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At least 1,027 records · Page 57

Computing with Spikes: The Advantage of Fine-Grained Timing

Neural-inspired spike-based computing machines often claim to achieve considerable advantages in terms of energy and time efficiency by using spikes for computation and communication. However, fundamental questions about spike-based computation remain unanswered. For instance, how much advantage do spike-based approaches have over conventional methods, and under what circumstances does spike-based computing provide a comparative advantage? Simply implementing existing algorithms using spikes as the medium of computation and communication is not guaranteed to yield an advantage. Here, we demonstrate that spike-based communication and computation within algorithms can increase throughput, and they can decrease energy cost in some cases. We present several spiking algorithms, including sorting a set of numbers in ascending/descending order, as well as finding the maximum or minimum or median of a set of numbers. We also provide an example application: a spiking median-filtering approach for image processing providing a low-energy, parallel implementation. Furthermore, the algorithms and analyses presented here demonstrate that spiking algorithms can provide performance advantages and offer efficient computation of fundamental operations useful in more complex algorithms.

97 MATHEMATICS AND COMPUTING↗

3D Coded SUMMA: Communication-Efficient and Robust Parallel Matrix Multiplication

In this paper, we propose a novel fault-tolerant parallel matrix multiplication algorithm called 3D Coded SUMMA that achieves higher failure-tolerance than replication-based schemes for the same amount of redundancy. This work bridges the gap between recent developments in coded computing and fault-tolerance in high-performance computing (HPC). The core idea of coded computing is the same as algorithm-based fault-tolerance (ABFT), which is weaving redundancy in the computation using error-correcting codes. In particular, we show that MatDot codes, an innovative code construction for parallel matrix multiplications, can be integrated into three-dimensional SUMMA (Scalable Universal Matrix Multiplication Algorithm [30]) in a communication-avoiding manner. To tolerate any two node failures, the proposed 3D Coded SUMMA requires ~50% less redundancy than replication, while the overhead in execution time is only about 5–10%.

97 MATHEMATICS AND COMPUTING↗

Distributed-memory lattice H-matrix factorization

We parallelize the LU factorization of a hierarchical low-rank matrix (H-matrix) on a distributed-memory computer. This is much more difficult than the H-matrix-vector multiplication due to the dataflow of the factorization, and it is much harder than the parallelization of a dense matrix factorization due to the irregular hierarchical block structure of the matrix. Block low-rank (BLR) format gets rid of the hierarchy and simplifies the parallelization, often increasing concurrency. However, this comes at a price of losing the near-linear complexity of the H-matrix factorization. In this work, we propose to factorize the matrix using a “lattice H-matrix” format that generalizes the BLR format by storing each of the blocks (both diagonals and off-diagonals) in the H-matrix format. These blocks stored in the H-matrix format are referred to as lattices. Thus, this lattice format aims to combine the parallel scalability of BLR factorization with the near-linear complexity of H-matrix factorization. We first compare factorization performances using the H-matrix, BLR, and lattice H-matrix formats under various conditions on a shared-memory computer. Our performance results show that the lattice format has storage and computational complexities similar to those of the H-matrix format, and hence a much lower cost of factorization than BLR. In conclusion, we then compare the BLR and lattice H-matrix factorization on distributed-memory computers. Our performance results demonstrate that compared with BLR, the lattice format with the lower cost of factorization may lead to faster factorization on the distributed-memory computer.

97 MATHEMATICS AND COMPUTING↗

Parallel Memory-Independent Communication Bounds for SYRK

In this paper, we focus on the parallel communication cost of multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK). SYRK requires half the computation of general matrix multiplication because of the symmetry of the output matrix. Recent work (Beaumont et al., SPAA '22) has demonstrated that the sequential I/O complexity of SYRK is also a constant factor smaller than that of general matrix multiplication. Inspired by this progress, we establish memory-independent parallel communication lower bounds for SYRK with smaller constants than general matrix multiplication, and we show that these constants are tight by presenting communication-optimal algorithms. The crux of the lower bound proof relies on extending a key geometric inequality to symmetric computations and analytically solving a constrained nonlinear optimization problem. Here, the optimal algorithms use a triangular blocking scheme for parallel distribution of the symmetric output matrix and corresponding computation.

Communication costs↗

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid–base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Role of local stresses on co-zone twin-twin junction formation in HCP magnesium

Twin-twin interactions control the formation of twin-twin junctions (TTJ) in hexagonal metals when multiple twin variants are activated in a grain. In this work, we employ a combination of two computational techniques, a 3D full-field crystal plasticity model (CP) and large-scale molecular dynamics (MD), to study the TTJ formation associated with two non-parallel {101¯2} twins in Mg. The local intra-granular stresses generated by discrete twins are computed using a spatially resolved CP model. Atomic-scale knowledge regarding formation processes and local stresses is revealed by MD. The combined analyses suggest that the twin junction forms by the migration of the boundaries of both, the impinging and impinged twin, taking place in the immediate vicinity of the contact point. It is further shown that local stress fields that are generated after initial contact promote thickening of the impinging twin, and may facilitate nucleation of a new twin on the opposite boundary of the recipient twin. In conclusion, calculations of the strain energies suggest that formation of the co-zone twin-twin junction is energetically favorable but detwinning of the TTJ upon load reversal or under cyclic loading is not.

36 MATERIALS SCIENCE↗

Developing an ELM Ecosystem Dynamics Model on GPU with OpenACC

Porting a complex scientific code, such as the E3SM land model (ELM), onto a new computing architecture is challenging. The paper presents design strategies and technical approaches to develop an ELM ecosystem dynamics model with compiler directives (OpenACC) on NVIDIA GPUs. The code has been refactored with advanced OpenACC features (such as deepcopy and routine directives) to reduce memory consumption and to increase the levels of parallelism through parallel loop reconstruction and new data structures. As a result, the optimized parallel implementation achieved more than a 140-time speedup (50 ms vs 7600 ms), compared to a naive implementation that uses OpenACC routine directive and parallelizes the code across existing loops on a single NVIDIA V100. On a fully loaded computing node with 44 CPUs and 6 GPUs, the code achieved over a 3.0-times speedup, compared to the original code on the CPU. Furthermore, the memory footprint of the optimized parallel implementation is 300 MB, which is around 15% of the 2.15 GB of memory consumed by a naive implementation. This study is the first effort to develop the ELM component on GPUs efficiently to support ultra-high-resolution land simulations at continental scales.

Schwartz, Peter↗

A Scalable Hybrid Scheme for Ray-Casting of Unstructured Volume Data

We present an algorithm for parallel volume rendering that is a hybrid between classical object order and image order techniques. The algorithm operates on unstructured grids (and structured ones), and thus can deal with block boundaries interleaving in complex ways. It also deals effectively with cases that are prone to load imbalance, i.e., cases where cell sizes differ dramatically, either because of the nature of the input data, or because of the effects of the camera transformation. The algorithm divides work over resources such that each phase of its processing is bounded in the amount of computation it can perform. We demonstrate its efficacy through a series of studies, varying over camera position, data set size, transfer function, image size, and processor count. At its biggest, our experiments scaled up to 8,192 processors and operated on data sets with more than one billion cells. In total, we find that our hybrid algorithm performs well in all cases. This is because our algorithm naturally adapts its computation based on workload, and can operate like either an object order technique or an image order technique in scenarios where those techniques are efficient.

97 MATHEMATICS AND COMPUTING↗

The Persistent Challenge of Data Locality in the Post-Exascale Era

The era of exascale computing, exemplified by systems like Frontier achieving exaflop-level performance, marks a milestone. However, the quest for sheer compute power leads to strong imbalance in system design. Hence, scaling advancements in memory, network bandwidth, and storage are also necessary and pose challenges, with a crucial need to address data locality issues. This article underscores the fundamental importance of data locality as a key abstraction for optimizing application performance. Despite notable software solutions, the growing complexity of parallelism and memory hierarchy demands performance-portable data locality solutions across diverse computing platforms. Additionally, the article revisits data locality aspects, covering hardware considerations, application perspectives, software stack abstractions, and tool support. It concludes with insights into data locality challenges and opportunities, emphasizing the ongoing significance of collaborative research for progress in this critical issue.

Unat, Didem [Koc University, Istanbul (Turkey)] (O↗

SPADES (Scalable Parallel Discrete Events Simulation) [SWR-24-99]

SPADES (Solver for PArallel Discrete Event Simulation) is an open-source parallel discrete event simulation (PDES) package built on the AMReX library. Targeted at solving discrete event systems in parallel, this software package aims to be performance portable and scalable on heterogeneous computing architectures, e.g., graphic processing units (GPU). SPADES implements optimistic synchronization with rollback through an implementation of the Time Warp algorithm. An alternative conservative synchronization approach is also implemented using the Lower Bound on Incoming Time Stamp. In our implementation, logical processes are represented as cells in a grid and event messages are represented as particles. SPADES supports various parallel decomposition strategies, including the use of the Message Passing Interface (MPI) and OpenMP threading. All major GPU architectures (e.g., Intel, AMD, NVIDIA) are supported through the use of performance portability functionalities implemented in AMReX. The SPADES software is released in NREL Software Record SWR-24-99 “SPADES (Scalable Parallel Discrete Events Simulation)”.

Henry de Frahan, Marc [National Renewable Energy L↗

Multiply accelerated ReaxFF molecular dynamics: coupling parallel replica dynamics with collective variable hyper dynamics

To address the time scales required to study complex chemical reactions, methods performing accelerated molecular dynamics are necessary even with the recent advancement in high-performance computing. A number of different acceleration techniques are available. Here we explore potential synergies between two popular acceleration methods – Parallel Replica Dynamics (PRD) and Collective Variable Hyperdynamics (CVHD), by analysing the speedup obtained for the pyrolysis of n-dodecane. We determine that PRD + CVHD provides additional speedup to CVHD by reaching the required time scales for the reaction at an earlier wall-clock time. Although some speedup is obtained with the additional replicas, we found that the effectiveness of the inclusion of PRD is depreciated for systems where there is a dramatic increase in reaction rates induced by CVHD. Similar observations were made in the simulation of ethylene-carbonate/Li system, which is inherently more reactive than pyrolysis, suggest that the speedup obtained via the combination of the two acceleration methods can be generalised to most practical chemical systems.

42 ENGINEERING↗

Deploy threading in Nalu solver stack

The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines, and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary code in the ExaWind project is Nalu, which is an unstructured-grid solver for the acousticallyincompressible Navier-Stokes equations, and mass continuity is maintained through pressure projection. The model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as re-initialization of matrices and re-computation of preconditioners is required at every time step In this Milestone, we examine the effect of threading on the solver stack performance against flat-MPI results obtained from previous milestones using Haswell performance data full-turbine simulations. Whereas the momentum equations are solved only with the Trilinos solvers, we investigate two algebraic-multigrid preconditioners for the continuity equations: Trilinos/Muelu and HYPRE/BoomerAMG. These two packages embody smoothed-aggregation and classical Ruge-Stiiben AMG methods, respectively. In our FY18 Q2 report, we described our efforts to improve setup and solve of the continuity equations under flat-MPI parallelism. While significant improvement was demonstrated in the solve phase, setup times remained larger than expected. Starting with the optimized settings described in the Q2 report, we explore here simulation performance where OpenMP threading is employed in the solver stack. For Trilinos, threading is acheived through the Kokkos abstraction where, whereas HYPRE/BoomerAMG employs straight OpenMP. We examined results for our mid-resolution baseline turbine simulation configuration (229M DOF). Simulations on 2048 Haswell cores explored the effect of decreasing the number of MPI ranks while increasing the number of threads. Both HYPRE and Trilinos exhibited similar overal solution times, and both showed dramatic increases in simulation time in the shift from MPI ranks to OpenMP threads. This increase is attributed to the large amount of work per MPI rank starting at the single-thread configuration. Decreasing MPI ranks, while increasing threads, may be increasing simulation time due to thread synchronization and start-up overhead contributing to the latency and serial time in the model. These result showed that an MPI+OpenMP parallel decomposition will be more effective as the amount per MPI rank computation per MPI rank decreases and the communication latency increases. This idea was demonstrated in a strong scaling study of our low-resolution baseline model (29M DOF) with the Trilinos-HYPRE configuration. While MPI-only results showed scaling improvement out to about 1536 cores, engaging threading carried scaling improvements out to 4128 cores — roughly 7000 DOF per core. This is an important result as improved strong scaling is needed for simulations to be executed over sufficiently long simulated durations (i.e., for many timesteps). In addition to threading work described above, the team examined solver-performance improvements by exploring communication-overhead in the HYPRE-GMRES implementation through a communicationoptimal- GMRE algorithm (CO-GMRES), and offloading compute-intensive solver actions to GPUs. To those ends, a HYPRE mini-app was allow us to easily test different solver approaches and HYPRE parameter settings without running the entire Nalu code. With GPU acceleration on the Summitdev supercomputer, a 20x speedup was achieved for the overall preconditioner and solver execution time for the mini-app. A study on Haswell processors showed that CO-GMRES provides benefits as one increases MPI ranks.

17 WIND ENERGY↗

Rigorous justification for the space–split sensitivity algorithm to compute linear response in Anosov systems

Ruelle gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations of Ruelle's formula have emerged that potentially enable sensitivity analysis of certain high-dimensional chaotic numerical simulations encountered in the applied sciences. In this paper, we provide full mathematical justification for the convergence of one such efficient computation, the space–split sensitivity, or S3, algorithm. In S3, Ruelle's formula is computed as a sum of two terms obtained by decomposing the perturbation vector field into a coboundary and a remainder that is parallel to the unstable direction. Such a decomposition results in a splitting of Ruelle's formula that is amenable to efficient computation. Here, we prove the existence of the S3 decomposition and the convergence of the computations of both resulting components of Ruelle's formula.

97 MATHEMATICS AND COMPUTING↗

Parallel performance of algebraic multigrid domain decomposition

Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits its scalability as processor counts continue to grow on modern machines. This article examines the design, implementation, and parallel performance of a novel algorithm, algebraic multigrid domain decomposition (AMG-DD), designed specifically to limit communication. The goal of AMG-DD is to provide a low-communication alternative to standard AMG V-cycles by trading some additional computational overhead for a significant reduction in communication cost. Numerical results show that AMG-DD achieves superior accuracy per communication cost compared with AMG, and speedup over AMG is demonstrated on a large GPU cluster.

97 MATHEMATICS AND COMPUTING↗

Evaluating asynchronous Schwarz solvers on GPUs

With the commencement of the exascale computing era, we realize that the majority of the leadership supercomputers are heterogeneous and massively parallel. Even a single node can contain multiple co-processors such as GPUs and multiple CPU cores. For example, ORNL’s Summit accumulates six NVIDIA Tesla V100 GPUs and 42 IBM Power9 cores on each node. Synchronizing across compute resources of multiple nodes can be prohibitively expensive. Hence, it is necessary to develop and study asynchronous algorithms that circumvent this issue of bulk-synchronous computing. In this study, we examine the asynchronous version of the abstract Restricted Additive Schwarz method as a solver. We do not explicitly synchronize, but allow the communication between the sub-domains to be completely asynchronous, thereby removing the bulk synchronous nature of the algorithm. We accomplish this by using the one-sided Remote Memory Access (RMA) functions of the MPI standard. We study the benefits of using such an asynchronous solver over its synchronous counterpart. We also study the communication patterns governed by the partitioning and the overlap between the sub-domains on the global solver. Finally, we show that this concept can render attractive performance benefits over the synchronous counterparts even for a well-balanced problem.

Nayak, Pratik↗

Introduction: Neuromorphic Materials

The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.

Circuits↗

Scale-up Unlearnable Examples Learning with High-performance Computing

Recent advancements in AI models, like ChatGPT, are structured to retain user interactions, which could inadvertently include sensitive healthcare data. In the healthcare field, particularly when radiologists use AI-driven diagnostic tools hosted on online platforms, there is a risk that medical imaging data may be repurposed for future AI training without explicit consent, spotlighting critical privacy and intellectual property concerns around healthcare data usage. Addressing these privacy challenges, a novel approach known as Unlearnable Examples (UEs) has been introduced, aiming to make data unlearnable to deep learning models. A prominent method within this area, called Unlearnable Clustering (UC), has shown improved UE performance with larger batch sizes but was previously limited by computational resources (e.g., a single workstation). To push the boundaries of UE performance with theoretically unlimited resources, we scaled up UC learning across various datasets using Distributed Data Parallel (DDP) training on the Summit supercomputer. Our goal was to examine UE efficacy at high-performance computing (HPC) levels to prevent unauthorized learning and enhance data security, particularly exploring the impact of batch size on UE’s unlearnability. Utilizing the robust computational capabilities of the Summit, extensive experiments were conducted on diverse datasets such as Pets, MedMNist, Flowers, and Flowers102. Our findings reveal that both overly large and overly small batch sizes can lead to performance instability and affect accuracy. However, the relationship between batch size and unlearnability varied across datasets, highlighting the necessity for tailored batch size strategies to achieve optimal data protection. The use of Summit’s high-performance GPUs, along with the efficiency of the DDP framework, facilitated rapid updates of model parameters and consistent training across nodes. Our results underscore the critical role of selecting appropriate batch sizes based on the specific characteristics of each dataset to prevent learning and ensure data security in deep learning applications. The source code is publicly available at https: // github. com/ hrlblab/ UE_ HPC .

Zhu, Yanfan [Vanderbilt University, Nashville, TN,↗

Controlling Cation-Cation Interactions in Uranyl Coordination Dimers by Varying the Length of the Dicarboxylate Linker

The chemistry of linear uranyl(V/VI) dioxo cations, [O yl –U–O yl ] +/2+ , is dominated by coordination of uranium in the equatorial plane. Effects of this constraint were evaluated by experiment and theory for gas-phase mixed-valence U V/VI coordination dimers in which uranyl moieties are linked by alkyl dicarboxylates, [(UO 2 + )(UO 2 2+ )(OOC-(CH 2 ) n-2 -COO 2– ) 2 ] – (n = 3–12). Faster O 2 -addition to dimers with short linkers n = 3 and 4, vs. n ≥ 5, suggests a structural difference. Computed structures with the shortest linkers have bridging dicarboxylates and nearly parallel, non-interacting uranyls. Longer linkers, n = 5–7, accommodate uranyl orientations with distinct U V –U VI end-on cation-cation interactions (CCIs), whereby Lewis base O yl from U V coordinates to the acid U VI , denoted as U V O yl ···U VI . The dimer structure for n = 8 has a U V –U VI side-on diamond-shape CCI, with U V O yl ···U VI and U VI O yl ···U V interactions. Addition of O 2 to the n = 4 and 5 dimers yields [(UO22+)2(OOC-(CH2)n-2-COO2–)2(O2–)]–, with U V oxidized to U VI and O 2 reduced to O 2 – . Whereas O 2 can associate to and oxidize the exposed U V center for dimers with n = 3 and 4, the more crowded U V site in the CCI structures inhibits O 2 addition. Finally, the results demonstrate rational structural control of uranyl-uranyl bonding and reactivity in small coordination complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗