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DOE OSTI2025

Scaling the memory wall using mixed-precision - HPG-MxP on an exascale-class machine

Mixed-precision algorithms have been proposed as a way for scientific computing to benefit from some of the gains seen for AI on recent high performance computing (HPC) platforms. A few applications dominated by dense matrix operations have seen substantial speedups by utilizing low precision formats such as FP16. However, a majority of scientific simulation applications are memory bandwidth limited. Beyond preliminary studies, the practical gain from using mixed-precision algorithms on a given high-performance computing (HPC) system is largely unclear. The High Performance GMRES Mixed Precision (HPG-MxP) benchmark has been proposed to measure the useful performance of a HPC system on sparse matrix-based mixed-precision applications. In this work, we present an implementation of the HPG-MxP benchmark for an exascale system and describe our algorithm enhancements. We show for the first time a speedup of 1.6x using a combination of double- and single-precision keeping the same residual level on modern GPU-based supercomputers.

Kashi, Aditya [ORNL] (ORCID:0000000325893792)↗

NASA NTRS1985

Investigation of outside visual cues required for low speed and hover

Knowledge of the visual cues required in the performance of stabilized hover in VTOL aircraft is a prerequisite for the development of both cockpit displays and ground-based simulation systems. Attention is presently given to the viability of experimental test flight techniques as the bases for the identification of essential external cues in aggressive and precise low speed and hovering tasks. The analysis and flight test program conducted employed a helicopter and a pilot wearing lenses that could be electronically fogged, where the primary variables were field-of-view, large object 'macrotexture', and fine detail 'microtexture', in six different fields-of-view. Fundamental metrics are proposed for the quantification of the visual field, to allow comparisons between tests, simulations, and aircraft displays.

Hoh, R. H.↗

DOE OSTI2023

Model-based quantification of margins and uncertainties in metal additive manufacturing for process design and qualification

Laser powder bed fusion (LPBF) Additive Manufacturing (AM) has the potential to enable the production of components with novel designs and material properties unachievable otherwise. However, process repeatability is a challenge, making qualification ill-defined and greatly reducing the utility of what could be an important manufacturing technology. In this work, a combination of modeling, uncertainty quantification (UQ), and experimentation are used in an effort to predict and bound the range of possible outcomes of the LPBF process. Quantities of interest predicted are melt pool dimensions, microstructure features, and mechanical distortions. A combination of high fidelity thermal-fluid models, microstructure growth models, and reduced fidelity, rapid thermal and mechanical models are used. Uncertainty propagation techniques are used to predict probability distributions of quantities of interest from estimates of process uncertainties. Repeated experiments are done to quantify observed probability distributions and compared to predicted distributions to determine if predictions are precise and accurate. Novel modeling methods are microstrucutre characterization techniques are also discussed. It is found that high fidelity models do a generally good job bounding experimentally observed melt pool morphologies for both bead-on-plate and powder bed cases. Microstructure models are able to bound a number of experimentally observed microstructure statistics, but with low precision due to challenges with calibrating the microstructure growth model parameters. A developed modified inherent strain distortion model does not accurately predict observed distortions. A lumped laser distortion model shows promise in being both accurately and precisely bounding observed outcomes from the deflection comb build, but requires further evaluation on more builds and geometries.

36 MATERIALS SCIENCE↗

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↗

NASA NTRS2009

Silicon Microleaks for Inlets of Mass Spectrometers

Microleaks for inlets of mass spectrometers used to analyze atmospheric gases can be fabricated in silicon wafers by means of photolithography, etching, and other techniques that are commonly used in the manufacture of integrated circuits and microelectromechanical systems. The microleaks serve to limit the flows of the gases into the mass-spectrometer vacuums to specified very small flow rates consistent with the capacities of the spectrometer vacuum pumps. There is a need to be able to precisely tailor the dimensions of each microleak so as to tailor its conductance to a precise low value. (As used here, "conductance" signifies the ratio between the rate of flow in the leak and the pressure drop from the upstream to the downstream end of the leak.) To date, microleaks have been made, variously, of crimped metal tubes, pulled glass tubes, or frits. Crimped-metal and pulled-glass-tube microleaks cannot readily be fabricated repeatably to precise dimensions and are susceptible to clogging with droplets or particles. Frits tend to be differentially chemically reactive with various gas constituents and, hence, to distort the gas mixtures to be analyzed. The present approach involving microfabrication in silicon largely overcomes the disadvantages of the prior approaches.

Harpold, Dan↗

DOE OSTI2025

Architecture-Aware Models of AI Engines for High-Performance Matrix Matrix Multiplication

The AI Engine (AIE) architecture, available in systems from mobile SoCs to server-class FPGAs, aims to efficiently execute AI/ML tasks through a two-dimensional array of compute tiles. Previous work on AIEs has explored different approaches to mapping computation across spatial arrays, but the compute kernel running on each tile has not been the focus. Additionally, the AIE-ML architecture introduces memory tiles and omits programmable logic, requiring new approaches to staging and moving data throughout the array. In this work we update analytical models developed for CPUs to produce the design of high performance kernels while introducing new model considerations such as memory structure, throughput, and latency as required by the AIE hardware. We evaluate our models by developing AIE-ML kernels for matrix multiplication in low-precision data types showing performance up to 95% of compute peak for the kernel when data resides in local memory and above 90% of compute peak when data resides in main memory.

Binder, Elliott D. [Carnegie Mellon University, Pi↗

DOE OSTI2024

MAGMA: Enabling exascale performance with accelerated BLAS and LAPACK for diverse GPU architectures

MAGMA (Matrix Algebra for GPU and Multicore Architectures) is a pivotal open-source library in the landscape of GPU-enabled dense and sparse linear algebra computations. With a repertoire of approximately 750 numerical routines across four precisions, MAGMA is deeply ingrained in the DOE software stack, playing a crucial role in high-performance computing. Notable projects such as ExaConstit, HiOP, MARBL, and STRUMPACK, among others, directly harness the capabilities of MAGMA. In addition, the MAGMA development team has been acknowledged multiple times for contributing to the vendors’ numerical software stacks. Looking back over the time of the Exascale Computing Project (ECP), we highlight how MAGMA has adapted to recent changes in modern HPC systems, especially the growing gap between CPU and GPU compute capabilities, as well as the introduction of low precision arithmetic in modern GPUs. We also describe MAGMA’s direct impact on several ECP projects. Maintaining portable performance across NVIDIA and AMD GPUs, and with current efforts toward supporting Intel GPUs, MAGMA ensures its adaptability and relevance in the ever-evolving landscape of GPU architectures.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2014

3D Printing In Zero-G ISS Technology Demonstration

The National Aeronautics and Space Administration (NASA) has a long term strategy to fabricate components and equipment on‐demand for manned missions to the Moon, Mars, and beyond. To support this strategy, NASA and Made in Space, Inc. are developing the 3D Printing In Zero‐G payload as a Technology Demonstration for the International Space Station (ISS). The 3D Printing In Zero‐G experiment ('3D Print') will be the first machine to perform 3D printing in space. The greater the distance from Earth and the longer the mission duration, the more difficult resupply becomes; this requires a change from the current spares, maintenance, repair, and hardware design model that has been used on the International Space Station (ISS) up until now. Given the extension of the ISS Program, which will inevitably result in replacement parts being required, the ISS is an ideal platform to begin changing the current model for resupply and repair to one that is more suitable for all exploration missions. 3D Printing, more formally known as Additive Manufacturing, is the method of building parts/objects/tools layer‐by‐layer. The 3D Print experiment will use extrusion‐based additive manufacturing, which involves building an object out of plastic deposited by a wire‐feed via an extruder head. Parts can be printed from data files loaded on the device at launch, as well as additional files uplinked to the device while on‐orbit. The plastic extrusion additive manufacturing process is a low‐energy, low‐mass solution to many common needs on board the ISS. The 3D Print payload will serve as the ideal first step to proving that process in space. It is unreasonable to expect NASA to launch large blocks of material from which parts or tools can be traditionally machined, and even more unreasonable to fly up multiple drill bits that would be required to machine parts from aerospace‐grade materials such as titanium 6‐4 alloy and Inconel. The technology to produce parts on demand, in space, offers unique design options that are not possible through traditional manufacturing methods while offering cost-effective, high‐precision, low‐unit on‐demand manufacturing. Thus, Additive Manufacturing capabilities are the foundation of an advanced manufacturing in space roadmap. The 3D Printing In Zero‐G experiment will demonstrate the capability of utilizing Additive Manufacturing technology in space. This will serve as the enabling first step to realizing an additive manufacturing, print‐on‐demand "machine shop" for long‐duration missions and sustaining human exploration of other planets, where there is extremely limited ability and availability of Earth‐based logistics support. Simply put, Additive Manufacturing in space is a critical enabling technology for NASA. It will provide the capability to produce hardware on‐demand, directly lowering cost and decreasing risk by having the exact part or tool needed in the time it takes to print. This capability will also provide the much‐needed solution to the cost, volume, and up‐mass constraints that prohibit launching everything needed for long‐duration or long‐distance missions from Earth, including spare parts and replacement systems. A successful mission for the 3D Printing In Zero‐G payload is the first step to demonstrate the capability of printing on orbit. The data gathered and lessons learned from this demonstration will be applied to the next generation of additive manufacturing technology on orbit. It is expected that Additive Manufacturing technology will quickly become a critical part of any mission's infrastructure.

Werkheiser, Niki↗

NASA NTRS2011

Bonding Thin Mirror Segments Without Distortion for the International X-Ray Observatory

The International X-Ray Observatory (IXO) uses thin glass optics to maximize large effective area and precise low angular resolution. The thin glass mirror segments must be transferred from their fabricated state to a permanent structure without imparting distortion. IXO will incorporate about fourteen thousand thin mirror segments to achieve the mission goal of 3.0 square meters of effective area at 1.25 keV with an angular resolution of five arcseconds. To preserve figure and alignment, the mirror segment must be bonded with sub-micron movement at each corner. Recent advances in technology development have produced significant x-ray test results of a bonded pair of mirrors. Three specific bonding cycles will be described highlighting the improvements in procedure, temperature control, and precision bonding. This paper will highlight the recent advances in alignment and permanent bonding as well as the results they have produced.

Evans, Tyler C.↗

DOE OSTI2020

GPS-Based Gamma Survey for Characterizing and Decommissioning NORM Sites - 20389

Gamma survey techniques are an especially powerful decommissioning tool at naturally occurring radioactive material (NORM) sites due to both the low cost to obtain data over a large spatial scale and the abundance of gamma emitters in the uranium and thorium decay series. Gamma surveys are executed by coupling a detector - most often a sodium iodide crystal - to a global positioning system (GPS), then reporting a location and gross gamma reading coincidentally to a data logger. Systems may be carried by workers or mounted to a car, all-terrain vehicle, or unmanned aerial system (UAS). The resulting data set provides a high-resolution but low precision map of the gamma radiation field over the area surveyed. Frequently this map is also correlated to soil concentrations of NORM radionuclides (most often, Ra-226) and/or exposure rate. Gamma survey parameters such as movement speed, transect spacing, and data logging frequency define the spatial resolution of the resulting surface, and can be optimized depending on the desired survey sensitivity. This paper examines gamma survey as a tool for decommissioning NORM sites and provides an overview of current gamma survey technology designed to improve the efficiency and effectiveness of the decommissioning process. Topics to be discussed in the paper include: - An overview of gamma survey systems, and the utility of different delivery vehicles depending on desired cost, desired spatial resolution, and site topography. - The influence of physical detector characteristics on detection sensitivity and survey planning. - The tradeoff between high-resolution and large spatial extent, but inherently uncertain data, and low-resolution, low spatial extent, but highly certain data, as well as the specific utility of each of these types of data during NORM facility decommissioning. - Confounding variables that may limit the utility of gamma survey at some sites (e.g., radon gas and spatial heterogeneity / hot spots), and methods to plan for and control these conditions. Results show that the confounding variables, such as radon and data output can greatly influence the overall data quality associated with the decommissioning process. In addition, the use of real-time and aerial survey platforms provides a method for ensuring proper spatial extent of the data. When applied thoughtfully, gamma survey is a powerful tool for detecting NORM radionuclides in the environment and a cost-effective technique for identifying areas requiring remediation. However, entities performing or using gamma survey as a decommissioning tool must be aware of both its advantages and its limitations before basing remediation or regulatory action on gamma survey results. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Assessment of Low-Level Pu Isotope Ratio Measurements Using Multicollector Inductively Coupled Plasma Mass Spectrometry (MC-ICP-MS/MS) Equipped with a Pre-Mass Filter

We present an initial investigation into the performance of a multicollector inductively coupled plasmamass spectrometer equipped with a pre-mass filter (Neoma MC-ICP-MS/MS) for making plutonium (Pu) isotope ratio measurements on solutions containing low level (i.e., pg mL –1 ) Pu concentrations. This assessment was achieved by comparison of the 240 Pu/ 239 Pu, 241 Pu/ 239 Pu, and 242 Pu/ 239 Pu ratios attained over a one month period on the MC-ICP-MS/MS with the long-term (∼1 year) performance observed on the predecessor MC-ICP-MS (Neptune Plus) instrument each equipped with an equipped with an APEXΩ desolvating nebulizer for repeated measurements of certified reference materials from New Brunswick Program Office (NBL PO) CRM 136a and CRM 137. The MC-ICP-MS/MS performance of repeated measurement of CRM 136a (n = 20) resulted in mean values of 240 Pu/ 239 Pu = 0.1448 ± 0.0006, 241 Pu/ 239 Pu = 0.00371 ± 0.00006, and 242 Pu/ 239 Pu = 0.00682 ± 0.00006 (k = 2). The CRM 137 (n = 20), analyzed during the same analytical sessions, produced mean values for 240 Pu/ 239 Pu = 0.2414 ± 0.0006, 241 Pu/ 239 Pu = 0.00464 ± 0.00007, and 242 Pu/ 239 Pu = 0.0157 ± 0.0001 (k = 2). These results closely align with the certificate values for CRM 136a and CRM 137 and are within the k = 2 envelopes defined by the long-term performance of the traditional MC-ICP-MS approach (Neptune Plus). Examination of the performance of the various Pu isotope ratios as a function of total Pu content revealed accurate results (<3% relative difference, or RD) above ∼50 fg total Pu. The results presented here demonstrate the capability of the MC-ICP-MS/MS making accurate and precise low level Pu isotopic measurements. While the intent of this work was not to investigate the functionality of the collision cell, the pre-mass filter was employed. Future studies are warranted to investigate the entire capability of the MC-ICP-MS/MS collision cell and pre-cell mass filter optimization for performing low level Pu isotope measurements, even in mixed matrix samples.

CRM↗

DOE OSTI2024

HDBind: encoding of molecular structure with hyperdimensional binary representations

Traditional methods for identifying “hit” molecules from a large collection of potential drug-like candidates rely on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have a significant limitation in that they require exceptional computing capabilities for even relatively small collections of molecules. Increasingly large and complex state-of-the-art deep learning approaches have gained popularity with the promise to improve the productivity of drug design, notorious for its numerous failures. However, as deep learning models increase in their size and complexity, their acceleration at the hardware level becomes more challenging. Hyperdimensional Computing (HDC) has recently gained attention in the computer hardware community due to its algorithmic simplicity relative to deep learning approaches. The HDC learning paradigm, which represents data with high-dimension binary vectors, allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas (computer vision, bioinformatics, mass spectrometery, remote sensing, edge devices, etc.). To the best of our knowledge, our work is the first to consider HDC for the task of fast and efficient screening of modern drug-like compound libraries. We also propose the first HDC graph-based encoding methods for molecular data, demonstrating consistent and substantial improvement over previous work. We compare our approaches to alternative approaches on the well-studied MoleculeNet dataset and the recently proposed LIT-PCBA dataset derived from high quality PubChem assays. We demonstrate our methods on multiple target hardware platforms, including Graphics Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs), showing at least an order of magnitude improvement in energy efficiency versus even our smallest neural network baseline model with a single hidden layer. Our work thus motivates further investigation into molecular representation learning to develop ultra-efficient pre-screening tools. We make our code publicly available at https://github.com/LLNL/hdbind.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Towards High-Performance AI4NP Applications on Modern GPU Platforms

The evolution of modern heterogeneous accelerators, such as GPUs, has significantly advanced the landscape of artificial intelligence (AI). There is a notable surge to adopt AI within the nuclear physics domain (AI4NP). While most AI4NP studies focus on feasibility analysis, our attention is directed towards evaluating their performance on contemporary GPUs that integrate tensor cores. We first benchmark the throughput of hyperparameterized multi-layer perceptron (MLP) models. We then examine the performance of an AI4NP application: Hydra. We assess the performance gain and accuracy loss caused by the tensor cores for low-precision floating-point operations. Our experiments encompass the PyTorch and TensorFlow Keras frameworks on NVIDIA’s T4 and A100 GPUs. We explore the behavior of different GPU hardware platforms and AI software tools. This study can be a valuable resource for guiding the performance optimization of larger-scale deployments of AI4NP applications.

Mei, Xinxin↗

DOE OSTI2023

Fast b -tagging at the high-level trigger of the ATLAS experiment in LHC Run 3

The ATLAS experiment relies on real-time hadronic jet reconstruction and b-tagging to record fully hadronic events containing b-jets. These algorithms require track reconstruction, which is computationally expensive and could overwhelm the high-level-trigger farm, even at the reduced event rate that passes the ATLAS first stage hardware-based trigger. In LHC Run 3, ATLAS has mitigated these computational demands by introducing a fast neural-network-based b-tagger, which acts as a low-precision filter using input from hadronic jets and tracks. It runs after a hardware trigger and before the remaining high-level-trigger reconstruction. This design relies on the negligible cost of neural-network inference as compared to track reconstruction, and the cost reduction from limiting tracking to specific regions of the detector. In the case of Standard Model HH → bb̅bb̅, a key signature relying on b-jet triggers, the filter lowers the input rate to the remaining high-level trigger by a factor of five at the small cost of reducing the overall signal efficiency by roughly 2%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

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 OSTI2020

PANTHER: A Programmable Architecture for Neural Network Training Harnessing Energy-Efficient ReRAM

The wide adoption of deep neural networks has been accompanied by ever-increasing energy and performance demands due to the expensive nature of training them. Additionally, numerous special-purpose architectures have been proposed to accelerate training: both digital and hybrid digital-analog using resistive RAM (ReRAM) crossbars. ReRAM-based accelerators have demonstrated the effectiveness of ReRAM crossbars at performing matrix-vector multiplication operations that are prevalent in training. However, they still suffer from inefficiency due to the use of serial reads and writes for performing the weight gradient and update step. A few works have demonstrated the possibility of performing outer products in crossbars, which can be used to realize the weight gradient and update step without the use of serial reads and writes. However, these works have been limited to low precision operations which are not sufficient for typical training workloads. Moreover, they have been confined to a limited set of training algorithms for fully-connected layers only. To address these limitations, we propose a bit-slicing technique for enhancing the precision of ReRAM-based outer products, which is substantially different from bit-slicing for matrix-vector multiplication only. We incorporate this technique into a crossbar architecture with three variants catered to different training algorithms. To evaluate our design on different types of layers in neural networks (fully-connected, convolutional, etc.) and training algorithms, we develop PANTHER, an ISA-programmable training accelerator with compiler support. Our design can also be integrated into other accelerators in the literature to enhance their efficiency. Our evaluation shows that PANTHER achieves up to 8.02×, 54.21×, and 103× energy reductions as well as 7.16×, 4.02×, and 16× execution time reductions compared to digital accelerators, ReRAM-based accelerators, and GPUs, respectively.

42 ENGINEERING↗

DOE OSTI2022

Dissecting Tensor Cores via Microbenchmarks: Latency, Throughput and Numeric Behaviors

Tensor Cores have been an important unit to accelerate Fused Matrix Multiplication Accumulation (MMA) in all NVIDIA GPUs since Volta Architecture. To program Tensor Cores, users have to use either legacy wmma APIs or current mma APIs. Legacy wmma APIs are more easy-to-use but can only exploit limited features and power of Tensor Cores. Specifically, wmma APIs support fewer operand shapes and can not leverage the new sparse matrix multiplication feature of the newest Ampere Tensor Cores. However, the performance of current programming interface has not been well explored. Furthermore, the computation numeric behaviors of low-precision floating points (TF32, BF16, and FP16) supported by the newest Ampere Tensor Cores are also mysterious. In this paper, we explore the throughput and latency of current programming APIs. Further, we intuitively study the numeric behaviors of Tensor Cores MMA and profile the intermediate operations including multiplication, addition of inner product, and accumulation. All codes used in this work can be found in https://github.com/sunlex0717/DissectingTensorCores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗