third, the optimal operation of the system must be determined by solving an optimal control problem. And fourth, we must quantify uncertainties as they propagate through all of the preceding problems, from data to model inference to prediction and finally to optimal design and control. Optimal mathematical methods and algorithms for such end-to-end, data-to-decisions modeling and simulation of complex problems—requiring integrated solution of forward, inverse, optimization, and UQ problems for large, multiphysics, multiscale models—entails challenges of the highest order, while also presenting great opportunities for applied mathematics research. Unfortunately, research on forward, inverse, optimization, and UQ problems has all-too-often progressed in isolation. This has led to mathematical methods that perform well when considering the forward simulation in isolation, but are prohibitive or suboptimal or unstable when combined with other methods within the framework of inversion, optimization, or UQ. The reverse is also true: general-purpose methods developed within the inversion, optimization, and UQ fields often become prohibitive when applied to complex CS&E problems since they do not exploit their structure.

58 GEOSCIENCES↗
DOE OSTI2023

Multi-scale models of whole cells: progress and challenges

Whole-cell modeling is “the ultimate goal” of computational systems biology and “a grand challenge for 21st century”. These complex, highly detailed models account for the activity of every molecule in a cell and serve as comprehensive knowledgebases for the modeled system. Their scope and utility far surpass those of other systems models. In fact, whole-cell models (WCMs) are an amalgam of several types of “system” models. The models are simulated using a hybrid modeling method where the appropriate mathematical methods for each biological process are used to simulate their behavior. Given the complexity of the models, the process of developing and curating these models is labor-intensive and to date only a handful of these models have been developed. While whole-cell models provide valuable and novel biological insights, and to date have identified some novel biological phenomena, their most important contribution has been to highlight the discrepancy between available data and observations that are used for the parametrization and validation of complex biological models. Another realization has been that current whole-cell modeling simulators are slow and to run models that mimic more complex (e.g., multi-cellular) biosystems, those need to be executed in an accelerated fashion on high-performance computing platforms. In this manuscript, we review the progress of whole-cell modeling to date and discuss some of the ways that they can be improved.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Direct and Inverse Problems of Thermomechanics Concerning the Optimization and Identification of the Thermal Stressed State of Deformed Solids

We describe the main stages of the development of investigations originated by Prof. Vihak in the fields of the theory and methods of optimal control over the thermal processes and thermal stressed state of deformed solids, theory of inverse problems of heat conduction and thermomechanics, and the mathematical methods in the mechanics of deformable solids. We indicate the existence of close relationship between the obtained theoretical results and the applied problems of thermal power engineering motivating investigations of this kind. We describe a significant contribution made by the researchers of the Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of the Ukrainian National Academy of Sciences to the development of investigations in these fields. The prospects of further development of these studies are analyzed and some facts from the life and creative activity of Prof. V. М. Vihak are presented.

42 ENGINEERING↗
DOE OSTI2022

Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results of our research show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Overview of the Tolerance Limit Calculations with Application to TSURFER

To establish confidence in the results of computerized physics models, a key regulatory requirement is to develop a scientifically defendable process. The methods employed for confidence, characterization, and consolidation, or C3, are statistically involved and are often accessible only to avid statisticians. This manuscript serves as a pedagogical presentation of the C3 process to all stakeholders—including researchers, industrial practitioners, and regulators—to impart an intuitive understanding of the key concepts and mathematical methods entailed by C3. The primary focus is on calculation of tolerance limits, which is the overall goal of the C3 process. Tolerance limits encode the confidence in the calculation results as communicated to the regulator. Understanding the C3 process is especially critical today, as the nuclear industry is considering more innovative ways to assess new technologies, including new reactor and fuel concepts, via an integrated approach that optimally combines modeling and simulation and minimal targeted validation experiments. This manuscript employs intuitive, analytical, numerical, and visual representations to explain how tolerance limits may be calculated for a wide range of configurations, and it also describes how their values may be interpreted. Various verification tests have been developed to test the calculated tolerance limits and to help delineate their values. The manuscript demonstrates the calculation of tolerance limits for TSURFER, a computer code developed by the Oak Ridge National Laboratory for criticality safety applications. The goal is to evaluate the tolerance limit for TSURFER-determined criticality biases to support the determination of upper, subcritical limits for regulatory purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

2025 Workshop on Envisioning Frontiers in AI and Computing for Biological Research: Position Papers

This workshop aims to identify key research directions for transforming biology using artificial intelligence (AI), machine learning (ML) and computational methods to facilitate the discovery of new behaviors, mechanisms, and designs of biological processes relevant to DOE missions, underpinning a broader U.S. bioeconomy. By developing novel AI/ML technologies to analyze and interpret complex biological data, researchers can organize and simulate biological processes at various scales as well as advance predictive understanding and manipulation of biological systems. This integration of computation, experimentation, and next-generation experimental technologies can lead to discoveries in new biological behaviors and mechanisms relevant to DOE missions. The focus is on how advanced computational and mathematical methods can impact this mission by exploring digital twins, foundation models, automated laboratory experiments, modeling of complex living systems, and data-driven approaches for the biodesign of plants and microbial systems. While data management is important, it is not the primary focus of this workshop, which will assess the current state, trends, and AI/ML challenges at the interface between biology and computational science to identify opportunities for high-impact research at their intersection. The goal is to define research needs and opportunities that align with biological sciences, computational sciences, and applied mathematics research.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

A Review of Physical and Numerical Approaches for the Study of Gas Stirring in Ladle Metallurgy

This article presents a review of the research into gas stirring in ladle metallurgy carried out over the past few decades. Herein, the physical modeling experiments are divided into four major areas: (1) mixing and homogenization in the ladle; (2) gas bubble formation, transformation, and interactions in the plume zone; (3) inclusion behavior at the steel–slag interface and in the molten steel; and (4) open eye formation. Several industrial trials have also been carried out to optimize gas stirring and open eye formation. Approaches for selecting criteria for scaling to guarantee flow similarity between industrial trials and physical modeling experiments are discussed. To describe the bubble behavior and two-phase plume structure, four main mathematical models have been used in different research fields: (1) the quasi-single-phase model, (2) the volume of fluid (VOF) model, (3) the Eulerian multiphase (E–E) model, and (4) the Eulerian–Lagrangian (E–L) model. In recent years, the E–E model has been used to predict gas stirring conditions in the ladle, and specific models in commercial packages, as well as research codes, have been developed gradually to describe the complex physical and chemical phenomena. Furthermore, the coupling of turbulence models with multiphase models is also discussed. For physical modeling, some general empirical rules have not been analyzed sufficiently. Based on a comparison with the available experimental results, it is found that the mathematical models focusing on the mass transfer phenomenon and inclusion behaviors at the steel-slag interface, vacuum degassing at the gas–liquid interface, dissolution rate of the solid alloy at the liquid–solid interface, and the combination of fluid dynamics and thermodynamics need to be improved further. To describe industrial conditions using mathematical methods and improve numerical modeling, the results of physical modeling experiments and industrial trials must offer satisfactory validations for the improvement of numerical modeling.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Notes on Regression Analysis for Radar Parameter Estimation

A fundamental task of radar, beyond merely detecting a target, is to estimate some parameters associated with it. For example, this might include range, direction, velocity, etc. In any case, multiple measurements, often noisy, need to be processed to yield a ‘best estimate’ of the parameter. A common mathematical method for doing so is called “Regression” analysis. The goal is to minimize the expected squared error in the estimate. Even when alternate algorithms are considered, the least squared-error regression analysis is the benchmark against which alternatives are compared.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Discussion of “Is reliability a new science?”

I would like to thank the participants of the panel at the 10th International Conference on Mathematical Methods in Reliability (MMR 2017) for their thoughtful and thorough discussion on this topic. In considering the fundamentals of a discipline, it is often possible to gain additional understanding about its strengths, weaknesses, and potential gaps. I confess that my perspective on the topic most closely matches thoughts expressed by William Meeker about the crux of the matter being tied to the choice of definitions. There are a multitude of candidate definitions, and each of the panelists chose to focus on different aspects from different sources. I opted for the Oxford English Dictionary definition of “The intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.” Based on this definition, I would conclude that reliability can qualify as a science because (1) it shares elements of intellectual and practical activity through the development of methodologies to characterize observed patterns, (2) it considers both the structure and behavior of the systems that it seeks to characterize, and (3) it involves notions of obtaining data (observation) and prioritizes the collection of high-quality data with known pedigree through experimentation. More broadly, however, I think that it has elements that expand beyond just a science and contain elements of engineering. To illustrate this, I present some of the thinking that has recently been occurring related to the distinction between statistical science and statistical engineering.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Can machine learning accelerate process understanding and decision‐relevant predictions of river water quality?

Abstract The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Hypergraph Analytics of Domain Name System Relationships

We report on the use of novel mathematical methods in hypergraph analytice over a large quantity of DNS data. Hypergraphs generalize graphs, as used in network science, to better model complex multiway relations in cyber data. Specifically, casting DNS data from Georgia Tech's ActiveDNS repository as hypergraphs allows us to fully represent the interactions between {\em collections} of domains and IP addresses. To facilitate large-scale analytics, we fielded an analytical pipeline of two capabilities. HyperNetX (HNX) is a Python package for the exploration and visualization of hypergraphs, acting as a frontend. For the backend, the Chapel HyperGraph Library (CHGL) is a library for high performance hypergraph analytics written in the exascale programming language Chapel. CHGL was used to process gigascale DNS data, performing compute-intensive calculations for data reduction and segmentation. Identified portions are then sent to HNX for both exploratory analysis and knowledge discovery targeting known tactics, techniques, and procedures.

Joslyn, Cliff A.↗
DOE OSTI2019

Transient dynamics, damping, and mode coupling of nonlinear systems with internal resonances

The study of both linear and nonlinear structural vibrations routinely circles the concise yet complex problem of choosing a set of coordinates which yield simple equations of motion. In both experimental and mathematical methods, that choice is a difficult one because of measurement, computational, and interpretation difficulties. Often times, researchers choose to solve their problems in terms of linear, undamped mode shapes because they are easy to obtain; however, this is known to give rise to complicated phenomena such as mode coupling and internal resonance. This work considers the nature of mode coupling and internal resonance in systems containing non-proportional damping, linear detuning, and cubic nonlinearities through the method of multiple scales as well as instantaneous measures of effective damping. The energy decay observed in the structural modes is well approximated by the slow-flow equations in terms of the modal amplitudes, and it is shown how mode coupling enhances the damping observed in the system. Moreover, in the presence of a 3:1 internal resonance between two modes, the nonlinearities not only enhance the dissipation, but can allow for the exchange and transfer of energy between the resonant modes. However, this exchange depends on the resonant phase between the modes and is proportional to the energy in the lowest mode. The results of the analysis tie together interpretations used by both experimentalists and theoreticians to study such systems and provide a more concrete way to interpret these phenomena.

42 ENGINEERING↗