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At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Recurrent neural network-based multiaxial plasticity model with regularization for physics-informed constraints

We report a recurrent neural network (RNN) based model is developed as a surrogate to predict nonlinear plastic response under multiaxial loading. The RNN-based model is trained and tested on stress versus strain curves generated using a numerical solution based on the classical radial return method. Besides simply learning the basic constitutive relationship, a novel approach is taken to enforce certain physical conditions. Specifically, regularization is employed to maintain non-negative plastic power density throughout the loading history thereby ensuring monotonically increasing plastic work and thermodynamic consistency. Enforcing physics in this manner permits coupling of the data-driven RNN approach with physics-based knowledge and laws. This has the effect of reducing the necessary amount of data and ensuring known physical laws are not violated. Since, once trained, the model need not perform the expensive task of solving nonlinear equations, its efficiency is orders of magnitude greater than its numerical counterpart. The RNN-based model has been trained on varied sets of data and the accuracy on test datasets validated. The developed model is general and robust and has widespread application such as in the simulation of metal forming, large scale plasticity, and part life prediction.

42 ENGINEERING↗

NASA NTRS2007

Process for High-Rate Fabrication of Alumina Nanotemplates

An anodizing process, at an early stage of development at the time of reporting the information for this article, has shown promise as a means of fabricating alumina nanotemplates integrated with silicon wafers. Alumina nanotemplates are basically layers of alumina, typically several microns thick, in which are formed approximately regular hexagonal arrays of holes having typical diameters of the order of 10 to 100 nm. Interest in alumina nanotemplates has grown in recent years because they have been found to be useful as templates in the fabrication of nanoscale magnetic, electronic, optoelectronic, and other devices. The present anodizing process is attractive for the fabrication of alumina nanotemplates integrated with silicon wafers in two respects: (1) the process involves self-ordering of the holes; that is, the holes as formed by the process are spontaneously arranged in approximately regular hexagonal arrays; and (2) the rates of growth (that is, elongation) of the holes are high enough to make the process compatible with other processes used in the mass production of integrated circuits. In preparation for fabrication of alumina nanotemplates in this process, one first uses electron-beam evaporation to deposit thin films of titanium, followed by thin films of aluminum, on silicon wafers. Then the alumina nanotemplates are formed by anodizing the aluminum layers, as described below. In experiments in which the process was partially developed, the titanium films were 200 A thick and the aluminum films were 5 m thick. The aluminum films were oxidized to alumina, and the arrays of holes were formed by anodizing the aluminum in aqueous solutions of sulfuric and/or oxalic acid at room temperature (see figure). The diameters, spacings, and rates of growth of the holes were found to depend, variously, on the composition of the anodizing solution, the applied current, or the applied potential, as follows: In galvanostatically controlled anodizing, regardless of the chemical composition of the solution, relatively high current densities (50 to 100 mA/cm2) resulted in arrays of holes that were more nearly regular than were those formed at lower current densities. . The rates of elongation of the holes were found to depend linearly on the applied current density: the observed factor of proportionality was 1.2 (m/h)/(mA/cm2). For a given fixed current density and room temperature, the hole diameters were found to depend mainly on the chemical compositions of the anodizing solutions. The holes produced in sulfuric acid solutions were smaller than those produced in oxalic acid solutions. The arrays of holes produced in sulfuric acid were more ordered than were those produced in oxalic acid. . The breakdown voltage was found to decrease logarithmically with increasing concentration of sulfuric acid. The breakdown voltage was also found to decrease with temperature and to be accompanied by a decrease in hole diameter. The hole diameter was found to vary linearly with applied potential, with a slope of 2.1 nm/V. This slope differs from slopes (2.2 and 2.77 nm/V) reported for similar prior measurements on nanotemplates made from bulk aluminum. The differences among these slopes may be attributable to differences among impurities and defects in bulk and electron-beam-evaporated aluminum specimens.

Myung, Nosang↗

NASA NTRS1994

Echo mapping of active galactic nuclei broad-line regions: Fundamental algorithms

We formulate and test a series of algorithms for echo mapping the emission-line regions near active galactic nuclei from measurements of correlated variability in their line and continuum light curves. The linear regularization method (LRM) employs a direct inversion of evenly spaced light-curve data, with a regularization parameter that can be used to control the trade-off between noise and resolution. Matrix formulas express the formal solution as well as its variance and covariance in terms of uncertainties in the measurements. Unlike the maximum-entropy method (MEM), LRM applies to kernels with both positive and negative values, but the results are somewhat limited by ringing effects. A positivity constraint proves effective in controlling the ringing. MEM combines regularization and positivity in a natural way, but similar results are also found using positivity constraints with nonentropic regularization functions. Direct inversions of unevenly sampled light curves require interpolating the noisy data. In this case better results are found by solving for both the continuum light curve and kernel function in a simultaneous fit to the data. Our conclusion is that while echo mapping currently gives ambiguous results, the algorithms are not the limiting factor. Progress depends on efforts to increase the accuracy and completeness of sampling of the observed light curves.

Vio, Roberto↗

DOE OSTI2022

Rethinking the ill-posedness of the spectral function reconstruction — Why is it fundamentally hard and how Artificial Neural Networks can help

Reconstructing hadron spectral functions through Euclidean correlation functions are of the important missions in lattice QCD calculations. However, in a Källen–Lehmann (KL) spectral representation, the reconstruction is observed to be ill-posed in practice. It is usually ascribed to the fewer observation points compared to the number of points in the spectral function. In this paper, by solving the eigenvalue problem of continuous KL convolution, we show analytically that the ill-posedness of the inversion is fundamental and it exists even for continuous correlation functions. We discussed how to introduce regulators to alleviate the predicament, in which include the Artificial Neural Networks (ANNs) representations recently proposed by the Authors in another study. The uniqueness of solutions using ANNs representations is manifested analytically and validated numerically. Reconstructed spectral functions using different regularization schemes are also demonstrated, together with their eigen-mode decomposition. We observe that components with large eigenvalues can be reliably reconstructed by all methods, whereas those with low eigenvalues need to be constrained by regulators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

BioXTAS RAW 2 : new developments for a free open-source program for small-angle scattering data reduction and analysis

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI ; updated automated Guinier fitting and D max finding algorithms; automated series ( e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares ( REGALS ); creation of electron-density reconstructions using electron density via solution scattering ( DENSS ); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗

NASA NTRS1972

Mariner 9 celestial mechanics experiment - Gravity field and pole direction of Mars.

Analysis of the Mariner 9 radio-tracking data shows that the Martian gravity field is rougher than that of earth or the moon, and that the accepted direction of the Mars rotation axis is in error by about 0.5 deg. Contours of equivalent surface heights deduced from a sixth-degree solution for the Martian gravity field are presented. These contours represent the deviations from sphericity of a uniformly dense body with an external potential which is given by the first sixth-degree solution. In addition to Doppler observations, ranging or group-delay measurements have been made regularly since orbit insertion.

Lorell, J.↗

DOE OSTI2024

Calcium-organic matter fouling in nanofiltration: Synchrotron-based X-ray fluorescence and absorption near-edge structure spectroscopy for speciation

Calcium (Ca)-enhanced organic matter (OM) fouling of nanofiltration (NF) membranes leads to reduced flux during desalination and requires frequent cleaning. Fouling mechanisms are not fully understood, which limits the development of targeted fouling control methods. This study employed synchrotron-based X-ray fluorescence (XRF) and X-ray absorption near-edge structure (XANES) spectroscopy to quantify the spatial distribution and mass of Ca deposition as well as changes in the Ca coordination environment characteristic of specific fouling mechanisms, respectively. Bench-scale filtration experiments were performed using feed solutions containing Ca and ten different types of organic matter (OM), as well as the common scalants, calcium carbonate (CaCO 3 ) and calcium sulfate (CaSO 4 ). Osmotic backwash (OB) was performed at regular intervals for fouling control. Ca-OM aggregation resulted in greater flux decline and lower flux recovery during OB than Ca conditioning of membranes followed by filtration of feed solution with OM. Linear combination fitting (LCF) of XANES absorption spectra from fouled membranes indicated that Ca-OM aggregation preferentially occurred for OM types that exhibited both high carboxylic group and negative charge density. Consequently, these OM types exhibited greater deposition of Ca and TOC on the membrane surface when compared to other OM types. For the coexistence of scalants and OM, Ca speciation within the fouling layer was characteristic of both Ca bound to the membrane (i.e. potential bridging, charge screening) as well as Ca-OM aggregation and deposition mechanisms, while a range of crystal polymorphs were observed to occur simultaneously. XRF and XANES represent powerful tools for the elucidation of NF fouling mechanisms by quantification of Ca deposition as well as Ca speciation. Fouling control methods should target OM types with high carboxyl group density and negative charge to neutralize or eliminate interactions with Ca.

42 ENGINEERING↗

DOE OSTI2021

A priori error analysis of high-order LL* (FOSLL*) finite element methods

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are LL* methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. Here, we show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design

Microgrids are frequently employed in remote regions, in part because access to a larger electric grid is impossible, difficult, or compromises reliability and independence. Although small microgrids often employ spot generation, in which a diesel generator is attached directly to a load, microgrids that combine these individual loads and augment generators with photovoltaic cells and batteries as a distributed energy system are emerging as a safer, less costly alternative. In this work, we present a model that seeks the minimum-cost microgrid design and ideal dispatched power to support a small remote site for one year with hourly fidelity under a detailed battery model; this mixed-integer nonlinear program (MINLP) is intractable with commercial solvers but loosely coupled with respect to time. A mixed-integer linear program (MIP) approximates the model, and a partitioning scheme linearizes the bilinear terms. We introduce a novel policy for loosely coupled MIPs in which the system reverts to equivalent conditions at regular time intervals; this separates the problem into subproblems that we solve in parallel. We obtain solutions within 5% of optimality in at most six minutes across 14 MIP instances from the literature and solutions within 5% of optimality to the MINLP instances within 20 minutes.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1978

Finite element concepts in computational aerodynamics

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Baker, A. J.↗

DOE OSTI2022

An ℓ 0 ℓ 2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

In this work we introduce ℓ 0 ℓ 2 -norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ 2 -norm regularization is used to suppress intrinsic data noise, while the ℓ 0 -norm is used to penalize the number of nonzero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ 0 ℓ 2 -norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ 1 -norm regularized cluster expansion models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Cardinality-Regularized Hawkes-Granger Model

We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning algorithms for the Hawkes process suffer from a singularity in maximum likelihood estimation. As a result, their sparse solutions can appear only as numerical artifacts. In this paper, we propose a mathematically well-defined sparse causal learning framework based on a cardinality-regularized Hawkes process, which remedies the pathological issues of existing approaches. We leverage the proposed algorithm for the task of instance-wise causal event analysis, where sparsity plays a critical role. We validate the proposed framework with two real use-cases, one from the power grid and the other from the cloud data center management domain.

Ide, Tsuyoshi↗

NASA NTRS2003

Thermocapillary Convection Due to a Stationary Bubble - A Paradox

We analyze the velocity and temperature fields at steady state due to thermocapillary convection around a gas bubble that is stationary in a liquid. A linear temperature field is imposed in the undisturbed liquid. Our interest is in investigating the effect of convective transport of momentum and energy on the velocity and temperature fields. We assume the pertinent physical properties to be constant, and that buoyant convection is negligible. Suitably defined Reynolds and Marangoni numbers are assumed to be small compared with unity. When both the Reynolds and Marangoni numbers are set equal to zero, a solution can be found. In this solution, far from the bubble, the velocity field decays as the inverse of the distance from the bubble, and the disturbance temperature field decays as the inverse of the square of this distance. We now attempt to obtain a solution when the Reynolds number is zero, but the Marangoni number is small, but non-zero, by a perturbation expansion in the Marangoni number. When the temperature field is expanded in a regular perturbation series in the Marangoni number, we show that the problem for the first correction field is ill-posed. The governing equation for this perturbation field contains an inhomogeneity, and the corresponding particular solution neither decays far from the bubble, nor can be canceled by a homogeneous solution. Additional information is included in the original extended abstract.

Balasubramaniam, R.↗

DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

High frequency scattering from corrugated stratified cylinders

Interest in applying radar remote sensing for the study of forested areas led to the development of a model for scattering from corrugated stratified dielectric cylinders. The model is used to investigate the effect of bark and its roughness on scattering from tree trunks and branches. The outer layer of the cylinder (bark) is assumed to be a low-loss dielectric material and to have a regular (periodic) corrugation pattern. The inner layers are treated as lossy dielectrics with smooth boundaries. A hybrid solution based on the moment method and the physical optics approximation is obtained. In the solution, the corrugations are replaced with polarization currents that are identical to those of the local tangential periodic corrugated surface, and the stratified cylinder is replaced with equivalent surface currents. New expressions for the equivalent physical-optics currents are used which are more convenient than the standard ones. It is shown that the bark layer and its roughness both reduce the radar cross-section. It is also demonstrated that the corrugations can be replaced by an equivalent anisotropic layer.

Sarabandi, Kamal↗