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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Training data selection for accuracy and transferability of interatomic potentials

Abstract Advances in machine learning (ML) have enabled the development of interatomic potentials that promise the accuracy of first principles methods and the low-cost, parallel efficiency of empirical potentials. However, ML-based potentials struggle to achieve transferability, i.e., provide consistent accuracy across configurations that differ from those used during training. In order to realize the promise of ML-based potentials, systematic and scalable approaches to generate diverse training sets need to be developed. This work creates a diverse training set for tungsten in an automated manner using an entropy optimization approach. Subsequently, multiple polynomial and neural network potentials are trained on the entropy-optimized dataset. A corresponding set of potentials are trained on an expert-curated dataset for tungsten for comparison. The models trained to the entropy-optimized data exhibited superior transferability compared to the expert-curated models. Furthermore, the models trained to the expert-curated set exhibited a significant decrease in performance when evaluated on out-of-sample configurations.

36 MATERIALS SCIENCE↗
DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗
DOE OSTI2020

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code was efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Stochastic evaluation of fourth-order many-body perturbation energies

A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green’s functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n 5.3 ) size-dependence of cost, which is nearly two ranks lower than the O(n 7 ) dependence of the deterministic MP4 algorithm. Furthermore, it evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mE h (1.1% of the total basis-set correlation energy), 38 mE h (2.6%), 110 mE h (5.5%), and 280 mE h (9.0%), respectively, after about 10 9 MC steps.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

GPU acceleration of rank-reduced coupled-cluster singles and doubles

Here, we have developed a graphical processing unit (GPU) accelerated implementation of our recently introduced rank-reduced coupled-cluster singles and doubles (RR-CCSD) method. RR-CCSD introduces a low-rank approximation of the doubles amplitudes. This is combined with a low-rank approximation of the electron repulsion integrals via Cholesky decomposition. The result of these two low-rank approximations is the replacement of the usual fourth-order CCSD tensors with products of second- and third-order tensors. In our implementation, only a single fourth-order tensor must be constructed as an intermediate during the solution of the amplitude equations. Owing in large part to the compression of the doubles amplitudes, the GPU-accelerated implementation shows excellent parallel efficiency (95% on eight GPUs). Our implementation can solve the RR-CCSD equations for up to 400 electrons and 1550 basis functions—roughly 50% larger than the largest canonical CCSD computations that have been performed on any hardware. In addition to increased scalability, the RR-CCSD computations are faster than the corresponding CCSD computations for all but the smallest molecules. We test the accuracy of RR-CCSD for a variety of chemical systems including up to 1000 basis functions and determine that accuracy to better than 0.1% error in the correlation energy can be achieved with roughly 95% compression of the ov space for the largest systems considered. We also demonstrate that conformational energies can be predicted to be within 0.1 kcal mol -1 with efficient compression applied to the wavefunction. Finally, we find that low-rank approximations of the CCSD doubles amplitudes used in the similarity transformation of the Hamiltonian prior to a conventional equation-of-motion CCSD computation will not introduce significant errors (on the order of a few hundredths of an electronvolt) into the resulting excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within “chemical accuracy” (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob’s ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 − N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Chemistry↗
DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗
DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗
DOE OSTI2021

New method for detecting fast neutrino flavor conversions in core-collapse supernova models with two-moment neutrino transport

Fast-pairwise neutrino oscillations potentially affect many aspects of core-collapse supernovae (CCSNe): the explosion mechanism, neutrino signals, and nucleosynthesis in the ejecta. This particular mode of collective neutrino oscillations has a deep connection to the angular structure of neutrinos in momentum space; for instance, the appearance of electron-neutrino lepton number (ELN) angular crossings in momentum space is a good indicator of the occurrence of flavor conversions. However, many multidimensional CCSN simulations are carried out with approximate neutrino transport (such as two-moment methods), which limits access to the angular distributions of neutrinos, i.e., inhibits ELNcrossing searches. In this paper, we develop a new method of searching for ELN crossing in these CCSN simulations. The required data is the zeroth and first angular moments of neutrinos and the matter profile, all of which are available in CCSN models with the two-moment method. One of the novelties of our new method is the use of a ray-tracing neutrino transport to determine ELNs in the direction of the stellar center. It is designed to compensate for shortcomings of the crossing searches with only two angular moments. We assess the capability of the method by carrying out a detailed comparison with results of full Boltzmann neutrino transport in 1D and 2D CCSN models. In this work, we find that the ray-tracing neutrino transport improves the accuracy of crossing searches; indeed, the appearance/disappearance of the crossings is accurately detected even in the region of forward-peaked angular distributions. The new method is computationally cheap and has the benefit of efficient parallelization; hence, it will be useful for ELN-crossing searches in any CCSN models that employ two-moment neutrino transport.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Solving the electronic structure problem for over 100000 atoms in real space

Using a real-space high-order finite-difference approach, we investigate the electronic structure of large spherical silicon nanoclusters. Within Kohn-Sham density functional theory and using pseudopotentials, we report the self-consistent field convergence of a system with over 100000 atoms: a Si 107,641 ⁢H 9,084 nanocluster with a diameter of 16 nm. Our approach uses Chebyshev-filtered subspace iteration to speed up the convergence of the eigenspace, and blockwise Hilbert space-filling curves to speed up sparse matrix-vector multiplications, all of which are implemented in the parsec code. For the largest system, we utilized 2048 nodes (114 688 cores) on the Frontera machine in the Texas Advanced Computing Center. Our quantitative analysis of the electronic structure shows how it gradually approaches its bulk counterpart as a function of nanocluster size. The band gap is enlarged due to quantum confinement in nanoclusters, but decreases as the system size increases, as expected. In conclusion, our work serves as a proof of concept for the capacity of the real-space approach in efficiently parallelizing very large calculations using high-performance computer platforms, which can straightforwardly be replicated in other systems with more than 10 5 atoms.

0-dimensional systems↗
DOE OSTI2022

An Algorithmic and Software Pipeline for Very Large Scale Scientific Data Compression with Error Guarantees

Efficient data compression is becoming increasingly critical for storing scientific data because many scientific applications produce vast amounts of data. This paper presents an end-to-end algorithmic and software pipeline for data compression that guarantees both error bounds on primary data (PD) and derived data, known as Quantities of Interest (QoI).We demonstrate the effectiveness of the pipeline by compressing fusion data generated by a large-scale fusion code, XGC, which produces tens of petabytes of data in a single day. We demonstrate that the compression is conducted by setting aside computational resources known as staging nodes, and does not impact the simulation performance. For efficient parallel I/O, the pipeline uses ADIOS2, which many codes such as XGC already use for their parallel I/O. We show that our approach can compress the data by two orders of magnitude while guaranteeing high accuracy on both the PD and the QoIs. Further, the amount of resources required by compression is a few percent of the resources required by simulation while ensuring that the compression time for each stage is less than the corresponding simulation time.This pipeline consists of three main steps. The first step decomposes the data using domain decomposition into small subdomains. Each subdomain is then compressed independently to achieve a high level of parallelism. The second step uses existing techniques that guarantee error bounds on the primary data for each subdomain. The third step uses a post-processing optimization technique based on Lagrange multipliers to reduce the QoI errors for data corresponding to each subdomain. The Lagrange multipliers generated can be further quantized or truncated to increase the compression level. All of the above characteristics of our approach make it highly practical to apply on-the-fly compression while guaranteeing errors on QoIs that are critical to the scientists.

Banerjee, Tania↗
DOE OSTI2022

Exaflops Biomedical Knowledge Graph Analytics

We are motivated by newly proposed methods for mining large-scale corpora of scholarly publications (e.g., full biomedical literature), which consists of tens of millions of papers spanning decades of research. In this setting, analysts seek to discover relationships among concepts. They construct graph representations from annotated text databases and then formulate the relationship-mining problem as an all-pairs shortest paths (APSP) and validate connective paths against curated biomedical knowledge graphs (e.g., Spoke). In this context, we present Coast (Exascale Communication-Optimized All-Pairs Shortest Path) and demonstrate 1.004 EF/s on 9,200 Frontier nodes (73,600 GCDs). We develop hyperbolic performance models (HYPERMOD), which guide optimizations and parametric tuning. The proposed Coast algorithm achieved the memory constant parallel efficiency of 99% in the single-precision tropical semiring. Looking forward, Coast will enable the integration of scholarly corpora like PubMed into the Spoke biomedical knowledge graph.

Kannan, Ramakrishnan {ramki}↗
DOE OSTI2020

Scalable Knowledge Graph Analytics at 136 Petaflop/s

We are motivated by newly proposed methods for data mining large-scale corpora of scholarly publications, such as the full biomedical literature, which may consist of tens of millions of papers spanning decades of research. In this setting, analysts seek to discover how concepts relate to one another. They construct graph representations from annotated text databases and then formulate the relationship-mining problem as one of computing all-pairs shortest paths (APSP), which becomes a significant bottleneck. In this context, we present a new high-performance algorithm and implementation of the Floyd-Warshall algorithm for distributed-memory parallel computers accelerated by GPUs, which we call DSNAPSHOT (Distributed Accelerated Semiring All-Pairs Shortest Path). For our largest experiments, we ran DSNAPSHOT on a connected input graph with millions of vertices using 4, 096nodes (24,576GPUs) of the Oak Ridge National Laboratory's Summit supercomputer system. We find DSNAPSHOT achieves a sustained performance of 136×1015 floating-point operations per second (136petaflop/s) at a parallel efficiency of 90% under weak scaling and, in absolute speed, 70% of the best possible performance given our computation (in the single-precision tropical semiring or “min-plus” algebra). Looking forward, we believe this novel capability will enable the mining of scholarly knowledge corpora when embedded and integrated into artificial intelligence-driven natural language processing workflows at scale.

Kannan, Ramakrishnan {ramki}↗
DOE OSTI2023

Sparse Symmetric Format for Tucker Decomposition

Tensor-based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTM c ) in general sparse tensors, the $\underline{S}$ parse $\underline{S}$ ymmetric $\underline{T}$ ensor $\underline{T}$ imes $\underline{S}$ ame $\underline{M}$ atrix $\underline{c}$ hain (S 3 TTM c ) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S 3 TTM c operation. We theoretically establish that S 3 TTM c on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to 2.72× speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

42 ENGINEERING↗
DOE OSTI2023

ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

ArborX: A Performance Portable Geometric Search Library

Searching for geometric objects that are close in space is a fundamental component of many applications. The performance of search algorithms comes to the forefront as the size of a problem increases both in terms of total object count as well as in the total number of search queries performed. Scientific applications requiring modern leadership-class supercomputers also pose an additional requirement of performance portability, i.e., being able to efficiently utilize a variety of hardware architectures. In this article, we introduce a new open-source C++ search library, ArborX, which we have designed for modern supercomputing architectures. Herein, we examine scalable search algorithms with a focus on performance, including a highly efficient parallel bounding volume hierarchy implementation, and propose a flexible interface making it easy to integrate with existing applications. We demonstrate the performance portability of ArborX on multi-core CPUs and GPUs and compare it to the state-of-the-art libraries such as Boost.Geometry.Index and nanoflann.

97 MATHEMATICS AND COMPUTING↗