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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Communication-Avoiding and Memory-Constrained Sparse Matrix-Matrix Multiplication at Extreme Scale

Sparse matrix-matrix multiplication (SpGEMM) is a widely used kernel in various graph, scientific computing and machine learning algorithms. In this paper, we consider SpGEMMs performed on hundreds of thousands of processors generating trillions of nonzeros in the output matrix. Distributed SpGEMM at this extreme scale faces two key challenges: (1) high communication cost and (2) inadequate memory to generate the output. Furthermore, we address these challenges with an integrated communication-avoiding and memory-constrained SpGEMM algorithm that scales to 262,144 cores (more than 1 million hardware threads) and can multiply sparse matrices of any size as long as inputs and a fraction of output fit in the aggregated memory. As we go from 16,384 cores to 262,144 cores on a Cray XC40 supercomputer, the new SpGEMM algorithm runs 10x faster when multiplying large-scale protein-similarity matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗
DOE OSTI2023

Fast Parallel Tensor Times Same Vector for Hypergraphs

Hypergraphs are a popular paradigm to rep- resent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper- graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) oper- ation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVC computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph H-eigenvector centrality.

Shivakumar, Shruti↗
DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗
DOE OSTI2025

GSplit: Scaling Graph Neural Network Training on Large Graphs via Split-Parallelism

Graph neural networks (GNNs), an emerging class of machine learning models for graphs, have gained popularity for their superior performance in various graph analytical tasks. Mini-batch training is commonly used to train GNNs on large graphs, and data parallelism is the standard approach to scale mini-batch training across multiple GPUs. Data parallel approaches contain redundant work as subgraphs sampled by different GPUs contain significant overlap. To address this issue, we introduce a hybrid parallel mini-batch training paradigm called Split parallelism. Split parallelism avoids redundant work by splitting the sampling, loading, and training of each mini-batch across multiple GPUs. Split parallelism, however, introduces communication overheads that can be more than the savings from removing redundant work. We further present a lightweight partitioning algorithm that probabilistically minimizes these overheads. We implement spllit parllelism in GSplit and show that it outperforms state-of-the-art mini-batch training systems like DGL, Quiver, and P3.

Lim, Seung-Hwan [ORNL] (ORCID:0000000194616866)↗
DOE OSTI2024

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗
DOE OSTI2022

Bit-GraphBLAS: Bit-Level Optimizations of Matrix-Centric Graph Processing on GPU

In the graph data structure like adjacency matrix, the connectivity of two nodes can be sufficiently represented using only 1 bit, but they are generally treated as 32-bit full-precision in state-of-the-art graph frameworks to adopt common sparse format such as CSR. Meanwhile, bit-level parallelism has recently be explored to have high-performance potential and low storage requirement on GPUs with dense bit-tiles. To fill the gap, our solution is a hierarchical storage format that contains the bit-indexing base and dense bit-tile units. Inherently, the granularity of the bit-tile is an essential factor in achieving both storage compression and GPU parallelism. How to find a sweet spot that trades off between avoiding sparsity and exploiting is comprehensively researched in this work. In the experiment, we evaluate the proposed storage format and algorithms on modern generation GPUs, including Pascal and Volta, to figure out critical software co-designs in conjunction with existing hardware-specific optimization.

Chen, Jou-An↗
DOE OSTI2026

Energy-Screened Many-Body Expansion for Protein–Ligand Interactions: Examining Convergence for Metalloenzymes Through Seven–Body Interactions

Fragment-based quantum chemistry is a powerful strategy for calculating protein−ligand interaction energies using quantum chemistry methods. Rigorous convergence often requires hundreds of atoms in the protein binding-site model, especially if that model is constructed using distance-based criteria to select amino acid residues, while three- and four-body calculations exhibit instability related to combinatorial proliferation in the number of subsystem calculations. Here, we report an energy-based screening protocol for the many-body expansion applied to protein−ligand interactions, implemented in the open-source FRAGME∩T code. Using a combination of aggressive screening based on semiempirical quantum chemistry, with an improved graph-theoretical algorithm to eliminate unimportant subsystems, we are able to perform n-body calculations up to n = 7 using density functional theory in triple-ζ basis sets. Distance cutoffs further reduce the cost without compromising accuracy. Rapid and stable convergence of the many-body expansion is obtained by n = 4, for a pair of metalloenzymes in which a divalent ion coordinates directly to the ligand. As compared to previous results that relied solely on distance cutoffs, oscillations in the n-body corrections are reduced or eliminated, although residual errors remain in one case. This work demonstrates that benchmark-quality protein−ligand interaction energies can be systematically converged using a method with excellent parallel efficiency and scalability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

cuAlign: Scalable Network Alignment on GPU Accelerators

Given two graphs, the objective of network alignment is to find the best one-to-one mapping of vertices in one graph (??) to vertices in the other (??), such that the number of overlaps is maximized. We say that edges(??, ??) ???and(??', ??') ??? are overlapped if ?? is mapped to ??' and ?? is mapped to??'. Network alignment is an important optimization problem with several applications in bioinformatics, computer vision and ontology matching. Since it is an NP-hard problem, efficient heuristics and scalable implementations are necessary. In this work, we introduce a new framework that combines the concepts of intra-network proximity using vertex embedding,Belief Propagation (BP) and approximate weighted matching, and provides qualitative improvements up to22%over state-of-the-art approaches. We also provide scalable implementations on GPU accelerators, demonstrating up to19×speedup for Belief Propagation and 3× speedup for approximate weighted matching relative to previous multithreaded implementation. A combination of combinatorial and algebraic kernels within the network alignment algorithm poses significant hurdles for parallelization. Load imbalance and irregular DRAM traffic limit achievable performance on GPUs. Our novel approach identifies and exploits unique structural proper-ties of the BP-based algorithm and employs code fusion to reduce data movement between different steps of the algorithm. Using a diverse set of inputs, we demonstrate qualitative improvements of our algorithms, and performance gains of our GPU-accelerated implementation. We believe that our work will enable algorithmic improvements and practical applications of network alignment.

Xiang, Lizhi↗
DOE OSTI2024

Optimizing High-Throughput Inference on Graph Neural Networks at Shared Computing Facilities with the NVIDIA Triton Inference Server

Abstract With machine learning applications now spanning a variety of computational tasks, multi-user shared computing facilities are devoting a rapidly increasing proportion of their resources to such algorithms. Graph neural networks (GNNs), for example, have provided astounding improvements in extracting complex signatures from data and are now widely used in a variety of applications, such as particle jet classification in high energy physics (HEP). However, GNNs also come with an enormous computational penalty that requires the use of GPUs to maintain reasonable throughput. At shared computing facilities, such as those used by physicists at Fermi National Accelerator Laboratory (Fermilab), methodical resource allocation and high throughput at the many-user scale are key to ensuring that resources are being used as efficiently as possible. These facilities, however, primarily provide CPU-only nodes, which proves detrimental to time-to-insight and computational throughput for workflows that include machine learning inference. In this work, we describe how a shared computing facility can use the NVIDIA Triton Inference Server to optimize its resource allocation and computing structure, recovering high throughput while scaling out to multiple users by massively parallelizing their machine learning inference. To demonstrate the effectiveness of this system in a realistic multi-user environment, we use the Fermilab Elastic Analysis Facility augmented with the Triton Inference Server to provide scalable and high-throughput access to a HEP-specific GNN and report on the outcome.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Decentralized Schemes with Overlap for Solving Graph-Structured Optimization Problems

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it uses overlapping subdomains to promote and accelerate convergence. We show that the algorithm converges if the size of the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs. The proposed scheme is tested in an estimation problem for a 9241-node power network and we show that it outperforms the alternating direction method of multipliers.

asynchronous↗
DOE OSTI2021

Three practical workflow schedulers for easy maximum parallelism

Runtime scheduling and workflow systems are an increasingly popular algorithmic component in HPC because they allow full system utilization with relaxed synchronization requirements. There are so many special-purpose tools for task scheduling, one might wonder why more are needed. Use cases seen on the Summit supercomputer needed better integration with MPI and greater flexibility in job launch configurations. Preparation, execution, and analysis of computational chemistry simulations at the scale of tens of thousands of processors revealed three distinct workflow patterns. A separate job scheduler was implemented for each one using extremely simple and robust designs: file-based, task-list based, and bulk-synchronous. Comparing to existing methods shows unique benefits of this work, including simplicity of design, suitability for HPC centers, short startup time, and well-understood per-task overhead. All three new tools have been shown to scale to full utilization of Summit, and have been made publicly available with tests and documentation. This work presents a complete characterization of the minimum effective task granularity for efficient scheduler usage scenarios. Here, these schedulers have the same bottlenecks, and hence similar task granularities as those reported for existing tools following comparable paradigms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Scalable training of trustworthy and energy-efficient predictive graph foundation models for atomistic materials modeling: a case study with HydraGNN

We present our work on developing and training scalable, trustworthy, and energy-efficient predictive graph foundation models (GFMs) using HydraGNN, a multi-headed graph convolutional neural network architecture. HydraGNN expands the boundaries of graph neural network (GNN) computations in both training scale and data diversity. It abstracts over message passing algorithms, allowing both reproduction of and comparison across algorithmic innovations that define nearest-neighbor convolution in GNNs. This work discusses a series of optimizations that have allowed scaling up the GFMs training to tens of thousands of GPUs on datasets consisting of hundreds of millions of graphs. Our GFMs use multitask learning (MTL) to simultaneously learn graph-level and node-level properties of atomistic structures, such as energy and atomic forces. Using over 154 million atomistic structures for training, we illustrate the performance of our approach along with the lessons learned on two state-of-the-art US Department of Energy (US-DOE) supercomputers, namely the Perlmutter petascale system at the National Energy Research Scientific Computing Center and the Frontier exascale system at Oak Ridge Leadership Computing Facility. The HydraGNN architecture enables the GFM to achieve near-linear strong scaling performance using more than 2000 GPUs on Perlmutter and 16,000 GPUs on Frontier.

97 MATHEMATICS AND COMPUTING↗