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Analysis method utilizes graph-theoretic approach for evaluating computation cost and makes logical distinction between linear graph of a computation and linear graph of a program. It applies equally well to other processes which depend on quatitative edge nomenclature and precedence relationships between edges.
The identification of computational and experimental reduced-order models (ROMs) for the analysis of unsteady aerodynamic responses and for efficient aeroelastic analyses is presented. For the identification of a computational aeroelastic ROM, the CFL3Dv6.0 computational fluid dynamics (CFD) code is used. Flutter results for the AGARD 445.6 Wing and for a Rigid Semispan Model (RSM) computed using CFL3Dv6.0 are presented, including discussion of associated computational costs. Modal impulse responses of the unsteady aerodynamic system are computed using the CFL3Dv6.0 code and transformed into state-space form. The unsteady aerodynamic state-space ROM is then combined with a state-space model of the structure to create an aeroelastic simulation using the MATLAB/SIMULINK environment. The MATLAB/SIMULINK ROM is then used to rapidly compute aeroelastic transients, including flutter. The ROM shows excellent agreement with the aeroelastic analyses computed using the CFL3Dv6.0 code directly. For the identification of experimental unsteady pressure ROMs, results are presented for two configurations: the RSM and a Benchmark Supercritical Wing (BSCW). Both models were used to acquire unsteady pressure data due to pitching oscillations on the Oscillating Turntable (OTT) system at the Transonic Dynamics Tunnel (TDT). A deconvolution scheme involving a step input in pitch and the resultant step response in pressure, for several pressure transducers, is used to identify the unsteady pressure impulse responses. The identified impulse responses are then used to predict the pressure responses due to pitching oscillations at several frequencies. Comparisons with the experimental data are then presented.
The hybrid Finite Element Method(FEM)/Method of Moments(MoM) technique has become popular over the last few years due to its flexibility to handle arbitrarily shaped objects with complex materials. One of the disadvantages of this technique, however, is the computational cost involved in obtaining solutions over a frequency range as computations are repeated for each frequency. In this paper, the application of Model Based Parameter Estimation (MBPE) method[1] with the hybrid FEM/MoM technique is presented for fast computation of frequency response of cavity-backed apertures[2,3]. In MBPE, the electric field is expanded in a rational function of two polynomials. The coefficients of the rational function are obtained using the frequency-derivatives of the integro-differential equation formed by the hybrid FEM/MoM technique. Using the rational function approximation, the electric field is calculated at different frequencies from which the frequency response is obtained.
Several FORTRAN codes have been written to implement the reformulated version of the high-fidelity generalized method of cells (HFGMC). Various aspects of the HFGMC and its predecessors were described in several prior NASA Tech Briefs articles, the most recent being HFGMC Enhancement of MAC/GMC (LEW-17818-1), NASA Tech Briefs, Vol. 30, No. 3 (March 2006), page 34. The HFGMC is a mathematical model of micromechanics for simulating stress and strain responses of fiber/matrix and other composite materials. The HFGMC overcomes a major limitation of a prior version of the GMC by accounting for coupling of shear and normal stresses and thereby affords greater accuracy, albeit at a large computational cost. In the reformulation of the HFGMC, the issue of computational efficiency was addressed: as a result, codes that implement the reformulated HFGMC complete their calculations about 10 times as fast as do those that implement the HFGMC. The present FORTRAN implementations of the reformulated HFGMC were written to satisfy a need for compatibility with other FORTRAN programs used to analyze structures and composite materials. The FORTRAN implementations also afford capabilities, beyond those of the basic HFGMC, for modeling inelasticity, fiber/matrix debonding, and coupled thermal, mechanical, piezo, and electromagnetic effects.
Composite material systems generally exhibit a range of behavior on different length scales (from constituent level to macro); therefore, a multiscale framework is beneficial for the design and engineering of these material systems. The complex nature of the observed composite failure during experiments suggests the need for a three-dimensional (3D) multiscale model to attain a reliable prediction. However, the size of a multiscale three-dimensional finite element model can become prohibitively large and computationally costly. Two-dimensional (2D) models are preferred due to computational efficiency, especially if many different configurations have to be analyzed for an in-depth damage tolerance and durability design study. In this study, various 2D and 3D multiscale analyses will be employed to conduct a detailed investigation into the tensile failure of a given multidirectional, notched carbon fiber reinforced polymer laminate. Threedimensional finite element analysis is typically considered more accurate than a 2D finite element model, as compared with experiments. Nevertheless, in the absence of adequate mesh refinement, large differences may be observed between a 2D and 3D analysis, especially for a shear-dominated layup. This observed difference has not been widely addressed in previous literature and is the main focus of this paper.
We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.
The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. Here, we validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer’s disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.
We present a numerical modeling workflow based on machine learning (ML) which reproduces the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.
In this study, we aim to advance the structural analysis of wire and arc additive manufacturing (WAAM) by considering the thermomechanical features inherent in direct energy deposition. Simulation approaches including the iterative substructure method (ISM), dynamic mesh refining method (DMRM), and graphics processing unit (GPU) based explicit finite element method (FEM) were developed for accelerating additive manufacturing stress analysis that is very time consuming by conventional numerical methods. ISM and DMRM take advantage of the strong nonlinearity phenomenon near the moving heat source by reducing the global iterations and refining the local mesh, respectively. In addition to the use of GPUs, the explicit FEM is accelerated by a time scaling technique based on the inherent strain concept. The residual stress and distortion of two large builds were analyzed, showing very consistent numerical results and good agreement with experiments. Compared with the commercial software Abaqus, the novel approaches reduced the computational cost substantially without compromising accuracy. The GPU code showed the highest computational efficiency (30~70×), while DMRM and ISM had acceleration factors of 9× and 3×, respectively. Finally, such high-fidelity modeling approaches will be very useful for building up a digital twin of WAAM to reduce development time and cost.
Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.
To date, while the use of CFD for aerospace vehicle design and development is prevalent, the documentation of uncertainties associated with the simulations are rare. Instead, the current state-of-the-art relies heavily on the experience of the CFD practitioner to estimate the uncertainty associated with their simulations through simple sensitivity studies or subject matter expertise. This practice will have to be replaced with a formal uncertainty quantification (UQ) process if CFD is to play an expanded role in the research and engineering design community, test and evaluation community, and ultimately certification for flight. Accounting for uncertainties in a formal manner is a tedious process. Moreover, the typical CFD practitioner is not likely to be familiar with formal UQ methods. These factors have prevented the adoption of UQ methods in the engineering design and development cycle. This presentation will outline a credible approach to UQ using Probability Boxes that is straightforward to apply, and can readily be automated using existing UQ tool sets such as the DAKOTA packaged developed at Sandia. The added expense incurred when moving away from a deterministic CFD process to a stochastic one that captures uncertainties to enable risk-informed decision making will be discussed, as well as effective ways to reduce the computational costs.
The quasilinear diffusion coefficient (D QL ) derived from our machine learning framework shows comparable trends with the ground truth D QL obtained from GENRAY-CQL3D simulations. Additionally, for the strong absorption cases, the radial current drive profiles generated using the D QL from our model exhibit consistent behavior with those obtained from the original simulation. These findings indicate the potential of our surrogate modeling approach with physical restrictions to replicate key wave–plasma interaction characteristics while reducing computational costs. Traditionally, calculating D QL for wave–particle interactions relies on computationally intensive wave simulations coupled with Fokker–Planck solvers. To address this challenge, we developed a machine learning-based surrogate model with physical restrictions derived from cold plasma theory and bounce-averaged damping effects. First, we establish the propagation domain of Lower Hybrid Waves in the (N∥, ρ) space by identifying the accessibility limit and determining the upper and lower bounds of N∥ using the Potential Power Deposition (PPD) method. Subsequently, leveraging a database constructed using Latin hypercube sampling alongside the underlying physical restrictions (e.g. PPD), machine learning methods including U-Net and Recurrent Neural Networks are employed to design a physics-restricted machine learning framework capable of reconstructing D QL .
Economic dispatch in multi-microgrid (MMG) systems requires coordinating distributed energy resources (DERs) of different microgrids, which leads to a significant increase in the number of states for energy management. In these cases, traditional reinforcement learning (RL) approaches become computationally expensive or output a solution that causes extra-operating costs for the system. This paper proposes an RL approach that employs local learning agents to interact with microgrid environments in a distributed manner and aggregates the outcomes to train the global agent to learn the policy for the MMG system. This distributed exploration and aggregation process provides an effective solution and guides the global agent to learn the dispatch policy efficiently. Case studies are performed on a system with three microgrids with different types of DERs. Results obtained using the proposed RL and comparisons with conventional methods substantiate the effectiveness of the proposed approach in terms of operation costs, computation time, and peak-to-average ratio.
Neural network molecular dynamics (NNMD) simulations could revolutionize atomistic modeling of materials with quantum-mechanical accuracy at a fraction of computational cost. However, popular NNMD frameworks are generally implemented for a single computing node, and conventional energy-based NN models still suffer from large time-to-solution (T2S), prohibiting the application of NNMD to challenging materials simulations encompassing large spatiotemporal scales. Consequently, no leadership-scale NNMD simulation has thus far been reported. Here, we present a scalable parallel NNMD software (RXMD-NN) based on our scalable reactive molecular dynamics simulation engine named RXMD. RXMD-NN has achieved high scalability up to 786,432 IBM BlueGene/Q cores involving 1.7 billion atoms. Furthermore, we have achieved 4.6-fold reduction of T2S by using a novel network that directly predicts atomic forces from feature vectors. Reduced T2S has for the first time allowed the study of large-scale off-stoichiometry effect in a widely used phase change material, Ge 2 Se 2 Te 5 , thereby resolving its "firstsharp diffraction peak mystery".
Abstract Graph Convolutional Neural Network (GCNN) is a popular class of deep learning (DL) models in material science to predict material properties from the graph representation of molecular structures. Training an accurate and comprehensive GCNN surrogate for molecular design requires large-scale graph datasets and is usually a time-consuming process. Recent advances in GPUs and distributed computing open a path to reduce the computational cost for GCNN training effectively. However, efficient utilization of high performance computing (HPC) resources for training requires simultaneously optimizing large-scale data management and scalable stochastic batched optimization techniques. In this work, we focus on building GCNN models on HPC systems to predict material properties of millions of molecules. We use HydraGNN, our in-house library for large-scale GCNN training, leveraging distributed data parallelism in PyTorch. We use ADIOS, a high-performance data management framework for efficient storage and reading of large molecular graph data. We perform parallel training on two open-source large-scale graph datasets to build a GCNN predictor for an important quantum property known as the HOMO-LUMO gap. We measure the scalability, accuracy, and convergence of our approach on two DOE supercomputers: the Summit supercomputer at the Oak Ridge Leadership Computing Facility (OLCF) and the Perlmutter system at the National Energy Research Scientific Computing Center (NERSC). We present our experimental results with HydraGNN showing (i) reduction of data loading time up to 4.2 times compared with a conventional method and (ii) linear scaling performance for training up to 1024 GPUs on both Summit and Perlmutter.
A reduced-order model (ROM) is developed for aeroelastic analysis using the CFL3D version 6.0 computational fluid dynamics (CFD) code, recently developed at the NASA Langley Research Center. This latest version of the flow solver includes a deforming mesh capability, a modal structural definition for nonlinear aeroelastic analyses, and a parallelization capability that provides a significant increase in computational efficiency. Flutter results for the AGARD 445.6 Wing computed using CFL3D v6.0 are presented, including discussion of associated computational costs. Modal impulse responses of the unsteady aerodynamic system are then computed using the CFL3Dv6 code and transformed into state-space form. Important numerical issues associated with the computation of the impulse responses are presented. The unsteady aerodynamic state-space ROM is then combined with a state-space model of the structure to create an aeroelastic simulation using the MATLAB/SIMULINK environment. The MATLAB/SIMULINK ROM is used to rapidly compute aeroelastic transients including flutter. The ROM shows excellent agreement with the aeroelastic analyses computed using the CFL3Dv6.0 code directly.
We present a computational model based on the hypothesis that the higher-than-expected electron mobility across magnetic field lines observed in Hall thrusters is due to the growth and eventual saturation of the electron cyclotron drift instability. The key improvement of this model with respect to previous work is that it decouples the saturation of the instability from the correlation that exists between mobility and magnitude of the wave perturbations in linear theory, thereby enabling first-principles simulations. The model has been incorporated in the 2-D (r-z) multi-fluids code Hall2De and simulations of the H6 thruster at 300 V, 20 A are numerically stable and achieve a steady-state solution at a computational cost that is not significantly higher than previous Hall2De simulations. The computed location of the acceleration region is found to be within 10% of the length of the acceleration channel compared to that inferred by experiments. The simulations also capture well the plasma gradients along the channel centerline of this thruster. To further establish the validity of this model, we plan to conduct simulations of other thrusters and/or operating conditions.
Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light–matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori–Nakajima–Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method’s capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.