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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Binary operations on neuromorphic hardware with application to linear algebraic operations and stochastic equations

Abstract Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Understanding Mixed Precision GEMM with MPGemmFI: Insights into Fault Resilience

Emerging deep learning workloads urgently need fast general matrix multiplication (GEMM). Thus, one of the critical features of machine-learning-specific accelerators such as NVIDIA Tensor Cores, AMD Matrix Cores, and Google TPUs is the support of mixed-precision enabled GEMM. For DNN models, lower-precision FP data formats and computation offer acceptable correctness but significant performance, area, and memory footprint improvement. While promising, the mixed-precision computation on error resilience remains unexplored. To this end, we develop a fault injection framework that systematically injects fault into the mixed-precision computation results. We investigate how the faults affect the accuracy of machine learning applications. Based on the characteristics of error resilience, we offer lightweight error detection and correction solutions that significantly improve the overall model accuracy by 75% if the models experience hardware faults. The solutions can be efficiently integrated into the accelerator's pipelines.

Fang, Bo↗
DOE OSTI2024

Shifting Between Compute and Memory Bounds: A Compression-Enabled Roofline Model

In the evolving landscape of high-performance computing, especially to fight the end of Moore’s Law and Dennard’s Scaling, the ability to shift between compute-bound and memory-bound states is critical for enhancing adaptability and flexibility to diverse system and domain-specific architectures. Such capability is vital for optimizing performance across distinguished hardware configurations, such as accelerators, memory hierarchies, and cache systems. Despite that ad hoc optimization techniques, such as compressed/approximate computation, have been enabled for compute-/data-intensive computing for improved performance in distinct hardware settings, there lacks an understanding of 1) the rational behind performance improvement; 2) capability of different optimizations; 3) what optimization to respond to specific computational and memory demands. This work proposes a compression-enabled roofline model to facilitate this adaptability with data compression techniques to balance and transform between computational and memory demands. This model enables applications to adjust in response to the specific strengths and limitations of the underlying hardware and system to optimize resource utilization. The effectiveness of this approach is demonstrated with matrix multiplication kernels on different input sizes, with turning on/off various compression techniques, including 1) low-precision floating point; 2) sparse matrix formulation; and 3) compressed arrays with ZFP. By reducing memory transfer volumes and cache misses and increasing data locality and computational intensity through compression, the specific roofline model can transform between compute and memory bounds to align more efficiently with system capabilities. This advancement not only improves overall performance but also maximizes adaptability in diverse computing environments.

Naraparaju, Ramasoumya [University of Washington]↗
DOE OSTI2024

Efficient Scalable Contact Network Generation from Population Data

Modeling the contacts among a population is critical to understanding the dynamics of a disease outbreak. Contact networks, where nodes are individuals and edges are contacts among them, are used to represent these complex individual-level interactions. In this work, we are given the daily activity schedules of an urban population that represent the activity location and time of individuals in a population during a single twenty four hour period over multiple days. Using collocation to determine contact between individuals, our goal is to extract hourly contact networks from large-scale activity data. We improve upon the existing adjacency matrix-based method by implementing our custom sparse matrix multiplication algorithm. Starting with a Python implementation, we achieve a 1600x speed up in the computation with a fast custom designed sparse matrix multiplier algorithm implemented in the C++ language. This work is central to future parallel designs of the problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Fast Algorithm for Computing Zigzag Representatives

Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtrations encode the evolution of homological features. Although one can locate a particular feature at any index in the filtration using existing algorithms, the resulting representatives may not be compatible with the zigzag: a representative cycle at one index may not map into a representative cycle at its neighbor. For this, one needs to compute compatible representative cycles along each bar in the barcode. It is known that the barcode for a zigzag filtration with m insertions and deletions can be computed $O(m^ω)$ in time, where $ω < 2.373$ is the matrix multiplication exponent. However, it is not known how to compute the compatible representatives so efficiently. For a non-zigzag filtration, the classical matrix-based algorithm provides representatives in $O(m^3)$ time, which can be improved to $O(m^ω)$. However, no known algorithm for zigzag filtrations computes the representatives with the $O(m^3)$ time bound. We present an $O(m^3 n)$ time algorithm for this problem, where $n ≤ m$ is the size of the largest complex in the filtration.

Persistent homology↗
DOE OSTI2025

Multistate resistance in TaN/(Hf,Zr)O 2 /Ta ferroelectric tunnel junctions

Ferroelectric tunnel junctions (FTJs) utilizing hafnium zirconium oxide (HZO) have emerged as promising non-volatile memory elements for microelectronics, compatible with back end of line (BEOL) complementary–metal–oxide semiconductor fabrication. This study investigates asymmetric electrode TaN/HZO/Ta devices with a 6 nm thick HZO layer as FTJs for multistate resistive memory applications. The individual FTJs exhibit a resistance ratio exceeding 10× when utilized as a binary state device, with pulsing between −1.7 and +1.4 V to set the high resistance state (HRS) and low resistance state (LRS), respectively. Following with reduced write voltage pulses allows the ferroelectric device to operate with a selection of over 32 distinct resistance states (2 5 bits) between the LRS and HRS. This work then explores the stability of the resistance states during write/read pulse cycling, along with the stability of the state after multiple read pulses. Accessing the multibit state shows stability within 50 reads with the binary state remaining stable for more than 4000 reads pulses. With their multistate tunability and versatility, FTJs hold promise as BEOL memory elements for compute-in-memory (CiM) arrays, binary digital memory, or weighted vector matrix multiplication applications with low power consumption during computations.

CMOS↗
DOE OSTI2023

A fast, dense Chebyshev solver for electronic structure on GPUs

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. Furthermore, this improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

ReSpike: A Co-Design Framework for Evaluating SNNs on ReRAM-Based Neuromorphic Processors

With Moore’s law approaching its end, traditional von Neumann architectures are struggling to keep up with the exceeding performance and memory requirements of artificial intelligence and machine learning algorithms. Unconventional computing approaches such as neuromorphic computing that leverage spiking neural networks (SNNs) to perform computation are gaining traction and seek the paradigm shift necessary to sustain the increasing demands of modern applications. Novel memory technologies, such as resistive RAM (ReRAM), employ a crossbar architecture that possesses the inherent capability of efficiently computing vector-matrix multiplication—a dominant operation in SNNs. The prospect of naturally mapping SNNs to the crossbar structures provides a unique opportunity for achieving a high-performance, power-efficient neuromorphic system. In this work, we present ReSpike, which is a new framework, behavioral simulator, and architectural design based on ReRAM crossbar architectures, enabling modeling and co-design to achieve efficient execution of SNNs. We drive this co-design forward by quantifying the impact that ReRAM cell nonidealities have on the corresponding accuracy of an SNN application.

Asifuzzaman, Kazi [ORNL] (ORCID:0000000240044791)↗
DOE OSTI2022

Intrinsically stretchable neuromorphic devices for on-body processing of health data with artificial intelligence

For leveraging wearable technologies to advance precision medicine, personalized and learning-based analysis of continuously acquired health data is indispensable, for which neuromorphic computing could provide the most efficient implementation of artificial intelligence (AI) data processing. For realizing on-body neuromorphic computing, skin-like stretchability is required, but yet to be combined with the suite of desired neuromorphic metrics, including linear, symmetric weight update, and sufficient state retention, for achieving high computing efficiency. Here, we report an intrinsically stretchable neuromorphic device based on an electrochemical transistor, which provides a large number (>800) of states, linear/symmetric weight update, excellent switching endurance (>100 million), good state retention (>10 4 s), together with high stretchability of 100% strain. Further integration into a prototype array successfully realized the implementation of vector-matrix multiplication even at 100% strain. Finally, we demonstrate the feasibility of implementing AI-based classification of health signals (as exemplified by electrocardiograms) with a high accuracy that is minimally influenced by the stretched state of the neuromorphic hardware. Finally, this work breaks the ground for combining AI data analysis into skin-like wearable electronics for achieving human-integrated/mimetic intelligent systems.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network

In this work, time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix–matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree–Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S –1 . This factorization of S –1 , written as ZZT = S –1 , is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix–matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A High-Efficiency Delayed Update Algorithm for Evaluating Slater Determinants in Quantum Monte Carlo

For quantum Monte Carlo simulations of molecular systems or supercells with thousands of electrons, matrix operations related to Slater determinants lead the computational cost. McDaniel et al. [J. Chem. Phys. 2017, 147, 174107] proposed a delayed update algorithm to increase computational efficiency by using matrix–matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman–Morrison–Woodbury formula remained a bottleneck. Here, in this work, we introduce an improved algorithm for CPUs and GPUs that (1) reduces this bottleneck by iteratively updating the intermediate matrices and (2) is efficient at any acceptance ratio, with no cost for rejected moves on CPUs and minimal cost on GPUs. We show the full scheme of integrating the delayed update algorithm into a single-electron move. The high efficiency of our algorithm is demonstrated on CPUs and GPUs for a 512 atom/6144 valence electron calculation, with 12× and 2× overall speed-up compared to traditional rank-1 update schemes in diffusion quantum Monte Carlo, respectively.

Luo, Ye [Argonne National Laboratory (ANL), Argonn↗
DOE OSTI2026

Speeding Up Hartree–Fock in JuliaChem with Density Fitting

In this work, the density fitting (DF) approximation is added to the restricted Hartree–Fock (RHF) implementation in the JuliaChem computational chemistry code. Utilizing a DF algorithm that uses symmetry and integral screening, a significant reduction in time to compute the Fock matrix is achieved. The symmetry and screening DF-RHF techniques were adapted to be performed on graphics processing units (GPUs), which are well suited to perform the matrix multiplications that comprise the bulk of the Fock build time in DF-RHF. The JuliaChem DF-RHF GPU algorithm employs a novel approach that automatically switches between two DF-RHF algorithms depending on the number of basis functions in the calculation. The JuliaChem GPU DF-RHF implementation demonstrates up to 2× speedup for Fock build times compared to the existing best-in-class GPU DF-RHF implementation by operating directly on screened intermediate matrices. Due to the high portability of the Julia language code, the JuliaChem CPU and GPU DF-RHF implementations could be benchmarked on a variety of CPU and GPU architectures from multiple hardware vendors.

Hayes, John J. [Ames Laboratory, and Iowa State Un↗
DOE OSTI2024

Fiber optic computing using distributed feedback

Abstract The widespread adoption of machine learning and other matrix intensive computing algorithms has renewed interest in analog optical computing, which has the potential to perform large-scale matrix multiplications with superior energy scaling and lower latency than digital electronics. However, most optical techniques rely on spatial multiplexing, requiring a large number of modulators and detectors, and are typically restricted to performing a single kernel convolution operation per layer. Here, we introduce a fiber-optic computing architecture based on temporal multiplexing and distributed feedback that performs multiple convolutions on the input data in a single layer. Using Rayleigh backscattering in standard single mode fiber, we show that this technique can efficiently apply a series of random nonlinear projections to the input data, facilitating a variety of computing tasks. The approach enables efficient energy scaling with orders of magnitude lower power consumption than GPUs, while maintaining low latency and high data-throughput.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Towards Precision-Aware Fault Tolerance Approaches for Mixed-Precision Applications

Graphics Processing Units (GPUs), the dominantly adopted accelerators in HPC systems, are susceptible to transient hardware fault. New generation of GPUs feature mixed-precision architectures such as NVIDIA Tensor Cores to accelerate matrix multiplications. While being widely adapted, how would they behave under transient hardware faults remain unclear. In this study, we conduct a large-scale fault injection experiments on GEMM kernels implemented with different floating-point data types on the V100 and A100 Tensor Cores, and show distinct error resilience characteristics for the GEMMS with different formats. In the future, we plan to explore this space by building precision-aware floating-point fault tolerance techniques for applications such as DNNs that exercise low-precision computations.

Fang, Bo↗
DOE OSTI2023

IRIS-DMEM: Efficient Memory Management for Heterogeneous Computing

This paper proposes an efficient data memory management approach for the Intelligent RuntIme System (IRIS) heterogeneous computing framework along with new data transfer policies. IRIS provides a task-based programming model for extreme heterogeneous computing (e.g., CPU, GPU, DSP, FPGA) with support for today's most important programming languages (e.g., OpenMP, OpenCL, CUDA, HIP, OpenACC). However, the IRIS framework either forces the programmer to introduce data transfer commands for each task or relies on suboptimal memory management for automatic and transparent data transfers. The work described here extends IRIS with novel heterogeneous memory handling and introduces novel data transfer policies by employing the Distributed data MEMory handler (DMEM) for efficient and optimal movement of data among the various computing resources. The proposed approach achieves performance gains of up to 7× for tiled LU factorization and tiled DGEMM (i.e., matrix multiplication) benchmarks. Moreover, this approach also reduces data transfers by up to 71% when compared to previous IRIS heterogeneous memory management handlers. This work compares the performance results of the IRIS framework's novel DMEM with the StarPU runtime and MAGMA math library for GPUs. Experiments show a performance gain of up to 1.95× over StarPU and 2.1× over MAGMA.

Miniskar, Narasinga Rao↗
DOE OSTI2023

Evaluating performance and portability of high-level programming models: Julia, Python/Numba, and Kokkos on exascale nodes

We explore the performance and portability of the high-level programming models: the LLVM-based Julia and Python/Numba, and Kokkos on high-performance computing (HPC) nodes: AMD Epyc CPUs and MI250X graphical processing units (GPUs) on Frontier’s test bed Crusher system and Ampere’s Arm-based CPUs and NVIDIA’s A100 GPUs on the Wombat system at the Oak Ridge Leadership Computing Facilities. We compare the default performance of a hand-rolled dense matrix multiplication algorithm on CPUs against vendor-compiled C/OpenMP implementations, and on each GPU against CUDA and HIP. Rather than focusing on the kernel optimization per-se, we select this naive approach to resemble exploratory work in science and as a lower-bound for performance to isolate the effect of each programming model. Julia and Kokkos perform comparably with C/OpenMP on CPUs, while Julia implementations are competitive with CUDA and HIP on GPUs. Performance gaps are identified on NVIDIA A100 GPUs for Julia’s single precision and Kokkos, and for Python/Numba in all scenarios. We also comment on half-precision support, productivity, performance portability metrics, and platform readiness. We expect to contribute to the understanding and direction for high-level, high-productivity languages in HPC as the first-generation exascale systems are deployed.

Godoy, William↗
DOE OSTI2026

A Benchmark Suite for Evaluating Scientific AI Workloads on GPUs

AI applications have been steadily increasing in the allocation portfolio among leadership computing facilities. These applications depend on deep learning frameworks with hardware acceleration and underlying software systems. With the rapid development of applications, software stacks, and hardware devices, it is essential to evaluate the performance of core operations in AI workloads for direction of optimizations and procurement of next-generation high-performance computing (HPC) infrastructures. Currently, most benchmarks lack scientific AI workloads. So, we present DeepKernelBench and the experimental results of evaluating the benchmark suite for early observations and performance comparisons on datacenter GPUs using representative workloads for scientific AI, including Attentions, General matrix multiplications, Geometrics and Fourier neural operations.

Jin, Zheming [Advanced Micro Devices (AMD)]↗