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Results for “Nonlinear projection”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Reduced order models for thermal radiative transfer problems based on moment equations and data-driven approximations of the Eddington tensor

Here a new group of structure and asymptotic preserving reduced-order models (ROMs) for multidimensional nonlinear thermal radiative transfer (TRT) problems is presented. They are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation (BTE) to derive a hierarchy of low-order moment equations. Approximation of the Eddington tensor that provides exact closure for the system of moment equations is found with projection-based data-driven methodologies. These include the (i) proper orthogonal decomposition (POD), (ii) dynamic mode decomposition (DMD) and (iii) a variant of the DMD. A parameterization is derived for this ROM for the temperature of radiation incoming to the problem domain (the radiation drive temperature). This parameterization is informed from results of a dimensionless study of the TRT problem. Analysis of the ROMs is performed on the classical Fleck-Cummings TRT multigroup test problem in 2D geometry with a radiation-driven Marshak wave. Numerical results are presented to demonstrate the performance of these ROMs for the simulation of evolving radiation and heat waves. Results show these models to be sufficiently accurate for practical computations with rather low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of solutions generated by the ROMs gradually decreases.

42 ENGINEERING↗
DOE OSTI2022

IC Report for project “Developing nonlinear laser-plasma instability models for high-fidelity, multi-physics simulation capability for ICF/HED” [Slides]

We’ve achieved our technical goals: (1) Perform large-scale kinetic simulations of SRS and CBET a range of plasma and laser conditions; (2) Develop a new $\delta f$-Gaussian-mixture algorithm to represent non-Maxwellian distribution functions from particle trapping and time-dependent plasma response; (3) Develop physics-based preliminary nonlinear LPI models for coupling to LRT/ Mazinisin and AMP; and (4) Begin implementation of LPI sub-grid models into Mazinisin.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

Nonlinear optimization with linear constraints using a projection method

Nonlinear optimization problems that are encountered in science and industry are examined. A method of projecting the gradient vector onto a set of linear contraints is developed, and a program that uses this method is presented. The algorithm that generates this projection matrix is based on the Gram-Schmidt method and overcomes some of the objections to the Rosen projection method.

Fox, T.↗
DOE OSTI2024

Fiber optic computing using distributed feedback

Abstract The widespread adoption of machine learning and other matrix intensive computing algorithms has renewed interest in analog optical computing, which has the potential to perform large-scale matrix multiplications with superior energy scaling and lower latency than digital electronics. However, most optical techniques rely on spatial multiplexing, requiring a large number of modulators and detectors, and are typically restricted to performing a single kernel convolution operation per layer. Here, we introduce a fiber-optic computing architecture based on temporal multiplexing and distributed feedback that performs multiple convolutions on the input data in a single layer. Using Rayleigh backscattering in standard single mode fiber, we show that this technique can efficiently apply a series of random nonlinear projections to the input data, facilitating a variety of computing tasks. The approach enables efficient energy scaling with orders of magnitude lower power consumption than GPUs, while maintaining low latency and high data-throughput.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Collaborative Research: Polymer Macrocycles: A novel topology to control dynamics of rubbery materials

Understanding the dynamics of polymers of different topologies is an important field of study and one of the most important unanswered questions in this field is "how do circular polymers move," particularly in the melt state. New information suggests that molecular topology, specifically circular rings, impacts the response of materials in nanometer- scale confinement. The work performed here tackles these subjects through a collaboration in which specialists in polymer synthesis, polymer rheology and scattering methods, and in the physics of nanoconfinement work together to investigate the thermophysical behavior of circular macromolecules. The project goals are to use a novel synthesis method of "green" oxidative polymerization to produce high purity macrocycles and to investigate their linear viscoelastic behavior in order to fully characterize the dynamics of circular macromolecules to sizes that correspond to linear molecule entanglement densities higher than previously obtainable with synthetic polymers. Chemical chain end characterization and critical edge fractionation coupled with direct visualization of the prepared polymers through the use of polymer amplification methods are proposed in order to quantify the numbers of circular and linear molecules in each sample. The study of the linear viscoelastic response of blends of linear and circular molecules is also to be undertaken in the project. Nonlinear viscoelastic measurements, including extensional viscosity, are to be made. Strong differences in behavior between linear chains and circular ones also provides an important opportunity for new technology to break the "magic triangle" for tires: it is believed that improving one of the three key attributes - traction, wear, rolling resistance - necessarily sacrifices at least one of the others. Rubber made from cyclic polymers has the potential to break out of this triangle by reducing the so-called Payne effect in reinforced rubbers because circular macromolecules are less sensitive to nanoconfinement than their linear counterparts. The work has as one objective to characterize the impact of nanoconfinement on the behavior of large circular macromolecules. In addition, the dynamics of carbon black filled circular macromolecules are to be studied to test the hypothesis that the resulting rubbery materials will exhibit a reduced Payne effect.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1997

Ultrasonic Nondestructive Characterization of Adhesive Bonds

Qualitative measurements of adhesion or binding forces can be accomplished, for example, by using the reflection coefficient of an ultrasound or by using thermal waves (Light and Kwun, 1989, Achenbach and Parikh, 1991, and Bostrom and wickham, 1991). However, a quantitative determination of binding forces is rather difficult. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasound passes through a nonlinear material. It seems that such non-linearity can be effectively used to characterize the bond strength. Several theories have been developed to model this nonlinear effect (Adler and Nagy, 1991; Achenbach and Parikh, 1991; Parikh and Achenbach, 1992; and Hirose and Kitahara, 1992; Anastasi and Roberts, 1992). Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented by Pangraz and Arnold (1994). Recently, Tang, Cheng and Achenbach (1997) made a comparison between the experimental and simulated results based on this theoretical model. A water immersion mode-converted shear wave through-transmission setup was used by Berndt and Green (1997) to analyze the nonlinear acoustic behavior of the adhesive bond. In this project, the nonlinear responses of an adhesive joint was investigated through transmission tests of ultrasonic wave and analyzed by the finite element simulations. The higher order harmonics were obtained in the tests. It is found that the amplitude of higher harmonics increases as the aging increases, especially the 3dorder harmonics. Results from the numerical simulation show that the material nonlinearity does indeed generate higher order harmonics. In particular, the elastic-perfect plastic behavior generates significant 3rd and 5th order harmonics.

Qu, Jianmin↗
NASA NTRS1978

Curvilinear projection developments

Gradient projection is a powerful algorithm for minimization of a function subject to constraints. Constraint nonlinearities hamper projection computations. The constraints must then be restored before another projection cycle. The restoration steps taken in the process of following nonlinear constraint surfaces can be used as a guide to the construction of a curve which more nearly follows the constraints than does the straight line in the projected gradient direction. This scheme, termed 'curvilinear projection', was explored in earlier research. The study presently reported carries out some computational experiments using a related version of the technique. Some other details of projection computations which turn out to be practically important are taken up: rules for updating the variable metric in projection when early termination of the one-dimensional search on constraint violation occurs, and active-constraint logic for screening inequalities that makes use of the Kuhn-Tucker necessary conditions.

Kelley, H. J.↗
NASA NTRS2012

Nonlinear Aerodynamic Modeling From Flight Data Using Advanced Piloted Maneuvers and Fuzzy Logic

Results of the Aeronautics Research Mission Directorate Seedling Project Phase I research project entitled "Nonlinear Aerodynamics Modeling using Fuzzy Logic" are presented. Efficient and rapid flight test capabilities were developed for estimating highly nonlinear models of airplane aerodynamics over a large flight envelope. Results showed that the flight maneuvers developed, used in conjunction with the fuzzy-logic system identification algorithms, produced very good model fits of the data, with no model structure inputs required, for flight conditions ranging from cruise to departure and spin conditions.

Brandon, Jay M.↗
DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗
DOE OSTI2023

Energy conserving quadrature based dimensionality reduction for nonlinear hydrodynamics problems

Projection based dimensionality reduction is used to approximate the full discretiza tion of a PDE problem in order to reduce the cost of its numerical simulation while staying faithful to the full dynamics. For nonlinear problems, hyperreduction methods are additionally needed to remove the dependence of the nonlinear terms on the full problem’s size. In this project, we develop an energy conserving hyperreduction method and apply it to Eulerian-Lagrangian hydrodynamics problems, demonstrating that the reduced model successfully accelerates the numerical simulations while conserving the problem’s total energy with high accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗
DOE OSTI2021

Investigating Thaw and Plant Productivity Constraints on Old Soil Carbon Respiration From Permafrost

Isotopic radiocarbon (Δ 14 C) signatures of ecosystem respiration (Reco) can identify old soil carbon (C) loss and serve as an early indicator of permafrost destabilization in a warming climate. Warming also stimulates plant productivity causing plant respiration to dominate Reco Δ 14 C signatures and potentially obscuring old soil C loss. Here, we investigate how a wide spatio-temporal gradient of permafrost thaw and plant productivity affects Reco Δ 14 C patterns and isotopic partitioning. Spatial gradients came from a warming experiment with doubling thaw depth and variable biomass, and a vegetation removal manipulation to eliminate plant contributions. We sampled in August and September to capture transitions from high to low plant productivity, decreased surface soil temperature, and relatively small seasonal thaw extensions. We found that surface processes dominate spatial variation in old soil C loss and a process-based partitioning approach was crucial for constraining old soil C loss. Resampling the same plots in different times of the year revealed that old soil C losses tripled with cooling surface temperature, and the largest old soil C losses were detected when the organic-to-mineral soil horizons thawed (~50–60 cm). We suggest that the measured increase in old soil respiration over the season and when the organic-to-mineral horizon thawed, may be explained by mobilization of nitrogen that stimulates microbial decomposition at depth. Our results suggest that soil C in the organic to mineral horizon may be an important source of soil C loss as the entire Arctic region warms and could lead to nonlinearities in projected permafrost climate feedbacks.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Global field observations of tree die-off reveal hotter-drought fingerprint for Earth’s forests

Earth’s forests face grave challenges in the Anthropocene, including hotter droughts increasingly associated with widespread forest die-off events. But despite the vital importance of forests to global ecosystem services, their fates in a warming world remain highly uncertain. Lacking is quantitative determination of commonality in climate anomalies associated with pulses of tree mortality—from published, field-documented mortality events—required for understanding the role of extreme climate events in overall global tree die-off patterns. Here we established a geo-referenced global database documenting climate-induced mortality events spanning all tree-supporting biomes and continents, from 154 peer-reviewed studies since 1970. Our analysis quantifies a global “hotter-drought fingerprint” from these tree-mortality sites—effectively a hotter and drier climate signal for tree mortality—across 675 locations encompassing 1,303 plots. Frequency of these observed mortality-year climate conditions strongly increases nonlinearly under projected warming. Our database also provides initial footing for further community-developed, quantitative, ground-based monitoring of global tree mortality.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Lab Collaboration Project (LCP) for Marine Energy: Nonlinear Ocean Waves and PTO Control Strategy (Task 11)

The objectives for this task was to advance analysis and simulation capabilities for wave-WEC interactions and PTO analysis in nonlinear ocean waves. The improvements involve advancements in the generation of nonlinear wave time series and in nonlinear control strategies resulting in a detailed examination of WEC-wave interaction under scarcely-studied nonlinear conditions.

16 TIDAL AND WAVE POWER↗