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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

3-Manifolds and VOA Characters

Abstract By studying the properties ofq-series$$\widehat{Z}$$ Z ^ -invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for$$\widehat{Z}$$ Z ^ -invariants leads to many infinite families of new fermionic formulae for VOA characters.

Physics↗
DOE OSTI2020

MimicGAN: Robust Projection onto Image Manifolds with Corruption Mimicking

In the past few years, Generative Adversarial Networks (GANs) have dramatically advanced our ability to represent and parameterize high-dimensional, non-linear image manifolds. As a result, they have been widely adopted across a variety of applications, ranging from challenging inverse problems like image completion, to problems such as anomaly detection and adversarial defense. A recurring theme in many of these applications is the notion of projecting an image observation onto the manifold that is inferred by the generator. In this context, Projected Gradient Descent (PGD) has been the most popular approach, which essentially optimizes for a latent vector that minimizes the discrepancy between a generated image and the given observation. However, PGD is a brittle optimization technique that fails to identify the right projection (or latent vector) when the observation is corrupted, or perturbed even by a small amount. Such corruptions are common in the real world, for example images in the wild come with unknown crops, rotations, missing pixels, or other kinds of non-linear distributional shifts which break current encoding methods, rendering downstream applications unusable. To address this, we propose corruption mimicking—a new robust projection technique, that utilizes a surrogate network to approximate the unknown corruption directly at test time, without the need for additional supervision or data augmentation. The proposed method is significantly more robust than PGD and other competing methods under a wide variety of corruptions, thereby enabling a more effective use of GANs in real-world applications. Finally, more importantly, we show that our approach produces state-of-the-art performance in several GAN-based applications—anomaly detection, domain adaptation, and adversarial defense, that benefit from an accurate projection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
DOE OSTI2025

Generalized fiducial inference on differentiable manifolds

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. Here, this new approach uses generalized fiducial inference (GFI) to obtain a posterior-like distribution on the manifold, without needing to know local parameterizations that map to the constrained space from an unconstrained Euclidean space. Using mathematical tools from Riemannian geometry, we construct a constrained generalized fiducial distribution (CGFD). A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To illustrate the practical use of the CGFD, we provide a proof-of-concept example in the context of a linear logspline density estimation problem, and demonstrate that CGFD-based confidence sets exhibit desirable coverage properties via simulation. As an application, we fit a CGFD to COVID-19 case count data from North Carolina, USA.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold

Abstract Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Manifold projection image segmentation for nano-XANES imaging

As spectral imaging techniques are becoming more prominent in science, advanced image segmentation algorithms are required to identify appropriate domains in these images. We present a version of image segmentation called manifold projection image segmentation (MPIS) that is generally applicable to a broad range of systems without the need for training because MPIS uses unsupervised machine learning with a few physically motivated hyperparameters. We apply MPIS to nanoscale x-ray absorption near edge structure (XANES) imaging, where XANES spectra are collected with nanometer spatial resolution. We show the superiority of manifold projection over linear transformations, such as the commonly used principal component analysis (PCA). Moreover, MPIS maintains accuracy while reducing computation time and sensitivity to noise compared to the standard nano-XANES imaging analysis procedure. Finally, we demonstrate how multimodal information, such as x-ray fluorescence data and spatial location of pixels, can be incorporated into the MPIS framework. We propose that MPIS is adaptable for any spectral imaging technique, including scanning transmission x-ray microscopy, where the length scale of domains is larger than the resolution of the experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Design for Remanufacturing Framework Incorporating Identification, Evaluation, and Validation: A Case Study of Hydraulic Manifold

In recent years, academic researchers and engineers in the industry have widely recognized the necessity of integrating remanufacturing considerations into product design iterations to advance sustainability objectives. Acknowledging the importance of design for remanufacturing (DfRem), efforts were made to develop tools and guidelines that could be implemented in practice. However, such methods largely rely upon experiential insights and qualitative assessments, leaving a gap in the ability to quantitatively assess the economic and environmental impacts of design choices. To bridge this gap, we investigate existing efforts and present a framework for DfRem that integrates established design and remanufacturing practices into a cohesive workflow with quantitative assessments. To demonstrate its efficacy for making practical design changes for remanufacturing, we apply the framework to a hydraulic manifold in a transmission system for heavy-duty tractors. Through this industry-relevant case study, we focus on showcasing the practical utility of our framework. Based on the identified design modifications from remanufacturability analysis, we estimate the reductions in life cycle costs, energy consumption, and emissions. Afterward, the modifications are tested using physical experiments with plans for integration into future iterations of the hydraulic manifold design and production. Here, we anticipate this framework can illustrate the process of remanufacturing that ensures improvements in sustainability while maintaining performance and reliability standards.

design for X↗
DOE OSTI2024

Domain-decomposition nonlinear manifold reduced order model

This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of ROM training for extreme-scale problems. To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains, computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters needed, decreases the dimensional requirements of subdomain FOM training data, and allows for customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR), simplifying the nonlinear complexities and enhancing computational speed. This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and employs a sequential quadratic programming (SQP) solver for the evaluation of the coupled global NMROM. The effectiveness of the DD NM-ROM with HR is numerically demonstrated on the 2D steady-state Burgers' equation, showing an order of magnitude improvement in accuracy over the DD LS-ROM with HR.

Diaz, AlejandroN↗
DOE OSTI2022

Quantum Manifold Learning

SAND2022-12600 O Quantum Manifold Learning is a Python code to perform manifold learning from point clouds. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Sarovar, Mohan↗
DOE OSTI2020

General Bayesian Inference over the Stiefel Manifold via the Givens Transform

We introduce here an approach based on the Givens representation for posterior inference in statistical models with orthogonal matrix parameters, such as factor models and probabilistic principal component analysis (PPCA). We show how the Givens representation can be used to develop practical methods for transforming densities over the Stiefel manifold into densities over subsets of Euclidean space. We demonstrate how to deal with issues arising from the topology of the Stiefel manifold and how to inexpensively compute the change-of-measure terms. We introduce an auxiliary parameter approach that limits the impact of topological issues. We provide both analysis of our methods and numerical examples demonstrating the effectiveness of the approach. We also discuss how our Givens representation can be used to define general classes of distributions over the space of orthogonal matrices. We then give demonstrations on several examples showing how the Givens approach performs in practice in comparison with other methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Data-Driven Exploration of Climate Attractor Manifolds For Long-Term Predictability

Focal Area: This white paper responds to Focal Area 3. We seek to gain insight into decadal-scale climate predictability by applying novel manifold-finding probabilistic AI techniques to the complex data produced by Earth System models (ESMs) such as E3SM. The associated portfolio of research activities leverages DOE’s asset mix of HPC platforms, climate expertise, climate simulation codes, and AI expertise. Science Challenge: Climate and climate models are dynamical systems exhibiting properties that are interpretable through chaos theory. The theory contains an important concept that is relevant to multi-decade-scale climate prediction: a chaotic attractor. While the space containing all the possible states of the Earth’s atmosphere and ocean, the possible weather, is large, the realized states tend to stay near the smaller-dimensioned attractor. This behavior is responsible for the “order behind the irregularity” [1] of climate phenomena. Climate change can be thought of as a change in the properties of the attractor, and predicting the climate over years to decades is equivalent to predicting how those properties will change. To date, the attractor has been a useful conceptual tool, but has not been amenable to direct characterization. A new development is the advent of efficient high-dimensional manifold-finding probabilistic AI techniques, which permit a data-driven characterization of the ESM attractor and its probability distribution over weather states. Such a characterization would result in a natural dimensional reduction — a “non-linear Principal Components Analysis (PCA) adapted to climate simulation data” — leading to important advances in scenario-based long-term climate prediction, long-term prediction of water cycle extremes, ESM verification, inter-model comparison, and process model development.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Trajectory Optimization via Unsupervised Probabilistic Learning On Manifolds

This report investigates the use of unsupervised probabilistic learning techniques for the analysis of hypersonic trajectories. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. Using the diffusion coordinates on the graph of training samples, the probabilistic framework augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path-planing algorithm. In this framework the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time. A 3DOF model was employed to generate optimal hypersonic trajectories that comprise the training datasets. The diffusion map algorithm identfied that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. In addition to the path-planing worflow we also propose an algorithm that utilizes the diffusion map coordinates along the manifold to label and possibly remove outlier samples from the training data. This algorithm can be used to both identify edge cases for further analysis as well as to remove them from the training set to create a more robust set of samples to be used for the path-planing process.

42 ENGINEERING↗
DOE OSTI2023

Multiscale Modeling of Corrosion and Oxidation Performance and Their Impact on High-temperature Fatigue of Automotive Exhaust Manifold Components

The persistent need to reducing automobile emissions has led to the wide adoption of turbocharger technology and engine downsizing, which results in a substantial raise in exhaust temperature, reaching as high as 950°C. Therefore, the material selection for exhaust manifolds and turbocharger housings becomes significantly challenging. The successful development of the multiscale models on oxidation and corrosion performance, and their impact on high-temperature fatigue will enable the acceleration of new, high-performance, heat-resistant alloy solutions and the reduction of time and cost in achieving a durable design. In this project, we developed and validated multiscale models that can accurately predict the corrosion and oxidation performance and their impact on high-temperature fatigue of high-temperature automotive exhaust manifold components. The capability of accurately predicting the corrosion/oxidation-fatigue damage can significantly reduce the time and cost of achieving a durable design. The models were used to guide the development of new high thermomechanical fatigue (TMF) performance alloys.

Li, Mei↗
NASA NTRS1982

Collimated beam manifold with the number of output beams variable at a given output angle

An optical manifold is described which transforms a collimated beam, such as a laser beam, into a plurality of parallel beams having uniform intensity or having a desired intensity ratio. The manifold comprises an optical substrate coated on its rear surface with a fully reflective layer and on its front surface with a partially reflecting layer having a reflectivity gradient. An input collimated beam entering the rear surface and impinging on the front surface is reflected, multiply between the front and rear surfaces producing a plurality of parallel beams that emerge from the front surface. The intensities of the emerging beams have a relationship that depends on the reflectivity of the front surface at the points where the beams emerge. By properly selecting the reflectivity gradient, the emerging beams have uniform intensity or a desired intensity ratio.

Campbell, C. W.↗
NASA NTRS1984

Detection of the J-10 Manifold of the Pure Rotational Band of Phosphine on Saturn

The detection of the J = 10 manifold of the pure rotational band of PH3 on Saturn is reported. The observations were made from the far-infrared cooled grating spectrometer. The wavelengths and observed brightness temperatures for the full disk plus rings are 89 + or - 3 K at 97.04 micrometer, 77 + or - 3 K at 102.72 micrometer, 77 + or - 3 K at 102.94 micrometer, and 83 + or - 3 K at 105.12 micrometers. The points of 97.04 and 105.12 micrometers establish the continuum level and the two points near 103 micrometers measure the depth of the PH3 manifold. After the flux due to the rings is subtracted, the depth of the feature is 16 + or - 6 K relative to the nearby 102 K continuum. These results are compared to theoretical models which parameterize the PH3 mixing ratio as x = x sub zero (P/P sub zero)(alpha) for P P sub zero and as x = x sub zero for P or = P, where P is the total pressure and alpha = H/h is the ratio of the dynamical scale height (H) and the scale height for decreasing the PH3 mixing ratio (h). The parameters x sub zero, P sub zero, and h were varied, as well as the H/He mixing ratio and the pressure-temperature profile. The data are well fitted using pressure-temperature profiles. The preferred values of h, P sub zero, and x sub zero imply that there is little or no PH3 above the thermal inversion and that the mixing ratio below the inversion is consistent with PH3 being 1 to 4 times overabundant relative to the solar P/H ratio.

Haas, M. R.↗
NASA NTRS1985

Experimental evaluation of an advanced Space Shuttle main engine hot-gas manifold design concept

This study, using an extensively modified, full-scale space shuttle main engine (SSME) hot-gas manifold (HGM), established a detailed aerodynamic data base to support development of an advanced, three-dimensional, fluid-dynamic analysis computer model. In addition, the advanced SSME hot-gas manifold design used in this study demonstrated improved flow environment (uniformity) in the fuel side turbine exit and transfer duct exit regions. Major modifications were incorporated in the full-scale HGM flow test article model using two large transfer ducts on the fuel turbine side of the HGM in place of the three small transfer ducts in the present design. Other model features included an increases in the flow areas downstream of the 180-degree turn and in the fishbowl regions.

Pelaccio, D. G.↗
NASA NTRS1986

Manifold Coal-Slurry Transport System

Feeding several slurry pipes into main pipeline reduces congestion in coal mines. System based on manifold concept: feeder pipelines from each working entry joined to main pipeline that carries coal slurry out of panel and onto surface. Manifold concept makes coal-slurry haulage much simpler than existing slurry systems.

Liddle, S. G.↗
NASA NTRS1986

Computational fluid dynamics as a design tool for the hot gas manifold of the Space Shuttle Main Engine

The paper discusses the application of computational fluid dynamics as a design tool for the Hot Gas Manifold of the Space Shuttle Main Engine. An improved Hot Gas Manifold configuration was arrived at computationally. This configuration was then built and air flow tested. Testing verified this configuration to be a substantial improvement over existing flight designs.

Ziebarth, J. P.↗