Unwarping GISAXS data
Explore the source record for details and available documents.
99 GENERAL AND MISCELLANEOUS↗
SEARCH · Search NASA
Results for “initial guess”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Gradient drift eigenmodes in the equatorial electrojet
The problem of kilometer-scale irregularities in the daytime equatorial electrojet is revisited by means of an eigenmode analysis of the gradient drift instability. Realistic physical parameters are used, including the modeled altitude variations of ion and electron collision frequencies and mobilities. The full fourth-order system of two coupled differential equations (each of second order) for the denisty and electrostatic potential perturbations is solved numerically by a relaxation technique. Under some approximations, the fourth-order system can be shown to reduce to a second-order differential equation for the perturbed potential or density. The latter is solved using a shooting technique and provides initial guesses for numerical solutions to the full problem. It is shown that the linear growth rate peaks for kilometer-scale waves, contrary to the findings of recent initial-value studies. This occurs because the equilibrium velocity shear is much more effective as a damping mechanism for short-wavelength modes than it is for the longer, kilometer-scale modes. These results provide a natural qualitative explanation for the observed dominance of kilometer-scale structures in the daytime electrojet spectrum.
Wang, X.-H.↗
A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors
Here, we present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations and many-body localization studies of quantum spin chains.
97 MATHEMATICS AND COMPUTING↗
MIR Measurements of Atmospheric Water Vapor Profiles
Three subjects related to atmospheric water vapor profiling using the 183.3 GHz absorption line are discussed in this paper. First, data acquired by an airborne millimeter-wave imaging radiometer (MIR) over ocean surface in the western Pacific are used to estimate three-dimensional (3-D) distribution of atmospheric water vapor. The instrument's radiometric measurements with mixed vertical and horizontal polarizations require modifications to the retrieval algorithm used in the past. It is demonstrated that, after the modifications, the new algorithm can provide adequate retrieval of water vapor profiles, even though the measured data are of mixed polarizations. Next, the retrieved profiles, in terms of water vapor mixing ratio rho (g/kg), are compared with those measured in near concurrence by dropsondes from a research aircraft in the western Pacific and by a ground-based Raman lidar at Wallops Island, Virginia. The ratio of the standard deviation to the mean rho is found to be 0.12 at 0.25 km altitude and gradually degraded to 0.67 at the highest altitude of the retrieval of 10.25 km. Finally, the effect of the "initial guess" relative humidity profile on the final retrieved product is analyzed with respect to the condition for the convergent retrieval. It is found that the effect is minimal if the initial profile is not unrealistically different from the true one. If the initial profile is very different from the true one, the final retrieved product could be subject to a substantial error. Tightening of the convergent condition in the retrieval helped reduce magnitude of the error, but not remove it totally. It is concluded that an initial profile based on climatology is likely to provide most reliable retrieval results.
Wang, J. R.↗
Termolecular ion-molecule reactions in Titan's atmosphere. IV. A search made at up to 1 micron in pure hydrocarbons
The results of a study of ion-molecule reactions occurring in pure methane, acetylene, ethylene, ethane, propyne, propene, propane, and diacetylene at pressures up to 40 microns of pressure are reported. A variety of experimental methods are used: The standard double resonance in an ICR, for determination of the precursor ions and the modulated double resonance ejection in an ICR, for the determination of the daughter ions. The FA-SIFT technique was used for validation and examination of termolecular reactions with rate coefficients that are less than 10(-26) cm(6) s(-1). An extensive database of reaction kinetics already exists for many of these reactions. The main point of this study was the determination of the accuracy of this database and to search for any missing reactions and reaction channels that may have been omitted from earlier investigations. A specific objective of this work was to extend the study to the highest pressures possible to find out if there were any important termolecular reaction channels occurring. A new approach was used here. In the pure hydrocarbon gases the mass spectra were followed as a function of the pressure changes of the gas. An initial guess was first made using the current literature as a source of the reaction kinetics that were expected. A model of the ion abundances was produced from the solution of the partial differential equations in terms of reaction rate coefficients and initial abundances. The experimental data was fitted to the model for all of the pressures by a least squares minimization to the reaction rate coefficients and initial abundances. The reaction rate coefficients obtained from the model were then compared to the literature values. Several new channels and reactions were discovered when the modeled fits were compared to the actual data. This is all explained in the text and the implications of these results are discussed for the Titan atmosphere.
Hydrocarbons, Acyclic/analysis↗
Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization
Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. Here in this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
First-guess dependence of a physically based set of temperature-humidity retrievals from HIRS2/MSU data
The first-guess dependence of temperature and humidity fields retrieved from HIRS2/MSU data using the GLA (Goddard Laboratory for Atmospheres) physically based retrieval scheme is examined. Retrievals were performed over the ALPEX region for two successive synoptic periods, 1200 UTC March 4 and 00000 UTC March 5, 1982, using three different initial guesses for each period. Results show rather low first-guess dependence for the thickness fields and larger first-guess dependence for the precipitable water fields, especially close to the surface. The humidity retrieval algorithm used is described. The processing system has the property of maintaining the accuracy of a good guess and improving a poor one for both thickness and precipitable water at all levels.
Reuter, D.↗
Stochastic machine learning via sigma profiles to build a digital chemical space
This work establishes a different paradigm on digital molecular spaces and their efficient navigation by exploiting sigma profiles. To do so, the remarkable capability of Gaussian processes (GPs), a type of stochastic machine learning model, to correlate and predict physicochemical properties from sigma profiles is demonstrated, outperforming state-of-the-art neural networks previously published. The amount of chemical information encoded in sigma profiles eases the learning burden of machine learning models, permitting the training of GPs on small datasets which, due to their negligible computational cost and ease of implementation, are ideal models to be combined with optimization tools such as gradient search or Bayesian optimization (BO). Gradient search is used to efficiently navigate the sigma profile digital space, quickly converging to local extrema of target physicochemical properties. While this requires the availability of pretrained GP models on existing datasets, such limitations are eliminated with the implementation of BO, which can find global extrema with a limited number of iterations. A remarkable example of this is that of BO toward boiling temperature optimization. Holding no knowledge of chemistry except for the sigma profile and boiling temperature of carbon monoxide (the worst possible initial guess), BO finds the global maximum of the available boiling temperature dataset (over 1,000 molecules encompassing more than 40 families of organic and inorganic compounds) in just 15 iterations (i.e., 15 property measurements), cementing sigma profiles as a powerful digital chemical space for molecular optimization and discovery, particularly when little to no experimental data is initially available.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An improved guess for the variational calculation of charge-transfer excitations in large systems
Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.
Bogo, Nicola↗
Contaminant point source localization error estimates as functions of data quantity and model quality
We develop empirically-grounded error envelopes for localization of a point contamination release event in the saturated zone of a previously uncharacterized heterogeneous aquifer into which a number of plume-intercepting wells have been drilled. We assume that flow direction in the aquifer is known exactly and velocity is known to within a factor of two of our best guess from well observations prior to source identification. Other aquifer and source parameters must be estimated by interpretation of well breakthrough data via the advection-dispersion equation. We employ high performance computing to generate numerous random realizations of aquifer parameters and well locations, simulate well breakthrough data, and then employ unsupervised machine optimization techniques to estimate the most likely spatial (or space-time) location of the source. Tabulating the accuracy of these estimates from the multiple realizations, we relate the size of 90% and 95% confidence envelopes to the data quantity (number of wells) and model quality (fidelity of ADE interpretation model to actual concentrations in a heterogeneous aquifer with channelized flow). We find that for purely spatial localization of the contaminant source, increased data quantities can make up for reduced model quality. For space-time localization, we find similar qualitative behavior, but significantly degraded spatial localization reliability and less improvement from extra data collection. Since the space-time source localization problem is much more challenging, we also tried a multiple-initial-guess optimization strategy. Furthermore, this greatly enhanced performance, but gains from additional data collection remained limited.
54 ENVIRONMENTAL SCIENCES↗
Divalent Ion Parameterization Strongly Affects Conformation and Interactions of an Anionic Biomimetic Polymer
The description of peptides and the use of molecular dynamics simulations to refine structures and investigate the dynamics on an atomistic scale are well developed. Through a consensus in this community over multiple decades, parameters were developed for molecular interactions that only require the sequence of amino-acids and an initial guess for the three-dimensional structure. The recent discovery of peptoids will require a retooling of the currently available interaction potentials in order to have the same level of confidence in the predicted structures and pathways as there is presently in the peptide counterparts. Here we present modeling of peptoids using a combination of ab initio molecular dynamics (AIMD) and atomistic resolution classical forcefield (FF) to span the relevant time and length scales. To properly account for the dominant forces that stabilize ordered structures of peptoids, namely steric-, electrostatic, and hydrophobic interactions mediated through sidechain-sidechain interactions in the FF model, those have to be first mapped out using high fidelity atomistic representations. A key feature here is not only to use gas phase quantum chemistry tools, but also account for solvation effects in the condensed phase through AIMD. One major challenge is to elucidate ion binding to charged or polar regions of the peptoid and its concomitant role in the creation of local order. Here, similar to proteins, a specific ion effect is observed suggesting that both the net charge and the precise chemical nature of the ion will need to be described. MDD was supported by MS3 (Materials Synthesis and Simulation Across Scales) Initiative at Pacific Northwest National Laboratory. Research was funded by the Laboratory Directed Research and Development program at Pacific Northwest National Laboratory. MDB acknowledges support from US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Material & Engineering. CJM acknowledges support from US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. PNNL is a multiprogram national laboratory operated by Battelle for the U.S. Department of Energy.
Daily, Michael D.↗
Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning
Determining process–structure–property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process–structure and structure–property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification framework based on push-forward probability measures, which combines techniques from measure theory and Bayes’ rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.
36 MATERIALS SCIENCE↗
On differential singular perturbation problems: a simple variational approach
An alternative approach for the analysis and the numerical approximation of singular perturbation problems, using a variational framework, is presented. It is based on the natural idea of minimizing the residual of the differential equation measured in the L{sup 2} norm. By this strategy, the approximation is based in the solution of a set of linear problems giving the descent step directions of the problem. This is the main advantage of our approach, since we can use stable and convergent methods for linear problems (without assuming the knowledge of good initial guesses used in the approximation of the associated non-linear systems necessary in Newton-type methods). Remember that for this type of problems, we should use implicit methods. We prove that our procedure can never get stuck in local minima, and the error decreases until getting to the original solution independent of the perturbation parameter. Finally, we include some numerical examples.
97 MATHEMATICS AND COMPUTING↗
A framework for forming thermoset polymer networks during laser powder bed fusion additive manufacturing
It is commonly reported that the limited availability of material types is a major barrier to widespread adoption for polymer laser powder bed fusion (PBF/L) additive manufacturing (AM). A deeper understanding of the physico-chemical relationships between AM process stimuli and polymer responsive behavior is needed to make data-driven decisions for PBF/L specific material development and formulation. Many researchers have cumulatively built the current state of PBF/L “science-based manufacturing” framework where an initial guess for process parameter values can be determined from measured polymer properties and the first-principles of physics. However, published literature has focused on developing this framework for thermoplastic processing of polymers omitting many specific concerns unique to processing thermosetting materials. The authors consider in the present work the implications of many specific aspects unique to thermosetting polymers during PBF/L manufacturing. These aspects are contextually discussed according to the five sub-functions of PBF/L and are described mathematically where appropriate alongside example data from thermosetting materials commercially available in powder form. Further, this expansion of the prevailing material development framework to include thermosetting polymers paves the way for the unique performance properties offered by that class to be manifest through AM’s geometric freedom.
36 MATERIALS SCIENCE↗
Deterministically estimated fission source distributions for Monte Carlo k-eigenvalue problems
The standard Monte Carlo (MC) k-eigenvalue algorithm involves iteratively converging the fission source distribution using a series of potentially time-consuming inactive cycles before quantities of interest can be tallied. One strategy for reducing the computational time requirements of these inactive cycles is the Sourcerer method, in which a deterministic eigenvalue calculation is performed to obtain an improved initial guess for the fission source distribution. This method has been implemented in the Exnihilo software suite within SCALE using the SPNSPN or SNSN solvers in Denovo and the Shift MC code. The efficacy of this method is assessed with different Denovo solution parameters for a series of typical k-eigenvalue problems including small criticality benchmarks, full-core reactors, and a fuel cask. Here it is found that, in most cases, when a large number of histories per cycle are required to obtain a detailed flux distribution, the Sourcerer method can be used to reduce the computational time requirements of the inactive cycles.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Prediction of α $IIb$ $β$ 3 integrin structures along its minimum free energy activation pathway
The adhesion protein integrin is a transmembrane heterodimer that plays a pivotal role in cellular processes such as cell signaling and cell migration. To execute its function, integrin undergoes extensive conformational changes from a bent-closed to an extended-open state. Resolving the structures across these changes remains a challenge with both experimental and computational methods, but it is crucial for understanding the activation mechanism of integrin. We address this challenge for the platelet integrin α IIb β 3 by employing finite temperature string method with structures of the images along the initial guess path generated by a multiscale data-driven framework. The full-length all-atom structures along the resulting minimum free energy path between the inactive bent-closed and active extended-open states of α IIb β 3 integrin are consistent with a variety of experimentally resolved structures. Changes in these predicted structures along the path show that the extension and separation of the α and β subunits from the bent-closed to the extended-open state require correlated movements between the subdomain pairs in α IIb β 3 . Furthermore, these results provide new insights into integrin activation mechanism, and the predicted structures have potential applications in guiding the design of integrin-targeting therapeutics.
Dasetty, Siva [University of Chicago, IL (United S↗
An error-in-constitutive equations strategy for topology optimization for frequency-domain dynamics
This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. In this work, we propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.
42 ENGINEERING↗
A sparse matrix–vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms
Here we present an efficient sparse matrix–vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev–Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix–matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev–Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix–vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.
42 ENGINEERING↗