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Results for “nonlinear dimensionality reduction”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

Davis, J. E.↗
NASA NTRS1992

Visual information processing; Proceedings of the Meeting, Orlando, FL, Apr. 20-22, 1992

Topics discussed in these proceedings include nonlinear processing and communications; feature extraction and recognition; image gathering, interpolation, and restoration; image coding; and wavelet transform. Papers are presented on noise reduction for signals from nonlinear systems; driving nonlinear systems with chaotic signals; edge detection and image segmentation of space scenes using fractal analyses; a vision system for telerobotic operation; a fidelity analysis of image gathering, interpolation, and restoration; restoration of images degraded by motion; and information, entropy, and fidelity in visual communication. Attention is also given to image coding methods and their assessment, hybrid JPEG/recursive block coding of images, modified wavelets that accommodate causality, modified wavelet transform for unbiased frequency representation, and continuous wavelet transform of one-dimensional signals by Fourier filtering.

Huck, Friedrich O.↗
DOE OSTI2024

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Evaluation of a three-dimensional empirically derived wing at supersonic speeds

A novel wing design concept is introduced which takes advantage of the existence of conical flow at supersonic speeds. The present wing design concept is to create a near conical wing geometry by redistributing airfoils in a spanwise direction. In addition, a set of graphs which review the supersonic aerodynamics of delta wings have been employed to select a design wing sweep and Mach number. An iteration through the wing design logic resulted in the selection of a 65 deg swept delta wing and a design Mach number of 1.62. Theoretical analysis was performed with a nonlinear full-potential analysis method to assess the merits of the wing design approach. The analysis showed large reductions in drag due to lift compared to delta wings configured with traditional thickness and airfoil distributions.

Wood, Richard M.↗
DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗
NASA NTRS1985

Atmospheric chlorine and stratospheric ozone nonlinearities and trend detection

It is pointed out that at the present time there is no experimental means to detect the current reduction of stratospheric ozone by chlorine from fluorocarbons relative to its unperturbed amount. The reason for this situation is related to the small changes involved and several possible masking effects. As a substitute for experimental detection, there have been many stratospheric modeling efforts. The history of these efforts has been reviewed by Cicerone et al. (1983). Results obtained by Cicerone et al. imply that the successful detection of net ozone destruction by chlorine would be delayed many years from the present time. The present paper is concerned with a reinvestigation of the photochemical problem discussed by Cicerone et al. on the basis of an independent one-dimensional model reported by Herman (1979). It is concluded that by the year 2020 the total ozone decrease due to ClX should be about 3 percent (2.5 percent with increasing methane). Such a change may already pose environmental problems.

Herman, J. R.↗
DOE OSTI2025

Seismic response of vertical dry storage casks under three-dimensional earthquake motions

Ensuring the long-term seismic safety of dry storage casks (DSCs) is becoming increasingly critical as these systems evolve from temporary to de facto permanent repositories for spent nuclear fuels. Traditional seismic soil–structure interaction (SSI) assessment methods use one-dimensional deconvolution or simplified boundary conditions to model incident waves. Although computationally appealing, simplifying assumptions may alter the seismic risk by neglecting the full complexity of three-dimensional (3D) wave propagation effects. To address this challenge, this paper introduces a novel high-fidelity computational framework that leverages the Domain Reduction Method (DRM) with perfectly matched layers (PML) to accurately transfer complex, 3D seismic wavefields from regional-scale fault-rupture simulations into local-scale finite element models of DSCs. Using broadband, physics-based ground motions from a generic M w 7.0 strike-slip event, both single-cask and multi-cask configurations were investigated under near- and far-field conditions. Emphasis is placed on capturing complex SSI, spatial variability in the ground motion, and nonlinear phenomena such as cask rocking and sliding. Numerical results demonstrate that near-field conditions, where forward directivity and fling-step effects dominate, lead to significantly higher DSC rocking and sliding. Far-field cases, by contrast, generally exhibit modest responses. Incorporating SSI tends to amplify or alter DSC response spectra and introduce response variability, which underscores the need for site-specific evaluations and robust modeling approaches to ensure the seismic integrity of DSCs in interim spent fuel storage installations.

Das, Tonmoy↗
NASA NTRS1988

Control of the boundary layer separation about an airfoil by active surface heating

Application of active control to separated flow on the RC(6)-08 airfoil at high angle of attack by localized surface heating is numerically simulated by integrating the compressible two-dimensional nonlinear Navier-Stokes equations solver. Active control is simulated by local modification of the temperature boundary condition over a narrow strip on the upper surface of the airfoil. Both mean and perturbed profiles are favorably altered when excited with the same natural frequency of the shear layer by moderate surface heating for both laminar and turbulent separation. The shear layer is found to be very sensitive to localized surface heating in the vicinity of the separation point. The excitation field at the surface sufficiently altered both the local as well as the global circulation to cause a significant increase in lift and reduction in drag.

Maestrello, Lucio↗
NASA NTRS1995

Aeroelasticity and structural optimization of composite helicopter rotor blades with swept tips

This report describes the development of an aeroelastic analysis capability for composite helicopter rotor blades with straight and swept tips, and its application to the simulation of helicopter vibration reduction through structural optimization. A new aeroelastic model is developed in this study which is suitable for composite rotor blades with swept tips in hover and in forward flight. The hingeless blade is modeled by beam type finite elements. A single finite element is used to model the swept tip. Arbitrary cross-sectional shape, generally anisotropic material behavior, transverse shears and out-of-plane warping are included in the blade model. The nonlinear equations of motion, derived using Hamilton's principle, are based on a moderate deflection theory. Composite blade cross-sectbnal properties are calculated by a separate linear, two-dimensional cross section analysis. The aerodynamic loads are obtained from quasi-steady, incompressible aerodynamics, based on an implicit formulation. The trim and steady state blade aeroelastic response are solved in a fully coupled manner. In forward flight, where the blade equations of motion are periodic, the coupled trim-aeroelastic response solution is obtained from the harmonic balance method. Subsequently, the periodic system is linearized about the steady state response, and its stability is determined from Floquet theory.

Yuan, K. A.↗
NASA NTRS2004

Two-Photon Fluorescence Microscopy Developed for Microgravity Fluid Physics

Recent research efforts within the Microgravity Fluid Physics Branch of the NASA Glenn Research Center have necessitated the development of a microscope capable of high-resolution, three-dimensional imaging of intracellular structure and tissue morphology. Standard optical microscopy works well for thin samples, but it does not allow the imaging of thick samples because of severe degradation caused by out-of-focus object structure. Confocal microscopy, which is a laser-based scanning microscopy, provides improved three-dimensional imaging and true optical sectioning by excluding the out-of-focus light. However, in confocal microscopy, out-of-focus object structure is still illuminated by the incoming beam, which can lead to substantial photo-bleaching. In addition, confocal microscopy is plagued by limited penetration depth, signal loss due to the presence of a confocal pinhole, and the possibility of live-cell damage. Two-photon microscopy is a novel form of laser-based scanning microscopy that allows three-dimensional imaging without many of the problems inherent in confocal microscopy. Unlike one-photon microscopy, it utilizes the nonlinear absorption of two near-infrared photons. However, the efficiency of two-photon absorption is much lower than that of one-photon absorption because of the nonlinear (i.e., quadratic) electric field dependence, so an ultrafast pulsed laser source must typically be employed. On the other hand, this stringent energy density requirement effectively localizes fluorophore excitation to the focal volume. Consequently, two-photon microscopy provides optical sectioning and confocal performance without the need for a signal-limiting pinhole. In addition, there is a reduction in photo-damage because of the longer excitation wavelength, a reduction in background fluorescence, and a 4 increase in penetration depth over confocal methods because of the reduction in Rayleigh scattering.

Fischer, David G.↗
DOE OSTI2024

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Analysis of aircraft tires via semianalytic finite elements

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell.

Noor, Ahmed K.↗
DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗
NASA NTRS1996

Nonlinear Analysis and Modeling of Tires

The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.

Noor, Ahmed K.↗
NASA NTRS1990

Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.

Kim, Kyun O.↗
NASA NTRS2005

Two-Photon Fluorescence Microscope for Microgravity Research

A two-photon fluorescence microscope has been developed for the study of biophysical phenomena. Two-photon microscopy is a novel form of laser-based scanning microscopy that enables three-dimensional imaging without many of the problems inherent in confocal microscopy. Unlike one-photon optical microscopy, two-photon microscopy utilizes the simultaneous nonlinear absorption of two near-infrared photons. However, the efficiency of two-photon absorption is much lower than that of one-photon absorption, so an ultra-fast pulsed laser source is typically employed. On the other hand, the critical energy threshold for two-photon absorption leads to fluorophore excitation that is intrinsically localized to the focal volume. Consequently, two-photon microscopy enables optical sectioning and confocal performance without the need for a signal-limiting pinhole. In addition, there is a reduction (relative to one-photon optical microscopy) in photon-induced damage because of the longer excitation wavelength. This reduction is especially advantageous for in vivo studies. Relative to confocal microscopy, there is also a reduction in background fluorescence, and, because of a reduction in Rayleigh scattering, there is a 4 increase of penetration depth. The prohibitive cost of a commercial two-photon fluorescence-microscope system, as well as a need for modularity, has led to the construction of a custom-built system (see Figure 1). This system includes a coherent mode-locked titanium: sapphire laser emitting 120-fs-duration pulses at a repetition rate of 80 MHz. The pulsed laser has an average output power of 800 mW and a wavelength tuning range of 700 to 980 nm, enabling the excitation of a variety of targeted fluorophores. The output from the laser is attenuated, spatially filtered, and then directed into a confocal scanning head that has been modified to provide for side entry of the laser beam. The laser output coupler has been replaced with a dichroic filter that reflects the longer-wavelength excitation light and passes the shorter-wavelength fluorescence light. Also, the confocal pinhole has been removed to increase the signal strength. The laser beam is scanned by a twoperpendicular- axis pair of galvanometer mirrors through a pupil transfer lens into the side port of an inverted microscope. Finally, the beam is focused by a 63-magnification, 1.3-numerical- aperture oil-immersion objective lens onto a specimen. The pupil transfer lens serves to match the intermediate image planes of the scanning head and the microscope, and its location is critical. In order to maximize the quality of the image, (that is, the point spread function of the objective lens for all scan positions), the entire system was modeled in optical-design software, and the various free design parameters (the parameters of the spatial-filter components as well as the separations of all of the system components) were determined through an iterative optimization process. A modular design was chosen to facilitate access to the optical train for future fluorescence correlation spectroscopy and fluorescence-lifetime experiments.

Fischer, David G.↗
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

The role of damage-softened material behavior in the fracture of composites and adhesives

Failure mechanisms of materials under very high strains experienced at and ahead of the crack tip such as formation, growth, and interaction of microvoids in ductile materials, microcracks in brittle solids or crazes in polymers and adhesives are represented by one-dimensional, nonlinear stress-strain relations possessing different ways by which the material loses capacity to carry load up to fracture or total separation. A double cantilever beam (DCB) type specimen is considered. The nonlinear material is confined to a thin strip between the two elastic beams loaded by a wedge. The problem is first modeled as a beam on a nonlinear foundation. The pertinent equation is solved numerically as a two-point boundary value problem for both the stationary and the quasi-stationay propagating crack. A finite element model is then used to model the problem in more detail in order to assess the adequacy of the beam model for the reduction of experimental data to determine in-situ properties of the thin interlayer.

Ungsuwarungsri, T.↗