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At least 127 records · Page 7

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

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

HSW-V v1.0: localized injections of interactive volcanic aerosols and their climate impacts in a simple general circulation model

Abstract. A new set of standalone parameterizations is presented for simulating the injection, evolution, and radiative forcing by stratospheric volcanic aerosols against an idealized Held–Suarez–Williamson (HSW) atmospheric background in the Energy Exascale Earth System Model version 2 (E3SMv2). In this model configuration (HSW with enabled volcanism, HSW-V), sulfur dioxide (SO2) and ash are injected into the atmosphere with a specified profile in the vertical, and they proceed to follow a simple exponential decay. The SO2 decay is modeled as a perfect conversion to a long-living sulfate aerosol which persists in the stratosphere. All three species are implemented as tracers in the model framework and are transported by the dynamical core's advection algorithm. The aerosols contribute simultaneously to local heating of the stratosphere and cooling of the surface by a simple plane-parallel Beer–Lambert law applied on two zonally symmetric radiation broadbands in the longwave and shortwave ranges. It is shown that the implementation parameters can be tuned to produce realistic temperature anomaly signatures of large volcanic events. In particular, results are shown for an ensemble of runs that mimic the volcanic eruption of Mt. Pinatubo in 1991. The design requires no coupling to microphysical subgrid-scale parameterizations and thus approaches the computational affordability of prescribed aerosol forcing strategies. The idealized simulations contain a single isolated volcanic event against a statistically uniform climate, where no background aerosols or other sources of externally forced variability are present. HSW-V represents a simpler-to-understand tool for the development of climate source-to-impact attribution methods.

Hollowed, Joseph P. (ORCID:0000000286581672)

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation

Fragme∩t: An Open‐Source Framework for Multiscale Quantum Chemistry Based on Fragmentation

Fragment-based quantum chemistry offers a means to circumvent the nonlinear computational scaling of conventional electronic structure calculations, by partitioning a large calculation into smaller subsystems then considering the many-body interactions between them. Variants of this approach have been used to parameterize classical force fields and machine learning potentials, applications that benefit from interoperability between quantum chemistry codes. However, there is a dearth of software that provides interoperability yet is purpose-built to handle the combinatorial complexity of fragment-based calculations. To fill this void we introduce “Fragme∩t”, an open-source software application that provides a tool for community validation of fragment-based methods, a platform for developing new approximations, and a framework for analyzing many-body interactions. Fragme∩t includes algorithms for automatic fragment generation and structure modification, and for distance- and energy-based screening of the requisite subsystems. Checkpointing, database management, and parallelization are handled internally and results are archived in a portable database. Interfaces to various quantum chemistry engines are easy to write and exist already for Q-Chem, PySCF, xTB, Orca, CP2K, MRCC, Psi4, NWChem, GAMESS, and MOPAC. Applications reported here demonstrate parallel efficiencies around 96% on more than 1000 processors but also showcase that the code can handle large-scale protein fragmentation using only workstation hardware, all with a codebase that is designed to be usable by non-experts. Fragme∩t conforms to modern software engineering best practices and is built upon well established technologies including Python, SQLite, and Ray. The source code is available under the Apache 2.0 license.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

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)

Numerical eigen-spectrum slicing, accurate orthogonal eigen-basis, and mixed-precision eigenvalue refinement using OpenMP data-dependent tasks and accelerator offload

Performing a variety of numerical computations efficiently and, at the same time, in a portable fashion requires both an overarching design followed by a number of implementation strategies. All of these are exemplified below as we present transitioning the PLASMA numerical library from relying on dependence-driven large tasks to achieving utilization of fine grain tasking and offload to hardware accelerators while keeping its core dependence sets: OpenMP source code pragmas and runtime for most system-level functionality and basic low-level numerical kernels provided directly by hardware vendors or open source projects with vendor contributions. We also present new algorithmic methods and their efficient parallel implementations including fine grained tasking for eigen-spectrum slicing and offload for mixed-precision eigenvalue refinement. We provide performance, scaling, and numerical results showing sizable gains over the available solutions from either the open source and vendor-provided packages.

Luszczek, Piotr

A semi-automated algorithm for designing stellarator divertor and limiter plates and application to HSX

We present a semi-automated algorithm for designing three-dimensional divertor or limiter plates targeting low heat loads. The algorithm designs the plates in two stages: firstly, the parallel heat flux distribution is caught on vertically-inclined plates at one or several toroidal locations. Secondly, the power per unit area is reduced by stretching, tilting and bending the plates toroidally. Heat transport is modelled using the EMC3-Lite code, which uses an anisotropic diffusion model. We apply this scheme to HSX, a medium-sized stellarator located at the University of Wisconsin–Madison. Starting from the current machine with an extended vessel wall, we construct plates which are able to effectively catch and spread the heat for three different magnetic configurations. The scheme has a computational cost in the order of tens of CPU-minutes, making it a powerful tool for semi-automated plasma-facing component design in three-dimensional environments.

anisotropic diffusion

In situ multi-tier auto-ignition detection applied to dual-fuel combustion simulations

Here we use an anomaly detection methodology that is centered on analyzing fourth-order joint moments (co-kurtosis), particularly focusing on its application in auto-ignition of combustion problems with large numbers of species. Unsupervised anomaly detection is challenging to generalize across problem types and domains. A recent technique, centered on analyzing information in the fourth-order joint moment co-kurtosis, has shown promise, especially for high-dimensional scientific data. In this work we present developments to the co-kurtosis based anomaly detection method needed to make it effective and scalable for large-scale distributed scientific data, such as those generated by massively parallel simulations. An in situ co-kurtosis algorithm is employed as the anomaly detection method for identifying ignition kernels in simulations of turbulent combustion. Here, we extend an existing methodology which identifies regions of the domain where anomalies are present, and add another tier of anomaly detection where the individual samples contributing to the anomaly are identified. We apply this algorithm on-the-fly to a variety of turbulent reacting flow problems and compare it to the widely used (but significantly more expensive) chemical explosive mode analysis (CEMA). We demonstrate the ability of the method to detect and identify the onset of low and high temperature ignition which can be used for computational steering, as chemical and combustion anomalies occur intermittently at spatio-temporal locations unknown a priori. Finally, we apply our lightweight in situ algorithm to an exascale high-fidelity simulation with a total of 2.4 Trillion degrees of freedom, performed using an adaptive mesh refinement solver. Furthermore, through a scalability analysis, we show that the relative computational cost of this in-situ anomaly detection algorithm compared to an iteration of the reacting flow solver is negligible.

97 MATHEMATICS AND COMPUTING

A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

The influence of the internal structure at micrometer length scales on the deformation of polycrystalline materials can be effectively captured using crystal plasticity finite element methods (CPFEM). However, the complexity and nonlinearity of the deformation equations CPFEM solves demand significant computational power and resources to achieve accurate predictions, limiting its broader application. To address this challenge, we have identified a reduced-order representation of the complex data in order to establish a computationally efficient reduced-order models (ROM) and drastically reduce the computational expense of CPFEM. Specifically, in this work, we developed a parametric, data-driven, and non-intrusive ROM framework for CPFEM using proper orthogonal decomposition (POD) and sparse variational Gaussian process (SVGP) regression for single-crystal microstructures under tensile loading conditions. The developed protocol enables one to compress field into a latent/low-dimensional space described by principal component analysis (PCA) via the singular value decomposition (SVD) algorithm. As a result, the high-dimensional data are reduced to a significantly smaller amount of dimensions with POD bases and POD coefficients. Furthermore, we deployed an ensemble of SVGPs—extended from the classical Gaussian process (GP) regression for scalability and handling big data—in a massively parallel manner to train and predict latent POD coefficients using known POD bases from a set of previously obtained simulations results. Lastly, using the predicted POD coefficients, we reconstructed the full-field results and showed reasonable agreement compared with the true values obtained from running CPFEM. The developed framework is validated with a set of CPFEM simulations of a single embedded void in single-crystal aluminum alloy. While the framework is broadly applicable, this work specifically focuses on single-crystal microstructures, a single load case (e.g., tensile), and a specific void geometry (spherical).

Anisotropy

Contextual subspace variational quantum eigensolver calculation of the dissociation curve of molecular nitrogen on a superconducting quantum computer

Abstract We present an experimental demonstration of the Contextual Subspace Variational Quantum Eigensolver on superconducting hardware. Calculating the potential energy curve of molecular nitrogen proves challenging for many conventional quantum chemistry techniques, since static correlation dominates in the dissociation limit. Our quantum simulations retain good agreement with the Full Configuration Interaction energy, outperforming all benchmarked single-reference wavefunction techniques in capturing the bond-breaking appropriately. Moreover, our methodology is competitive with multiconfigurational approaches but at a saving of quantum resource, meaning larger active spaces can be treated for a fixed qubit allowance. To achieve this result, we deploy an error mitigation/suppression strategy comprised of Dynamical Decoupling, Measurement-Error Mitigation and Zero-Noise Extrapolation. Circuit parallelization also provides passive noise-averaging and improves the effective shot yield to reduce the measurement overhead. Furthermore, we introduce a modified adaptive ansatz construction algorithm that incorporates hardware awareness into our variational circuits, minimizing the transpilation cost for the target qubit topology.

Physics

Enhanced PDV waveform search and analysis method using parallel circular-convolution / cross-correlation for improved dynamic surface velocity extraction [Poster]

Previous work on exhaustive search methodologies for extracting best-match parameters pertaining to dynamic surface quantities from PDV was done by cross-correlating synthetically generated PDV waveforms with observed counterparts using the circular-convolution theorem. This work was further developed into an open-source PDV analysis toolkit called CCPDVANALYSIS which expands upon and enhances the previously tested methods by parallelizing serial algorithmic components and incorporating a comprehensive script library for different flavors of instantaneous frequency functions utilized in generating synthetic PDV waveforms. Results of these enhancements have been shown to markedly decrease execution times of exhaustive search and extraction algorithms and produce improved velocity recoveries for low-velocity and dynamically varying velocity signals. The CCPDVANALYSIS script library demonstrates an advanced method for extracting velocities from low-velocity and non-constant velocity signals further extending and improving the methods beyond capabilities of traditional frequency domain tools.

97 MATHEMATICS AND COMPUTING

Refining HPCToolkit for application performance analysis at exascale

As part of the US Department of Energy’s Exascale Computing Project (ECP), Rice University has been refining its HPCToolkit performance tools to better support measurement and analysis of applications executing on exascale supercomputers. To efficiently collect performance measurements of GPU-accelerated applications, HPCToolkit employs novel non-blocking data structures to communicate performance measurements between tool threads and application threads. To attribute performance information in detail to source lines, loop nests, and inlined call chains, HPCToolkit performs parallel analysis of large CPU and GPU binaries involved in the execution of an exascale application to rapidly recover mappings between machine instructions and source code. To analyze terabytes of performance measurements gathered during executions at exascale, HPCToolkit employs distributed-memory parallelism, multithreading, sparse data structures, and out-of-core streaming analysis algorithms. To support interactive exploration of profiles up to terabytes in size, HPCToolkit’s hpcviewer graphical user interface uses out-of-core methods to visualize performance data. The result of these efforts is that HPCToolkit now supports collection, analysis, and presentation of profiles and traces of GPU-accelerated applications at exascale. These improvements have enabled HPCToolkit to efficiently measure, analyze and explore terabytes of performance data for executions using as many as 64K MPI ranks and 64K GPU tiles on ORNL’s Frontier supercomputer. HPCToolkit’s support for measurement and analysis of GPU-accelerated applications has been employed to study a collection of open-science applications developed as part of ECP. This paper reports on these experiences, which provided insight into opportunities for tuning applications, strengths and weaknesses of HPCToolkit itself, as well as unexpected behaviors in executions at exascale.

Adhianto, Laksono

Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty

This work focuses on visualizing uncertainty of local divergence of two-dimensional vector fields. Divergence is one of the fundamental attributes of fluid flows, as it can help domain scientists analyze potential positions of sources (positive divergence) and sinks (negative divergence) in the flow. However, uncertainty inherent in vector field data can lead to erroneous divergence computations, adversely impacting downstream analysis. While Monte Carlo (MC) sampling is a classical approach for estimating divergence uncertainty, it suffers from slow convergence and poor scalability with increasing data size and sample counts. Thus, we present a two-fold contribution that tackles the challenges of slow convergence and limited scalability of the MC approach. (1) We derive a closed-form approach for highly efficient and accurate uncertainty visualization of local divergence, assuming independently Gaussian-distributed vector uncertainties. (2) We further integrate our approach into Viskores, a platform-portable parallel library, to accelerate uncertainty visualization. In our results, we demonstrate significantly enhanced efficiency and accuracy of our serial analytical (speed-up up to 1946×) and parallel Viskores (speed-up up to 19698×) algorithms over the classical serial MC approach. We also demonstrate qualitative improvements of our probabilistic divergence visualizations over traditional mean-field visualization, which disregards uncertainty. We validate the accuracy and efficiency of our methods on wind forecast and ocean simulation datasets.

Ouermi, Timbwaoga [University of Utah]

ArborX 2.0

ArborX library tackles a problem of efficiently finding geometric objects that are close in space. Variations of this problem, such as finding the nearest neighbors of a point, or finding all objects within a certain distance, are inherent components of applications in many fields. The data may be large so that solving the problem efficiently may require significant computational resources, such as multiple processors or accelerators such as general purpose GPUs. ArborX' main advantage in its ability to solve large problems efficiently utilizing a combination of distributed and on-node parallelism. ArborX can be run efficiently on a wide variety of hardware, including GPUs from different vendors, which distinguishes it from other available libraries which typically choose only few of these. The other advantage is that it supports both types of user problems: spatial problems (useful for intersections and finding objects within certain distance), and nearest neighbor problems. ArborX also supports flexible interface in its interaction with a user. Particularly, it allows a user to call user's own function on a positive match, a functionality not rarely available in other libraries. ArborX implements construction and traversal algorithms using efficient tree structures, such as bounding volume hierarchy (BVH). At its core, ArborX uses linear BVH for its low construction cost and sufficient quality. ArborX implements both spatial and nearest-neighbor traversal algorithms. ArborX also provides several clustering algorithms (minimum spanning tree, DBSCAN, HDBSCAN*), interpolation using minimum least squares and ray tracing. ArborX is written using C++, and is parallelized using the message passing interface (MPI) for the distributed communication, and the Kokkos library for on-node parallelism. This approach allows ArborX to be run on a wide variety of hardware, from common laptops and desktops to supercomputers while using the same codebase.

Prokopenko, Andrey [Oak Ridge National Laboratory

Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems

Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.

Miao, Qiang [Duke Quantum Center, Duke University,

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE

DIMPLES: Distributed Influence Maximization for Pandemic pLanning on Exascale Systems

We study exascale parallel algorithms for the selection of intervention or monitoring strategies in massive realistic socio-technical networks through scalable Influence Maximization (InfMax) algorithms. We employ novel techniques to enable efficient scaling on up to 8k nodes of OLCF Frontier, with 65k AMD GPUs and 458k AMD CPU cores. Current state-of-the-art InfMax tools are limited to networks with only a few million actors (vertices) and a few hundred million interactions (edges). By overcoming these limitations, we show that our approach is capable of processing a realistic social contact network of the United States with 285 million nodes and about 8 billion edges. This two orders-of-magnitude improvement over the previous state-of-the-art is obtained by leveraging algorithmic advancements for the InfMax problem and designing several problem-specific approaches to overlap communication with computation, improve GPU efficiency, and lower the application’s memory requirements. We evaluate strong scaling for computing 10k most influential seeds using up to 8k nodes of an exascale system, and weak scaling from 128 to 8k system nodes for seed sets ranging from 625 to 40k seeds. We achieve the fastest-known runtime of 25 minutes while performing 48 million diffusion simulations totaling 2.31 petabytes to identify 40k influential seeds using 8k nodes, and take 5.75 minutes to identify 10k seeds while using 4k nodes.

Minutoli, Marco [Pacific Northwest National Labora