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

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A backward SDE method for uncertainty quantification in deep learning

Here, we develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

TriC: Distributed-memory Triangle Counting by Exploiting the Graph Structure

Graph analytics has emerged as an important tool in the analysis of large scale data from diverse application domains such as social networks, cyber security and bioinformatics. Counting the number of triangles in a graph is a fundamental kernel with several applications such as detecting the community structure of a graph or in identifying important vertices in a graph. The ubiquity of massive datasets is driving the need to scale graph analytics on parallel systems. However, numerous challenges exist in efficiently parallelizing graph algorithms, especially on distributed-memory systems. Irregular memory accesses and communication patterns, low computation to communication ratios, and the need for frequent synchronization are some of the leading challenges. In this paper, we present TriC, our distributed-memory implementation of triangle counting in graphs using the Message Passing Interface (MPI), as a submission to the 2020 GraphChallenge competition. Using a set of synthetic and real-world inputs from the challenge, we demonstrate a speedup of up to 90x relative to previous work on 32 processor-cores of a NERSC Cori node. We also provide details from distributed runs with up to8192 processes along with strong scaling results. The observations presented in this work provide an understanding of the system-level bottlenecks at scale that specifically impact sparse-irregular workloads and will therefore benefit other efforts to parallelize graph algorithms.

Halappanavar, Mahantesh↗
DOE OSTI2019

Modeling Mesoscale Processes of Scalable Synthesis (Final Report)

The main objective of the center is to develop tools that can help for the understanding of equilibrium and non-equilibrium properties of nanoparticles in aqueous electrolytes. To achieve this goal, we need to develop new computational methodologies that can integrate molecular level description such as the electronic structure analysis to mesoscale description such as generalized hydrodynamics. The challenge is to develop systematic coarse graining techniques that can adaptively choose the level of description needed for the particular task. For example, if bonding breaking is involved, then one should use appropriate models from quantum mechanics to accurately model the time scale and molecular mechanism for the breaking process. However, to model transport process or the process of self-assembly, much less detailed models can be used. There are two main components to this task. One is to develop accurate models that bridge different levels of description. The classical example is the QM/MM model that bridges quantum mechanics and molecular mechanics for studying chemical reactions of large molecules. This work was awarded the Nobel prize this year. For our purpose, we also need to develop methods that bridge molecular and continuum levels of description. Another main task is to develop systematic coarse-graining methods that can give rise to accurate mesoscale and macroscale models, starting from more detailed models at the atomic or molecular scale. None of these ideas are new. By now they have been fashionable topics for quite some time. But neither problem is satisfactorily resolved. The main problem is that uncontrolled approximations are used. As a result, we have very little idea about the validity and accuracy of these models. The main purpose of the center is to exploit the Mori-Zwanzig formalism to achieve the goals stated above. The Mori-Zwanzig formalism is a general tool for eliminating degrees of freedom from existing models. What is attractive about this formalism is its generality. The flip side is that it is also somewhat of a tautology. In order to make it a practical tool, one has to make approximations and this is where the trouble comes. Instead of focusing on Mori-Zwanzig formalism, the PI proposes to study the closely related renormalization group formalism (RG). Like Mori-Zwanzig, RG is a general strategy for eliminating small scale degrees of freedom in a model. Unlike Mori-Zwanzig, RG has the advantage that at least for some problems, one can write a PDE (partial differential equation) type of model for the exact RG flow, without any approximation. This gives us a solid starting point for discussing and analyzing approximations. The PI studied approximate RG flows for turbulent diffusion and related problems. However, extending it to more practical problems proved to be hard. The second line that the PI has pursued is to develop special numerical algorithms for studying particularly important events for dynamics processes in meso-scale systems. The PI succeeded in doing so for the problem of understanding phase transition in metallic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms

Here, we present the numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012). Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influence of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier–Stokes equations, with a highly parallel fast multipole method (fmm) as numerical engine, and match the current record in mesh size for this application, a cube of computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the fft algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm-based vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpus per node of the tsubame-2.0 system). The fft-based spectral method is able to achieve just 14% parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the fft algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

Computer Science↗
DOE OSTI2020

Improving climate model coupling through a complete mesh representation: a case study with E3SM (v1) and MOAB (v5.x)

One of the fundamental factors contributing to the spatiotemporal inaccuracy in climate modeling is the mapping of solution field data between different discretizations and numerical grids used in the coupled component models. The typical climate computational workflow involves evaluation and serialization of the remapping weights during the preprocessing step, which is then consumed by the coupled driver infrastructure during simulation to compute field projections. Tools like Earth System Modeling Framework (ESMF) and TempestRemap offer capability to generate conservative remapping weights, while the Model Coupling Toolkit (MCT) that is utilized in many production climate models exposes functionality to make use of the operators to solve the coupled problem. However, such multistep processes present several hurdles in terms of the scientific workflow and impede research productivity. In order to overcome these limitations, we present a fully integrated infrastructure based on the Mesh Oriented datABase (MOAB) library, which allows for a complete description of the numerical grids and solution data used in each submodel. Through a scalable advancing-front intersection algorithm, the supermesh of the source and target grids are computed, which is then used to assemble the high-order, conservative, and monotonicity-preserving remapping weights between discretization specifications. The Fortran-compatible interfaces in MOAB are utilized to directly link the submodels in the Energy Exascale Earth System Model (E3SM) to enable online remapping strategies in order to simplify the coupled workflow process. We demonstrate the superior computational efficiency of the remapping algorithms in comparison with other state-of-the-science tools and present strong scaling results on large-scale machines for computing remapping weights between the spectral element atmosphere and finite volume discretizations on the polygonal ocean grids.

58 GEOSCIENCES↗
DOE OSTI2016

Hybrid framework for the simulation of stochastic chemical kinetics

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

IoGET: Internet of Geophysical and Environmental Things

The objective of this project is to provide novel and fast reduced-order models for onboard computation at sensor nodes for real-time analysis. The approach will require that LANL perform high-fidelity numerical simulations, construct simple reduced-order models (ROMs) using machine learning and signal processing algorithms, and use real-time data analysis for ROMs and compressive sensing at sensor nodes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Optimization and supervised machine learning methods for fitting numerical physics models without derivatives

Here, we address the calibration of a computationally expensive nuclear physics model for which derivative information with respect to the fit parameters is not readily available. Of particular interest is the performance of optimization-based training algorithms when dozens, rather than millions or more, of training data are available and when the expense of the model places limitations on the number of concurrent model evaluations that can be performed. As a case study, we consider the Fayans energy density functional model, which has characteristics similar to many model fitting and calibration problems in nuclear physics. We analyze hyperparameter tuning considerations and variability associated with stochastic optimization algorithms and illustrate considerations for tuning in different computational settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Efficient spectral and pseudospectral algorithms for 3D simulations of whistler-mode waves in a plasma

Efficient spectral and pseudospectral algorithms for simulation of linear and nonlinear 3D whistler waves in a cold electron plasma are developed. These algorithms are applied to the simulation of whistler waves generated by loop antennas and spheromak-like stationary waves of considerable amplitude. The algorithms are linearly stable and show good stability properties for computations of nonlinear waves over tens of thousands of time steps. Additional speedups by factors of 10-20 (comparing single core CPU and one GPU) are achieved by using graphics processors (GPUs), which enable efficient numerical simulation of the wave propagation on relatively high resolution meshes (tens of millions nodes) in personal computing environment. Comparisons of the numerical results with analytical solutions and experiments show good agreement. The limitations of the codes and the performance of the GPU computing are discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading

Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count. Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 2048 3 on a single node to 32768 3 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 2048 3 where communication is entirely intra-node, and for 32768 3 , where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 32768 3 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.

3D fast Fourier transform↗
DOE OSTI2020

A geospatial model for the analysis of time-dependent land subsidence induced by reservoir depletion

Land subsidence due to fluid depletion is an outcome of physical processes operating across a wide range of time and length scales. Although geomechanical models are crucial to simulate reservoir compaction and predict its long-term fate, their use across large regions often bears prohibitive computational costs. To overcome this obstacle, this paper proposes a simplified modelling framework consisting of (i) a near-field numerical solver simulating the coupling between fluid flow and rock deformation with reference to a simplified one-dimensional geometry and (ii) a far-field geospatial algorithm mapping ground settlements across a region through the superposition of poroelastic computations at multiple wells. The model computes the delay between depletion history and reservoir compaction in proximity of a producing well by assuming basal depletion of a fluid-saturated deformable disk, while the Geertsma solution of nucleus of strain is used to extrapolate the impact of such time-varying reservoir compaction around the well. This approach has been used to back-analyze the spatio-temporal progression of subsidence at the Groningen gas field. The results are compared against measurements collected over 50 year of production at 25 benchmark locations scattered over an area of 900 km 2 . It is shown that coupled simulations based on average values of rock compressibility and permeability lead to nonlinear trends of subsidence evolution in good agreement with field measurements, while uncoupled analyses overpredict settlements by more than 70%. Lastly, synthetic forecasts based on different rates of depletion were provided. The results suggest that slower depletion rates lead to lower subsidence at a given time, and that residual subsidence may continue to develop for several decades after interruption of production activities.

58 GEOSCIENCES↗
DOE OSTI2015

Learn-as-you-go acceleration of cosmological parameter estimates

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

Over the recent decades, a number of fast approximate solutions of Lippmann–Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamic mode decomposition with core sketch

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Ab-initio Calculations of Absorption Spectra of Semiconducting Nanowires Within Many Body Perturbation Theory

We present a study of the optical absorption spectra of thin silicon nanowires using many-body perturbation theory. We solve the Bethe-Salpeter equation in the static approximation using a technique that avoids explicit calculation of empty electronic states, as well as storage and inversion of the dielectric matrix. We provide a detailed assessment of the numerical accuracy of this technique, when using plane wave basis sets and periodically repeated supercells. Our calculations show that establishing numerical error bars of computed spectra is critical, in order to draw meaningful comparisons with experiments and between results obtained within different algorithms. We also discuss the influence of surface structure on the absorption spectra of nanowires with {approx_equal}1-nm diameter. Finally, we compare our calculations with those obtained within time-dependent density functional theory and find substantial differences, more pronounced than in the case of Si nanoparticles with the same diameter.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Localized Evaluation for Constructing Discrete Vector Fields

Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. Here, we couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

A hybrid approach for rapid, accurate, and direct kilovoltage radiation dose calculations in CT voxel space

Purpose: To develop and validate a fast and accurate method that uses computed tomography (CT) voxel data to estimate absorbed radiation dose at a point of interest (POI) or series of POIs from a kilovoltage (kV) imaging procedure. Methods: The authors developed an approach that computes absorbed radiation dose at a POI by numerically evaluating the linear Boltzmann transport equation (LBTE) using a combination of deterministic and Monte Carlo (MC) techniques. This hybrid approach accounts for material heterogeneity with a level of accuracy comparable to the general MC algorithms. Also, the dose at a POI is computed within seconds using the Intel Core i7 CPU 920 2.67 GHz quad core architecture, and the calculations are performed using CT voxel data, making it flexible and feasible for clinical applications. To validate the method, the authors constructed and acquired a CT scan of a heterogeneous block phantom consisting of a succession of slab densities: Tissue (1.29 cm), bone (2.42 cm), lung (4.84 cm), bone (1.37 cm), and tissue (4.84 cm). Using the hybrid transport method, the authors computed the absorbed doses at a set of points along the central axis and x direction of the phantom for an isotropic 125 kVp photon spectral point source located along the central axis 92.7 cm above the phantom surface. The accuracy of the results was compared to those computed with MCNP, which was cross-validated with EGSnrc, and served as the benchmark for validation. Results: The error in the depth dose ranged from -1.45% to +1.39% with a mean and standard deviation of -0.12% and 0.66%, respectively. The error in the x profile ranged from -1.3% to +0.9%, with standard deviations of -0.3% and 0.5%, respectively. The number of photons required to achieve these results was 1x10{sup 6}. Conclusions: The voxel-based hybrid method evaluates the LBTE rapidly and accurately to estimate the absorbed x-ray dose at any POI or series of POIs from a kV imaging procedure.

60 APPLIED LIFE SCIENCES↗