SEARCH · Engineering Papers

Results for “Parameter 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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Probabilistic partition of unity networks for high–dimensional regression problems

We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly paralleliazable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. Here, we also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

Semi-analytical prediction of hydraulic resistance and heat transfer for pipe and channel flows of water at supercritical pressure

Within the Generation IV International Forum the Supercritical Water Reactor is investigated. For its core design and safety analysis the efficient prediction of flow and heat transfer parameters such as the wall-shear stress and the heat-transfer coefficient for pipe and channel flows is needed. For circular pipe flows a numerical model based on the one-dimensional conservation equations of mass, momentum end energy in the radial direction is presented, referred to as a 'semi-analytical' method. An accurate, high-order numerical method is employed to evaluate previously derived analytical solutions of the governing equations. Flow turbulence is modeled using the algebraic approach of Prandtl/van-Karman, including a model for the buffer layer. The influence of wall roughness is taken into account by a new modified numerical damping function of the turbulence model. The thermo-hydraulic properties of water are implemented according to the international standard of 1997. This method has the potential to be used within a sub-channel analysis code and as wall-functions for CFD codes to predict the wall shear stress and the wall temperature. The present study presents a validation of the method with comparison of model results with experiments and multi-dimensional computational (CFD) studies in a wide range of flow parameters. The focus is laid on forced convection flows related to reactor design and near-design conditions. It is found, that the method can accurately predict the wall temperature even under deterioration conditions as they occur in the selected experiments (Yamagata el al. 1972 at 24.5 MPa, Ornatski et al. 1971 at 25.5 and Swenson et al. 1963 at 22.75 MPa). Comparison of the friction coefficient under high heat flux conditions including significant viscosity and density reductions near the wall with various correlations for the hydraulic resistance will be presented; the best agreement is achieve with the correlation of Pioro et al. 2004. It is concluded, that the semi-analytical prediction method is accurate and efficient for forced convection flows even at high heat fluxes. The wall-roughness height is identified as an important model parameter. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

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 NTRS1992

Recognition and characterization of hierarchical interstellar structure. II - Structure tree statistics

A new method of image analysis is described, in which images partitioned into 'clouds' are represented by simplified skeleton images, called structure trees, that preserve the spatial relations of the component clouds while disregarding information concerning their sizes and shapes. The method can be used to discriminate between images of projected hierarchical (multiply nested) and random three-dimensional simulated collections of clouds constructed on the basis of observed interstellar properties, and even intermediate systems formed by combining random and hierarchical simulations. For a given structure type, the method can distinguish between different subclasses of models with different parameters and reliably estimate their hierarchical parameters: average number of children per parent, scale reduction factor per level of hierarchy, density contrast, and number of resolved levels. An application to a column density image of the Taurus complex constructed from IRAS data is given. Moderately strong evidence for a hierarchical structural component is found, and parameters of the hierarchy, as well as the average volume filling factor and mass efficiency of fragmentation per level of hierarchy, are estimated. The existence of nested structure contradicts models in which large molecular clouds are supposed to fragment, in a single stage, into roughly stellar-mass cores.

Houlahan, Padraig↗

NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗

DOE OSTI2021

Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

42 ENGINEERING↗

DOE OSTI2025

Experimental Realization of One-Dimensional Helium

Abstract As the spatial dimension is lowered, locally stabilizing interactions are reduced, leading to the emergence of strongly fluctuating phases of matter without classical analogues. Realizing 1D platforms has been elusive, due to their inherent lack of stability, with a few notable exceptions such as spin chains and ultracold low-density gasses. The inability of such systems to exhibit long range order is essential to their universal description in terms of the Tomonaga-Luttinger liquid theory. Here we report on the experimental observation of a one-dimensional quantum liquid of $$^4$$ 4 He using nanoengineering to confine it within a porous material preplated with a noble gas to enhance dimensional reduction. The resulting excitations of the confined $$^4$$ 4 He, confirmed by neutron scattering, are qualitatively different than three- and two-dimensional superfluid helium, and consistent with Quantum Monte Carlo calculations. The results can be analyzed in terms of a mobile impurity in an otherwise linear Luttinger liquid allowing for the extraction of the microscopic parameters describing the emergent quantum liquid.

Sokol, Paul E.↗

NASA NTRS1987

Suboptimal shape control for quasi-static distributed-parameter systems

An on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile is approached. The method makes use of distributed-parameter system theory and allows refocusing using a limited number of control actuators and sensors. The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. The controller gain calculation is computationally simpler than that previously proposed. The Galerkin (finite element) approximation method is used for model reduction. It is proved that both gain and state convergence can be achieved by using the proposed approximation scheme.

Balas, M. J.↗

DOE OSTI2024

Leptogenesis in parity solutions to the strong CP problem and Standard Model parameters

We study the simplest theories with exact spacetime parity that solve the strong CP problem and successfully generate the cosmological baryon asymmetry via decays of right-handed neutrinos. Lower bounds are derived for the masses of the right-handed neutrinos and for the scale of spontaneous parity breaking, v R . For generic thermal leptogenesis, v R ≳ 10 12 GeV, unless the small observed neutrino masses arise from fine-tuning. We compute v R in terms of the top quark mass, the QCD coupling, and the Higgs boson mass and find this bound is consistent with current data at 1σ. Future precision measurements of these parameters may provide support for the theory or, if v R is determined to be below 10 12 GeV, force modifications. However, modified cosmologies do not easily allow reductions in v R — no reduction is possible if leptogenesis occurs in the collisions of domain walls formed at parity breaking, and at most a factor 10 reduction is possible with non-thermal leptogenesis. Standard Model parameters that yield low values for v R can only be accommodated by having a high degree of degeneracy among the right-handed neutrinos involved in leptogenesis. If future precision measurements determine v R to be above 10 12 GeV, it is likely that higher-dimensional operators of the theory will yield a neutron electric dipole moment accessible to ongoing experiments. This is especially true in a simple UV completion of the neutrino sector, involving gauge singlet fermions, where the bound from successful leptogenesis is strengthened to v R ≳ 10 13 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2018

An Active Subspace Method for Accelerating Convergence in Delaunay-Based Optimization via Dimension Reduction

Delaunay-based derivative-free optimization, ∆DOGS, is an efﬁcient and provably-convergent global optimization method for the problems which has computationally expensive objection function and the analytical expression for the objective function is not available. ∆-DOGS is a novel optimization scheme in the family of response surface methods (RSMs); however, it suffers from the curse of dimensionality since the computational cost increases dramatically as the number of design parameters increases. As a result, the number of design parameters in ∆-DOGS algorithm is relatively low (n.10). To avoid such problems, this paper proposes a combination of derivative-free optimization, seeking the global minimizer of an expensive and nonconvex objective function f(x) and active subspace method, detecting the directions of the most variability using evaluations of the gradient. The contribution of other directions to the objective function is bounded by a sufﬁciently small constant. This new algorithm iteratively applied Delaunay-based derivative-free optimization to seek the minimizer on the d-dimensional active subspace that has most function variation. Inverse mapping is needed to project data from active subspace to full-model for evaluating function values. This task is overcome by solving an inequality constrained problem that curves the response surface of the objective function. The test results show that this strategy is effective on a handful of optimization problems.

Bewley, Thomas R.↗

NASA NTRS1973

Application of phase-change technique to thin sections with heating on both surfaces

A numerical digital computer program was developed to calculate the heat-transfer coefficients for both sides of a one-dimensional finite slab subject to the boundary conditions ascribed to the phase-change coating heat-transfer technique. In a typical tunnel test situation where a thin wing was exposed to heating on both sides, the data reduction procedures for a semi-infinite slab gave heat-transfer coefficients as much as 375 percent too high on the side with the lowest heating. The results from the one-dimensional finite-slab procedure are presented in the form of correction factors to the solution for a semi-infinite slab in terms of parameters normally used with the phase-change heat-transfer technique. These correlations are not restricted to slab thickness or thermophysical properties and are easily used to obtain accurate data on thin model sections.

Hunt, J. L.↗

NASA NTRS2014

Neural Network Machine Learning and Dimension Reduction for Data Visualization

Neural network machine learning in computer science is a continuously developing field of study. Although neural network models have been developed which can accurately predict a numeric value or nominal classification, a general purpose method for constructing neural network architecture has yet to be developed. Computer scientists are often forced to rely on a trial-and-error process of developing and improving accurate neural network models. In many cases, models are constructed from a large number of input parameters. Understanding which input parameters have the greatest impact on the prediction of the model is often difficult to surmise, especially when the number of input variables is very high. This challenge is often labeled the "curse of dimensionality" in scientific fields. However, techniques exist for reducing the dimensionality of problems to just two dimensions. Once a problem's dimensions have been mapped to two dimensions, it can be easily plotted and understood by humans. The ability to visualize a multi-dimensional dataset can provide a means of identifying which input variables have the highest effect on determining a nominal or numeric output. Identifying these variables can provide a better means of training neural network models; models can be more easily and quickly trained using only input variables which appear to affect the outcome variable. The purpose of this project is to explore varying means of training neural networks and to utilize dimensional reduction for visualizing and understanding complex datasets.

Liles, Charles A.↗

DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

NASA NTRS1996

Multigrid Approach to Incompressible Viscous Cavity Flows

Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.

Wood, William A.↗

DOE OSTI2021

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2015

Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons

Nonlinear propagation of ion-acoustic waves is investigated in a one-dimensional, unmagnetized plasma consisting of positive ions, negative ions, and nonthermal electrons featuring Tsallis distribution that is penetrated by a negative-ion-beam. The classical Gardner equation is derived to describe nonlinear behavior of ion-acoustic waves in the considered plasma system via reductive perturbation technique. We convert the classical Gardner equation into the time-fractional Gardner equation by Agrawal's method, where the time-fractional term is under the sense of Riesz fractional derivative. Employing variational iteration method, we construct solitary wave solutions of the time-fractional Gardner equation with initial condition which depends on the nonlinear and dispersion coefficients. The effect of the plasma parameters on the compressive and rarefactive ion-acoustic solitary waves is also discussed in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

(3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1991

Thermal postbuckling of thin-walled composite stiffeners

A study is made of the thermal postbuckling response of composite stiffeners subjected to prescribed edge displacement and a temperature rise. The flanges and web of the stiffeners are modeled by using two-dimensional plate finite elements. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. A reduction method is used in conjunction with mixed finite element models for determining the postbuckling response of the stiffeners. Sensitivity derivatives are evaluated and used to study the effects of variations in the different lamination and material parameters of the stiffeners on their postbuckling response characteristics. Numerical studies are presented for anisotropic stiffeners with Zee and channel sections.

Noor, Ahmed K.↗