Results for “Computational efficiency” — Page 34

DOE OSTI2024

Elucidating the formation mechanisms of zeolites using data-driven modelling and in-situ characterization

Zeolites are the main solid catalysts used by the chemical industry. The use of zeolites in separations and as shape selective catalysts requires control of the width and connectivity of their pores. 235 distinct zeolite frameworks have been synthesized to date, of over 2 million that have been proposed. Recent work indicates that the limitation is in large part kinetic: new synthetic pathways are required to access new zeolites. Organic cations are used to direct the synthesis towards specific zeolites. However, the molecular mechanisms by which cations direct the nucleation towards specific zeolites is not known. Elucidating these mechanisms is key to realize new zeolites for catalysis and separations, and is the focus of this project. This project developed and implemented a synergistic, data-driven computational and experimental approach to resolve the molecular pathways of nucleation, growth, and polymorph selection of zeolites and the role of organic cations in directing their formation. The project developed computationally efficient and accurate models for the study of the nucleation and growth of pure silica zeolites in molecular simulations, using machine learning with data from experiments. Simulations with these models were integrated with scanning tunneling electron microscopy, computer vision, and deep learning to unveil the molecular pathways of formation of a zeolite. Of particular interest in this project was to elucidate the role of amorphous precursors in the nucleation of the zeolite. Previous experiments indicate that zeolites are born within non-crystalline aggregates in which the silicates and organic cations have local and medium range order similar to that of the zeolite. The organic cations that direct the formation of zeolites and those that direct the formation of ordered mesoporous silicas are similar. We hypothesized that the frustrated attraction that for large organic cations leads to the formation of stable mesophases that direct the synthesis of mesoporous silicas, could promote the formation of metastable mesophases that can assist in the nucleation and polymorph selection of zeolites. The simulations resolved how structure directing agents build crystalline order and showed that mesoscopic pre-ordering occurs is not required to facilitate the nucleation of zeolites, because the synthesis occurs at high driving forces, where the barriers for nucleation are negligible. This project unveiled that polymorph selection in zeolite synthesis occurs after nucleation, opening a distinct area of control through the kinetics of growth and not through nucleation barriers.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Current capabilities for simulating the extreme distortion of thin structures subjected to severe impacts

The explicit transient dynamics technology in use today for simulating the impact and subsequent transient dynamic response of a structure has its origins in the 'hydrocodes' dating back to the late 1940's. The growth in capability in explicit transient dynamics technology parallels the growth in speed and size of digital computers. Computer software for simulating the explicit transient dynamic response of a structure is characterized by algorithms that use a large number of small steps. In explicit transient dynamics software there is a significant emphasis on speed and simplicity. The finite element technology used to generate the spatial discretization of a structure is based on a compromise between completeness of the representation for the physical processes modelled and speed in execution. That is, since it is expected in every calculation that the deformation will be finite and the material will be strained beyond the elastic range, the geometry and the associated gradient operators must be reconstructed, as well as complex stress-strain models evaluated at every time step. As a result, finite elements derived for explicit transient dynamics software use the simplest and barest constructions possible for computational efficiency while retaining an essential representation of the physical behavior. The best example of this technology is the four-node bending quadrilateral derived by Belytschko, Lin and Tsay. Today, the speed, memory capacity and availability of computer hardware allows a number of the previously used algorithms to be 'improved.' That is, it is possible with today's computing hardware to modify many of the standard algorithms to improve their representation of the physical process at the expense of added complexity and computational effort. The purpose is to review a number of these algorithms and identify the improvements possible. In many instances, both the older, faster version of the algorithm and the improved and somewhat slower version of the algorithm are found implemented together in software. Specifically, the following seven algorithmic items are examined: the invariant time derivatives of stress used in material models expressed in rate form; incremental objectivity and strain used in the numerical integration of the material models; the use of one-point element integration versus mean quadrature; shell elements used to represent the behavior of thin structural components; beam elements based on stress-resultant plasticity versus cross-section integration; the fidelity of elastic-plastic material models in their representation of ductile metals; and the use of Courant subcycling to reduce computational effort.

Key, Samuel W.↗

NASA NTRS2002

Particle Swarm Optimization

The purpose of this paper is to show how the search algorithm known as particle swarm optimization performs. Here, particle swarm optimization is applied to structural design problems, but the method has a much wider range of possible applications. The paper's new contributions are improvements to the particle swarm optimization algorithm and conclusions and recommendations as to the utility of the algorithm, Results of numerical experiments for both continuous and discrete applications are presented in the paper. The results indicate that the particle swarm optimization algorithm does locate the constrained minimum design in continuous applications with very good precision, albeit at a much higher computational cost than that of a typical gradient based optimizer. However, the true potential of particle swarm optimization is primarily in applications with discrete and/or discontinuous functions and variables. Additionally, particle swarm optimization has the potential of efficient computation with very large numbers of concurrently operating processors.

Venter, Gerhard↗

NASA NTRS2003

Validation of a High-Order Prefactored Compact Code on Nonlinear Flows with Complex Geometries

A finite-difference time domain solution of the airfoil gust problem is obtained using a high-accuracy nonlinear computational aeroacoustics code. For computational efficiency, the equations are cast in chain-rule curvilinear form, and a structured multiblock solver is used in parallel. In order to fully investigate the performance of this solver, a test matrix of eight problems are computed (two airfoil geometries, two gust frequencies, and two gust configurations). These results are compared to solutions obtained by the GUST3D frequency-domain solver both on the airfoil surface and in the far field. Grid density and domain size studies are included.

Hixon, R.↗

NASA NTRS2006

Application of the Convolution Formalism to the Ocean Tide Potential: Results from the Gravity and Recovery and Climate Experiment (GRACE)

A computationally efficient approach to reducing omission errors in ocean tide potential models is derived and evaluated using data from the Gravity Recovery and Climate Experiment (GRACE) mission. Ocean tide height models are usually explicitly available at a few frequencies, and a smooth unit response is assumed to infer the response across the tidal spectrum. The convolution formalism of Munk and Cartwright (1966) models this response function with a Fourier series. This allows the total ocean tide height, and therefore the total ocean tide potential, to be modeled as a weighted sum of past, present, and future values of the tide-generating potential. Previous applications of the convolution formalism have usually been limited to tide height models, but we extend it to ocean tide potential models. We use luni-solar ephemerides to derive the required tide-generating potential so that the complete spectrum of the ocean tide potential is efficiently represented. In contrast, the traditionally adopted harmonic model of the ocean tide potential requires the explicit sum of the contributions from individual tidal frequencies. It is therefore subject to omission errors from neglected frequencies and is computationally more intensive. Intersatellite range rate data from the GRACE mission are used to compare convolution and harmonic models of the ocean tide potential. The monthly range rate residual variance is smaller by 4-5%, and the daily residual variance is smaller by as much as 15% when using the convolution model than when using a harmonic model that is defined by twice the number of parameters.

models↗

NASA NTRS2011

Methane Sensitivity to Perturbations in Tropospheric Oxidizing Capacity

Methane is an important greenhouse gas and has a 25 times greater global warming potential than CO2 on a century timescale. Yet there are considerable uncertainties in the magnitude and variability of its sources and sinks. The response of the coupled non-linear methane-carbon monoxide-hydroxyl radical (OH) system is important in determining the tropospheric oxidizing capacity. Using the NASA Goddard Earth Observing System, Version 5 (GEOS-5) chemistry climate model, we study the response of methane to perturbations of OH and wetland emissions. We use a computationally-efficient option of the GEOS-5 CCM that includes an OH parameterization that accurately represents OH predicted by a full chemical mechanism. The OH parameterization allows for studying non-linear CH4-CO-OH feedbacks in computationally fast sensitivity experiments. We compare our results with surface observations (GMD) and discuss the range of uncertainty in OH and wetland emissions required to bring modeling results in better agreement with surface observations. Our results can be used to improve projections of methane emissions and methane growth.

Yegorova, Elena↗

NASA NTRS2023

Unsteady RANS and Scale Resolving Simulations of Open Rotor Noise

Computational simulations using structured curvilinear overset grids with the Launch Ascent and Vehicle Aerodynamics (LAVA) framework are presented for predicting the aerodynamic and aeroacoustic behavior of a contra-rotating open rotor (CROR) propulsion system using a newly developed and computationally efficient sliding mesh technique. A comprehensive evaluation of two turbulence closure treatments is carried out as part of the scope of this work: Unsteady Reynolds-Averaged Navier-Stokes Simulation (URANS), and Hybrid RANS/LES (HRLES). The computed results are then validated against existing experimental measurements at both the nominal take-off and cruise flight conditions. To propagate the noise generated by the near-field CROR system, aeroacoustic analysis based on a frequency-domain permeable surface Ffowcs Williams-Hawkings (FW-H) approach is applied.

ARMD↗

NASA NTRS2023

Unsteady RANS and Scale Resolving Simulations of Open Rotor Noise

Computational simulations using structured curvilinear overset grids with the Launch Ascent and Vehicle Aerodynamics (LAVA) framework are presented for predicting the aerodynamic and aeroacoustic behavior of a contra-rotating open rotor (CROR) propulsion system using a newly developed and computationally efficient sliding mesh technique. A comprehensive evaluation of two turbulence closure treatments is carried out as part of the scope of this work: Unsteady Reynolds-Averaged Navier-Stokes Simulation (URANS), and Hybrid RANS/LES (HRLES). The computed results are then validated against existing experimental measurements at both the nominal take-off and cruise flight conditions. To propagate the noise generated by the near-field CROR system, aeroacoustic analysis based on a frequency-domain permeable surface Ffowcs Williams-Hawkings (FW-H) approach is applied.

ARMD↗

NASA NTRS1985

Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms

In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.

Pulliam, T. H.↗

DOE OSTI2025

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗

NASA NTRS1974

Transient Response of Shells of Revolution by Direct Integration and Modal Superposition Methods

The results of an analytical effort to obtain and evaluate transient response data for a cylindrical and a conical shell by use of two different approaches: direct integration and modal superposition are described. The inclusion of nonlinear terms is more important than the inclusion of secondary linear effects (transverse shear deformation and rotary inertia) although there are thin-shell structures where these secondary effects are important. The advantages of the direct integration approach are that geometric nonlinear and secondary effects are easy to include and high-frequency response may be calculated. In comparison to the modal superposition technique the computer storage requirements are smaller. The advantages of the modal superposition approach are that the solution is independent of the previous time history and that once the modal data are obtained, the response for repeated cases may be efficiently computed. Also, any admissible set of initial conditions can be applied.

Stephens, W. B.↗

NASA NTRS1992

The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomials coefficients using trees

This note is concerned with the explicit symbolic computation of expressions involving differential operators and their actions on functions. The derivation of specialized numerical algorithms, the explicit symbolic computation of integrals of motion, and the explicit computation of normal forms for nonlinear systems all require such computations. More precisely, if R = k(x(sub 1),...,x(sub N)), where k = R or C, F denotes a differential operator with coefficients from R, and g member of R, we describe data structures and algorithms for efficiently computing g. The basic idea is to impose a multiplicative structure on the vector space with basis the set of finite rooted trees and whose nodes are labeled with the coefficients of the differential operators. Cancellations of two trees with r + 1 nodes translates into cancellation of O(N(exp r)) expressions involving the coefficient functions and their derivatives.

Crouch, P. E.↗

NASA NTRS1999

Regional Climate Simulation with a Variable Resolution Stretched Grid GCM: The Regional Down-Scaling Effects

The results obtained with the variable resolution stretched grid (SG) GEOS GCM (Goddard Earth Observing System General Circulation Models) are discussed, with the emphasis on the regional down-scaling effects and their dependence on the stretched grid design and parameters. A variable resolution SG-GCM and SG-DAS using a global stretched grid with fine resolution over an area of interest, is a viable new approach to REGIONAL and subregional CLIMATE studies and applications. The stretched grid approach is an ideal tool for representing regional to global scale interactions. It is an alternative to the widely used nested grid approach introduced a decade ago as a pioneering step in regional climate modeling. The GEOS SG-GCM is used for simulations of the anomalous U.S. climate events of 1988 drought and 1993 flood, with enhanced regional resolution. The height low level jet, precipitation and other diagnostic patterns are successfully simulated and show the efficient down-scaling over the area of interest the U.S. An imitation of the nested grid approach is performed using the developed SG-DAS (Data Assimilation System) that incorporates the SG-GCM. The SG-DAS is run with withholding data over the area of interest. The design immitates the nested grid framework with boundary conditions provided from analyses. No boundary condition buffer is needed for the case due to the global domain of integration used for the SG-GCM and SG-DAS. The experiments based on the newly developed versions of the GEOS SG-GCM and SG-DAS, with finer 0.5 degree (and higher) regional resolution, are briefly discussed. The major aspects of parallelization of the SG-GCM code are outlined. The KEY OBJECTIVES of the study are: 1) obtaining an efficient DOWN-SCALING over the area of interest with fine and very fine resolution; 2) providing CONSISTENT interactions between regional and global scales including the consistent representation of regional ENERGY and WATER BALANCES; 3) providing a high computational efficiency for future SG-GCM and SG-DAS versions using PARALLEL codes.

Fox-Rabinovitz, Michael S.↗

NASA NTRSDate not supplied

L'Ralph's Advanced Thermal Model Correlation Using Veritrek

Thermal model correlation uses data from thermal balance tests to better estimate uncertain input parameter values. During the correlation process, input parameters are modified in an iterative manner which can become computationally expensive since this requires that the high-fidelity thermal model be run for each iteration. Depending on the number of thermal balance test points there can be many sets of correlation parameters that satisfy correlation criteria; and having enough data to ascertain the best set of correlation parameters to use, further increases the computational expense. Reduced-order models (ROMs) provide computationally efficient surrogates of high-fidelity models and are often built to reduce development cycle times and cost. By leveraging the speed of reduced-order models and the Correlation Analysis feature in the Veritrek software, the typical computational expense of a traditional thermal model correlation process can be significantly reduced and having access to hundreds of thousands of iteration results provides an advanced means of intelligently determining the best set of correlation parameters to use. The L’Ralph thermal team at NASA Goddard Space Flight Center explored the use of the Veritrek software for their thermal model correlation efforts. The ROM that was created allowed for the variation of 15 input parameters to match 70 temperature sensor readouts from 3 thermal balance plateus and required 125 runs of the high-fidelity Thermal Desktop® model to generate a ROM that could predict the detailed model’s results to within 0.2 K (RMS). The ROM was then used to find dozens of plausible correlation parameter values based on L’Ralph instrument test data within a few seconds. By providing several plausible correlation parameter combinations, Veritrek allowed the thermal team to explore different uncertain parameter value combinations and provided insight into how deterministic each input parameter was. This allowed for a more confident decision on the best set of correlation parameters to use, compared to traditional model correlation techniques. In this presentation, the L’Ralph thermal team will be presenting their experience with the Veritrek software and how the software was utilized to provide additional insights during the correlation process.

Daniel Bae↗

NASA NTRSDate not supplied

L'Ralph's Advanced Thermal Model Correlation Using Veritrek

Thermal model correlation uses data from thermal balance tests to better estimate uncertain input parameter values. During the correlation process, input parameters are modified in an iterative manner which can become computationally expensive since this requires that the high-fidelity thermal model be run for each iteration. Depending on the number of thermal balance test points there can be many sets of correlation parameters that satisfy correlation criteria; and having enough data to ascertain the best set of correlation parameters to use, further increases the computational expense. Reduced-order models (ROMs) provide computationally efficient surrogates of high-fidelity models and are often built to reduce development cycle times and cost. By leveraging the speed of reduced-order models and the Correlation Analysis feature in the Veritrek software, the typical computational expense of a traditional thermal model correlation process can be significantly reduced and having access to hundreds of thousands of iteration results provides an advanced means of intelligently determining the best set of correlation parameters to use. The L’Ralph thermal team at NASA Goddard Space Flight Center explored the use of the Veritrek software for their thermal model correlation efforts. The ROM that was created allowed for the variation of 15 input parameters to match 70 temperature sensor readouts from 3 thermal balance plateus and required 125 runs of the high-fidelity Thermal Desktop® model to generate a ROM that could predict the detailed model’s results to within 0.2 K (RMS). The ROM was then used to find dozens of plausible correlation parameter values based on L’Ralph instrument test data within a few seconds. By providing several plausible correlation parameter combinations, Veritrek allowed the thermal team to explore different uncertain parameter value combinations and provided insight into how deterministic each input parameter was. This allowed for a more confident decision on the best set of correlation parameters to use, compared to traditional model correlation techniques. In this presentation, the L’Ralph thermal team will be presenting their experience with the Veritrek software and how the software was utilized to provide additional insights during the correlation process. "

Daniel Bae↗

NASA NTRS2011

Constraint Embedding Technique for Multibody System Dynamics

Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.

Woo, Simon S.↗

DOE OSTI2026

Arbitrary Polynomial Separations in Trainable Quantum Machine Learning

Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential separations in expressive power over classical machine learning models are believed to be infeasible as such QNNs take a time to train that is exponential in the model size. We here circumvent these negative results by constructing a hierarchy of efficiently trainable QNNs that exhibit unconditionally provable, polynomial memory separations of arbitrary constant degree over classical neural networks—including state-of-the-art models, such as Transformers—in performing a classical sequence modeling task. This construction is also computationally efficient, as each unit cell of the introduced class of QNNs only has constant gate complexity. We show that contextuality—informally, a quantitative notion of semantic ambiguity—is the source of the expressivity separation, suggesting that other learning tasks with this property may be a natural setting for the use of quantum learning algorithms.

Anschuetz, Eric R. [California Institute of Techno↗