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DOE OSTI2021

Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1986

Integrated analysis tools for trade studies of spacecraft controller and sensor locations

The present investigation was conducted with the aim to evaluate the practicality and difficulties of modern control design methods for large space structure controls. The evaluation is used as a basis for the identification of useful computer-based analysis tools which would provide insight into control characteristics of a spacecraft concept. A description is presented of the wrap-rib antenna and its packaging concept. Attention is given to active control requirements, a mathematical model of structural dynamics, aspects of sensor and actuator location, the analysis approach, controllability, observability, the concept of balanced realization, transmission zeros, singular value plots, analysis results, model reduction, and an interactive computer program. It is pointed out that the application of selected control analysis tools to the wrap-rib antenna demonstrates several capabilities which can be useful during conceptual design.

Rowell, L. F.↗

DOE OSTI2021

Implicit Multirate GARK Methods

This article considers multirate generalized-structure additively partitioned Runge–Kutta methods for solving stiff systems of ordinary differential equations with multiple time scales. These methods treat different partitions of the system with different timesteps for a more targeted and efficient solution compared to monolithic single rate approaches. With implicit methods used across all partitions, methods must find a balance between stability and the cost of solving nonlinear equations for the stages. In order to characterize this important trade-off, we explore multirate coupling strategies, problems for assessing linear stability, and techniques to efficiently implement Newton iterations for stage equations. Unlike much of the existing multirate stability analysis which is limited in scope to particular methods, we present general statements on stability and describe fundamental limitations for certain types of multirate schemes. New implicit multirate methods up to fourth order are derived, and their accuracy and efficiency properties are verified with numerical tests.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Toward Quantity-of-Interest Preserving Lossy Compression for Scientific Data

Today's scientific simulations and instruments are producing a large amount of data, leading to difficulties in storing, transmitting, and analyzing these data. While error-controlled lossy compressors are effective in significantly reducing data volumes and efficiently developing databases for multiple scientific applications, they mainly support error controls on raw data, which leaves a significant gap between the data and user's downstream analysis. This may cause unqualified uncertainties in the outcomes of the analysis, a.k.a quantities of interest (QoIs), which are the major concerns of users in adopting lossy compression in practice. In this paper, we propose rigorous mathematical theories to preserve four families of QoIs that are widely used in scientific analysis during lossy compression along with practical implementations. Specifically, we first develop the error control theory for univariate QoIs which are essential for computing physical properties such as kinetic energy, followed by multivariate QoIs that are more commonly used in real-world applications. The proposed method is integrated into a state-of-the-art compression framework in a modular fashion, which could easily adapt to new QoIs and new compression algorithms. Experiments on real-world datasets demonstrate that the proposed method provides faithful error control on important QoIs including kinetic energy, regional average, and isosurface without trials and errors, while offering compression ratios that are up to 4x of the compression ratios provided by state-of-the-art compressors.

Jiao, Pu↗

DOE OSTI2021

SAGE Intrusion Detection System: Sensitivity Analysis Guided Explainability for Machine Learning.

This report details the results of a three-fold investigation of sensitivity analysis (SA) for machine learning (ML) explainability (MLE): (1) the mathematical assessment of the fidelity of an explanation with respect to a learned ML model, (2) quantifying the trustworthiness of a prediction, and (3) the impact of MLE on the efficiency of end-users through multiple users studies. We focused on the cybersecurity domain as the data is inherently non-intuitive. As ML is being using in an increasing number of domains, including domains where being wrong can elicit high consequences, MLE has been proposed as a means of generating trust in a learned ML models by end users. However, little analysis has been performed to determine if the explanations accurately represent the target model and they themselves should be trusted beyond subjective inspection. Current state-of-the-art MLE techniques only provide a list of important features based on heuristic measures and/or make certain assumptions about the data and the model which are not representative of the real-world data and models. Further, most are designed without considering the usefulness by an end-user in a broader context. To address these issues, we present a notion of explanation fidelity based on Shapley values from cooperative game theory. We find that all of the investigated MLE explainability methods produce explanations that are incongruent with the ML model that is being explained. This is because they make critical assumptions about feature independence and linear feature interactions for computational reasons. We also find that in deployed, explanations are rarely used due to a variety of reason including that there are several other tools which are trusted more than the explanations and there is little incentive to use the explanations. In the cases when the explanations are used, we found that there is the danger that explanations persuade the end users to wrongly accept false positives and false negatives. However, ML model developers and maintainers find the explanations more useful to help ensure that the ML model does not have obvious biases. In light of these findings, we suggest a number of future directions including developing MLE methods that directly model non-linear model interactions and including design principles that take into account the usefulness of explanations to the end user. We also augment explanations with a set of trustworthiness measures that measure geometric aspects of the data to determine if the model output should be trusted.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Deep Bayesian local crystallography

Abstract The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume of information on materials structures, structural distortions, and physical functionalities. Harnessing this knowledge regarding local physical phenomena necessitates the development of the mathematical frameworks for extraction of relevant information. However, the analysis of atomically resolved images is often based on the adaptation of concepts from macroscopic physics, notably translational and point group symmetries and symmetry lowering phenomena. Here, we explore the bottom-up definition of structural units and symmetry in atomically resolved data using a Bayesian framework. We demonstrate the need for a Bayesian definition of symmetry using a simple toy model and demonstrate how this definition can be extended to the experimental data using deep learning networks in a Bayesian setting, namely rotationally invariant variational autoencoders.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Validation of Power Distribution Models using Load Flow Analysis in an ADMS Environment

Electric utilities are facing the need for better monitoring, analysis, and control of their distribution systems. An accurate mathematical model is a key to both the development of cutting-edge, scalable model-based algorithms and the assessment of emerging technologies such as distributed energy resources (DER) for grid planning and operation. However, the constantly evolving nature of power distribution systems poses challenges to maintaining accurate models. In this paper, we propose a novel load flow based approach to validate power distribution models. Networked equipment models described according to the Common Information Model (CIM) standard and a measurement model are used to formulate the distribution load flow problem. First, a system admittance matrix (Ybus) is derived from device-level CIM parameters. Next, the operational parameters (dynamic Ybus and nodal injections) are extracted from the measurement model using sensor configuration and equipment state. An iterative power flow method is then used to compute nodal voltages and branch flows that are compared against the measurement data to find any inconsistencies in the networked equipment model. This approach is implemented within GridAPPS-D, an open-source standards-based platform for advanced distribution management system (ADMS) application development, and demonstrated on the IEEE 13-bus, 123-bus, and 8500-node test feeders.

Common information model, model validation, power ↗

DOE OSTI2020

Initial Exploration of the Use of Mixed Precision in Iterative Solvers (B639388 Subcontract Quarter I Report)

The first quarter of the project was primarily spent identifying potential projects at the intersection of finite precision analysis, mixed precision computation, and Krylov subspace methods. We summarize our findings in the remainder of the document. Other activities include attending biweekly xSDK meetings as well as contributing material to the technical report and journal versions of the multiprecision landscape paper. The subsequent quarter will be spent selecting a subset of the described projects to focus on, performing initial numerical experiments to evaluate the potential for the use of mixed precision, and developing initial theoretical analysis.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Evaluating Symmetry in 3-dimensional Simulation Data

The increasing use of three-dimensional simulations has led to an increased need for effective verification and validation, or V&V. Unfortunately, the high computational cost associated with three-dimensional simulations makes many standard V&V techniques cost-prohibitive. Given these circumstances, we must pay close attention to V&V metrics that can be evaluated using only a single simulation. One of the simplest of these metrics is the evaluation of physical symmetries. This report details a method of computing the deviation from symmetry in a three-dimensional dataset with an arbitrarily distributed mesh. Examples are presented for spherical and axisymmetric systems using the Paraview post-processing analysis workflow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

From Ensemble Climate to Ensemble Impacts

Many climate-risk tools rely on ensemble mean projections or endpoint climate snapshots to characterize future hazards. Although convenient for communication, these representations remove the statistical, temporal, and physical information that real infrastructure systems respond to. Infrastructure degradation and failure arise from extremes, sequences, cumulative stress, compound hazards, and nonlinear fragility relationships, none of which survive ensemble averaging or temporal compression. Power-system failure statistics and cascading failure models further show that infrastructure risk is dominated by tail events and path-dependent dynamics rather than by mean conditions. This paper demonstrates why ensemble mean or endpoint-only climate representations are mathematically and physically inconsistent with engineering-grade risk analysis. We outline a model-resolved, time-series-based workflow that preserves extremes, variability, and sequencing by propagating each climate-model realization independently through hazard formation, exposure, fragility, and cascading failure mechanisms. Taking the ensemble of impacts—rather than the ensemble of climate—provides a defensible, physically coherent foundation for infrastructure resilience planning, regulatory compliance, and long-term investment decisions.

54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗

DOE OSTI2021

Targeting a cell surface vitamin D receptor on tumor-associated macrophages in triple-negative breast cancer

Triple-negative breast cancer (TNBC) is an aggressive tumor with limited treatment options and poor prognosis. We applied the in vivo phage display technology to isolate peptides homing to the immunosuppressive cellular microenvironment of TNBC as a strategy for non-malignant target discovery. We identified a cyclic peptide (CSSTRESAC) that specifically binds to a vitamin D receptor, protein disulfide-isomerase A3 (PDIA3) expressed on the cell surface of tumor-associated macrophages (TAM), and targets breast cancer in syngeneic TNBC, non-TNBC xenograft, and transgenic mouse models. Systemic administration of CSSTRESAC to TNBC-bearing mice shifted the cytokine profile toward an antitumor immune response and delayed tumor growth. Moreover, CSSTRESAC enabled ligand-directed theranostic delivery to tumors and a mathematical model confirmed our experimental findings. Finally, in silico analysis showed PDIA3-expressing TAM in TNBC patients. This work uncovers a functional interplay between a cell surface vitamin D receptor in TAM and antitumor immune response that could be therapeutically exploited.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1971

Modulation of ring-laser mode coupling.

This paper develops an analytical, algebraic formalism that predicts effects induced in ring lasers by phase modulation, corresponding both to mode-decoupling mechanisms deliberately incorporated in the ring laser and to naturally occurring periodic or random angular or linear accelerations. The analysis is based on an approach that seems potentially convenient in the analysis of other systems that are physically stable but mathematically nonlinear.

Whitney, C.↗

NASA NTRS1972

Wind speeds in lower atmosphere of Venus: Status report on possible measurement via differential VLBI tracking of entry probes

The potential of very-long-baseline interferometry (VLBI) is examined for use in the determination of wind speeds in Venus' lower atmosphere via the differential tracking of entry probes. A simplified mathematical model is presented in detail. An incomplete error analysis based on this model permits an educated guess to be made: an uncertainty in wind speed determination of no more than about 100/t m/sec, where t l is the corresponding time resolution in seconds, is an achievable goal, without the use of transponders on the miniprobes. If transponders are available on all probes, there should be little difficulty in estimating wind speeds with useful precision.

Shapiro, I. I.↗

NASA NTRS1974

Avoiding unrealistic overtest by notching the vibration test specification

The test specifications for spacecraft and components permit test levels to be reduced under a procedure commonly referred to as notching. A summary is provided of the steps required to comply with the notching criterion. Primary structural loads are discussed along with aspect of mathematical modelling of the spacecraft structure, a launch loads analysis, a vibration test loads analysis, and notching methods. It is shown that current, general vibration test specifications are capable of producing unrealistically high spacecraft structural loads.

Hershfeld, D. J.↗

NASA NTRS1978

A probabilistic model of insolation for the Mojave Desert area

A discussion of mathematical models of insolation characteristics suitable for use in analysis of solar energy systems is presented and shows why such models are essential for solar energy system design. A model of solar radiation for the Mojave Desert area is presented with probabilistic and deterministic components which reflect the occurrence and density of clouds and haze, and mimic their effects on both direct and indirect radiation. Multiple comparisons were made between measured total energy received per day and the corresponding simulated totals. The simulated totals were all within 11 percent of the measured total. The conclusion is that a useful probabilistic model of solar radiation for the Goldstone, California, area of the Mojave Desert has been constructed.

Hester, O. V.↗

NASA NTRS1979

A model for testing centerfinding algorithms for automated optical navigation

An efficient software simulation of the imaging process for optical navigation is presented, illustrating results using simple examples. The problems of image definition and optical system modeling, including ideal image containing features and realistic models of optical filtering performed by the entire camera system, are examined. A digital signal processing technique is applied to the problem of developing methods of automated optical navigation and the subsequent mathematical formulation is presented. Specific objectives such as an analysis of the effects of camera defocusing on centerfinding of planar targets, addition of noise filtering to the algorithm, and implementation of multiple frame capability were investigated.

Griffin, M. D.↗

NASA NTRS1982

Flight dynamics analysis and simulation of heavy lift airships. Volume 1: Executive summary

A generic, yet comprehensive mathematical model and computer simulation of the HLA flight dynamics over its entire flight envelope was developed. Implicit in this simulation development are the data reviews and analyses which support the equations of motion and the calculation of forces and moments acting on the vehicle. The simulation, HYBRDS, is addressed to the broad requirements and is intended for use as a synthesis and analysis tool for the evaluation of competing HLA design concepts.

Ringland, R. F.↗

NASA NTRS1983

A travelling wave approach to the dynamic analysis of large space structures

This paper investigates the dynamic analysis of certain large space structures via travelling wave mathematics. It is assumed that large space structures may be modelled as networks of interconnected one-dimensional structural members. Bodies with a finite number of internal dynamic degrees of freedom may be scattered throughout the network. The wave propagation behavior of one-dimensional continuous and periodic structural elements is investigated. A scattering matrix description of junctions and discontinuities is proposed. A time domain method of calculating network transient response using the wave propagation characteristics of the elements is briefly described.

Von Flotow, A. H.↗