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At least 1,657 records · Page 92

Bayesian analysis of cosmic ray propagation: evidence against homogeneous diffusion

We present the results of the most complete scan of the parameter space for cosmic ray (CR) injection and propagation. We perform a Bayesian search of the main GALPROP parameters, using the MultiNest nested sampling algorithm, augmented by the BAMBI neural network machine-learning package. This is the first study to separate out low-mass isotopes (p, p-bar , and He) from the usual light elements (Be, B, C, N, and O). We find that the propagation parameters that best-fit p, p-bar , and He data are significantly different from those that fit light elements, including the B/C and {sup 10}Be/{sup 9}Be secondary-to-primary ratios normally used to calibrate propagation parameters. This suggests that each set of species is probing a very different interstellar medium, and that the standard approach of calibrating propagation parameters using B/C can lead to incorrect results. We present posterior distributions and best-fit parameters for propagation of both sets of nuclei, as well as for the injection abundances of elements from H to Si. The input GALDEF files with these new parameters will be included in an upcoming public GALPROP update.

79 ASTRONOMY AND ASTROPHYSICS↗

Decision making and problem solving with computer assistance

In modern guidance and control systems, the human as manager, supervisor, decision maker, problem solver and trouble shooter, often has to cope with a marginal mental workload. To improve this situation, computers should be used to reduce the operator from mental stress. This should not solely be done by increased automation, but by a reasonable sharing of tasks in a human-computer team, where the computer supports the human intelligence. Recent developments in this area are summarized. It is shown that interactive support of operator by intelligent computer is feasible during information evaluation, decision making and problem solving. The applied artificial intelligence algorithms comprehend pattern recognition and classification, adaptation and machine learning as well as dynamic and heuristic programming. Elementary examples are presented to explain basic principles.

Kraiss, F.↗

Darwinian Spacecraft: Soft Computing Strategies Breeding Better, Faster Cheaper

Computers can create infinite lists of combinations to try to solve a particular problem, a process called "soft-computing." This process uses statistical comparables, neural networks, genetic algorithms, fuzzy variables in uncertain environments, and flexible machine learning to create a system which will allow spacecraft to increase robustness, and metric evaluation. These concepts will allow for the development of a spacecraft which will allow missions to be performed at lower costs.

Noever, David A.↗

CERES FluxByCldTyp NB2BB Fluxes Improvement based on Deep Neural Network

The NASA Clouds and the Earth's Radiant Energy System (CERES) product provides over 20 years of accurately observed top-of-the-atmosphere (TOA) and surface flux data record for climate monitoring and diagnostic studies. The interaction between clouds and radiation interaction is a key factor that dominate climate feedbacks but is not well understood. To further advance our understanding of the cloud-radiation interaction, a new CERES FluxByCldTyp (FBCT) product has been developed that contains radiative fluxes by cloud-type, which can provide more stringent constraints when validating models and reveal more insight into the interactions between clouds and climate. For CERES partly cloudy and multiple cloud-type footprints, the FBCT product utilizes Moderate Resolution Imaging Spectroradiometer (MODIS) narrow-band (NB) imager channel radiances partitioned by cloud-type within a CERES footprint to estimate the cloud-type broadband fluxes. The MODIS multi-channel derived broadband fluxes were compared with the CERES observed footprint fluxes and were found to be within 1% and 2.5% for LW and SW, respectively, as well as being mostly free of cloud property dependencies. The FBCT all-sky and clear-sky monthly averaged fluxes were found to be consistent with the CERES SSF1deg product. This study takes advantage of recent progress in machine learning (ML) field by applying deep neural network algorithm to improve fluxes based on MODIS NB radiances. The preliminary study shows ML produce are an improvement over the current FBCT Edition 4 NB2BB algorithm. Furthermore, unlike Ed4 NB2BB, the new ML method convert NB radiances directly to broadband fluxes. For future Ed5, new NB radiances are proposed and used by ML to improve fluxes calculation. Prelimary results show significant LW improvement.

Moguo Sun↗

Flux Improvement based on Machine Learning for the CERES FluxByCldTyp Data Product

The NASA Clouds and the Earth's Radiant Energy System (CERES) product provides over 20 years of accurately observed top-of-the-atmosphere (TOA) and surface flux data record for climate monitoring and diagnostic studies. The interaction between clouds and radiation interaction is a key factor that dominate climate feedbacks but is not well understood. To further advance our understanding of the cloud-radiation interaction, a new CERES FluxByCldTyp (FBCT) product has been developed that contains radiative fluxes by cloud-type, which can provide more stringent constraints when validating models and reveal more insight into the interactions between clouds and climate. For CERES partly cloudy and multiple cloud-type footprints, the FBCT product utilizes Moderate Resolution Imaging Spectroradiometer (MODIS) narrow-band (NB) imager channel radiances partitioned by cloud-type within a CERES footprint to estimate the cloud-type broadband fluxes. The MODIS multi-channel derived broadband fluxes were compared with the CERES observed footprint fluxes and were found to be within 1% and 2.5% for LW and SW, respectively, as well as being mostly free of cloud property dependencies. The FBCT all-sky and clear-sky monthly averaged fluxes were found to be consistent with the CERES SSF1deg product. This study takes advantage of recent progress in machine learning (ML) field by applying deep neural network algorithm to improve fluxes based on MODIS NB radiances. The preliminary study shows ML produce are an improvement over the current FBCT Edition 4 NB2BB algorithm. Furthermore, unlike Ed4 NB2BB, the new ML method convert NB radiances directly to broadband fluxes. For future Ed5, new NB radiances are proposed and used by ML to improve fluxes calculation. Prelimary results show significant LW improvement.

Moguo Sun↗

Improvement of Radiative Fluxes for the CERES FluxByCldTyp Data Product Based on Machine Learning Technique

The NASA Clouds and the Earth's Radiant Energy System (CERES) product provides over 20 years of accurately observed top-of-the-atmosphere and surface flux data for climate studies. The interaction between clouds and radiation interaction is a key factor that dominate climate feedbacks but is not well understood. To further advance our understanding of the cloud-radiation interaction, a new CERES FluxByCldTyp (FBCT) product has been developed that contains radiative fluxes by cloud-type, which can provide more stringent constraints when validating models. The FBCT product utilizes Moderate Resolution Imaging Spectroradiometer (MODIS) narrow-band (NB) imager channel radiances partitioned by cloud-type within a CERES footprint to estimate their broadband fluxes. The MODIS multi-channel derived broadband fluxes were compared with the CERES observed footprint fluxes and were found to be within 1% and 2.5% for LW and SW, respectively, as well as being mostly free of cloud property dependencies. The FBCT all-sky and clear-sky monthly averaged fluxes were found to be consistent with the CERES SSF1deg product. This study takes advantage of recent progress in machine learning (ML) field by applying deep neural network algorithm to improve fluxes based on MODIS NB radiances. The preliminary study shows ML produce are an improvement over the current FBCT Edition 4 NB2BB algorithm. Furthermore, unlike Ed4 NB2BB, the new ML method convert NB radiances directly to broadband fluxes. For future Ed5, new NB radiances are proposed and used by ML to improve fluxes calculation. Preliminary results show significant LW improvement.

Sun, Moguo↗

Improvement of Radiative Fluxes for the CERES FluxByCldTyp Data Product Based on Machine Learning Technique

The NASA Clouds and the Earth's Radiant Energy System (CERES) product provides over 20 years of accurately observed top-of-the-atmosphere (TOA) and surface flux data record for climate monitoring and diagnostic studies. The interaction between clouds and radiation interaction is a key factor that dominate climate feedbacks but is not well understood. To further advance our understanding of the cloud-radiation interaction, a new CERES FluxByCldTyp (FBCT) product has been developed that contains radiative fluxes by cloud-type, which can provide more stringent constraints when validating models and reveal more insight into the interactions between clouds and climate. For CERES partly cloudy and multiple cloud-type footprints, the FBCT product utilizes Moderate Resolution Imaging Spectroradiometer (MODIS) narrow-band (NB) imager channel radiances partitioned by cloud-type within a CERES footprint to estimate the cloud-type broadband fluxes. The MODIS multi-channel derived broadband fluxes were compared with the CERES observed footprint fluxes and were found to be within 1% and 2.5% for LW and SW, respectively, as well as being mostly free of cloud property dependencies. The FBCT all-sky and clear-sky monthly averaged fluxes were found to be consistent with the CERES SSF1deg product. This study takes advantage of recent progress in machine learning (ML) field by applying deep neural network algorithm to improve fluxes based on MODIS NB radiances. The preliminary study shows ML produce are an improvement over the current FBCT Edition 4 NB2BB algorithm. Furthermore, unlike Ed4 NB2BB, the new ML method convert NB radiances directly to broadband fluxes. For future Ed5, new NB radiances are proposed and used by ML to improve fluxes calculation. Prelimary results show significant LW improvement.

Moguo Sun↗

Improving Radiative Fluxes for the CERES FluxByCldTyp Data Product Using Deep Neural Network

The NASA Clouds and the Earth's Radiant Energy System (CERES) product provides over 20 years of accurately observed top-of-the-atmosphere (TOA) and surface flux data record for climate monitoring and diagnostic studies. The interaction between clouds and radiation interaction is a key factor that dominate climate feedbacks but is not well understood. To further advance our understanding of the cloud-radiation interaction, a new CERES FluxByCldTyp (FBCT) product has been developed that contains radiative fluxes by cloud-type, which can provide more stringent constraints when validating models and reveal more insight into the interactions between clouds and climate. For CERES partly cloudy and multiple cloud-type footprints, the FBCT product utilizes Moderate Resolution Imaging Spectroradiometer (MODIS) narrow-band (NB) imager channel radiances partitioned by cloud-type within a CERES footprint to estimate the cloud-type broadband fluxes. The MODIS multi-channel derived broadband fluxes were compared with the CERES observed footprint fluxes and were found to be within 1% and 2.5% for LW and SW, respectively, as well as being mostly free of cloud property dependencies. The FBCT all-sky and clear-sky monthly averaged fluxes were found to be consistent with the CERES SSF1deg product. This study takes advantage of recent progress in machine learning (ML) field by applying deep neural network algorithm to improve fluxes based on MODIS NB radiances. The preliminary study shows ML produce are an improvement over the current FBCT Edition 4 NB2BB algorithm. Furthermore, unlike Ed4 NB2BB, the new ML method convert NB radiances directly to broadband fluxes. For future Ed5, new NB radiances are proposed and used by ML to improve fluxes calculation. Preliminary results show significant LW improvement.

Sun, Moguo↗

How Should Machine Learning Be Successfully Used for Wind Speed Vertical Extrapolation?

An accurate characterization of the wind resource available at hub-height is required for an efficient and bankable wind farm project. However, direct measurement of wind speed at the constantly increasing height of the hub of commercial wind turbines is oftentimes challenging and expensive, so that it is common practice to vertically extrapolate the wind resource from lower and more easily accessible levels. Conventional techniques for wind speed vertical extrapolation include the use of a power law and a logarithmic profile. While simple, the limits in accuracy of these methods have been shown in various studies. Recently, machine learning has been proposed as a new method to vertically extrapolate winds. All the published studies on the topic assess the performance of machine learning techniques in vertically extrapolating the wind resource at the same location where the algorithm has been trained. However, in real-world applications, the wind resource is measured at the instrument location, but it then needs to be extrapolated at hub height at the location of the wind turbines within the find farm. To be able to fully recommend the use of machine learning techniques over the simple power law and logarithmic law, the spatial variability of the performance improvements of the machine learning approaches needs to be assessed. Here, we propose a round-robin validation of a machine learning-based method for wind speed extrapolation. We use 20 months of observations at four locations spanning a 100 km wide region at the Southern Great Plains (SGP) atmospheric observatory, in north-central Oklahoma. At each location, we train a random forest to predict 30-min average wind speed at 143 m AGL. We use as input features lidar wind speed at 65 m AGL, time of day, sonic anemometer wind speed at 4 m AGL, turbulent kinetic energy, and Obukhov length. First, we perform a same-site comparison of the performance of the proposed random forest against the conventional techniques for wind speed extrapolation (namely power law and logarithmic profile, with widely accepted stability corrections). We find that the random forest outperforms the power law in vertically extrapolating wind speed in all the considered stability regimes, with a 33% reduction in MAE for stable conditions, and a 31% reduction in unstable conditions. Similar results are found when comparing predictions of extrapolated winds from the logarithmic profile and the random forest with the observed values. Next, we propose a round-robin validation, to use the random forest trained at each site to extrapolate wind speed at the remaining three sites. We find that the performance of the random forest approach degrades when the algorithm is tested at a site different than the training one. However, even under those circumstances, the machine learning-based approach still outperforms the conventional techniques for wind speed extrapolation, with, on average, a reduction in mean absolute error between 15 and 20% over the conventional methods, with the largest benefits obtained under stable conditions.

Monte Carlo↗

A Computational Framework to design 3D stiffness gradient acoustic metamaterials for impedance matching

Acoustic waves play a crucial role in various applications, including medical imaging, non-destructive testing, and sonar systems. One of the significant challenges in these applications is impedance matching, which is essential for minimizing reflections and maximizing the transfer of acoustic energy between different media. Acoustic metamaterials offer a promising solution to this challenge. In addition to impedance control, gradient stiffness can enhance structural efficiency and enable spatial control of wave propagation, making it a valuable feature in acoustic metamaterial design. In this pa- per, we present our developed computational method to design 3D stiffness gradient acoustic metamaterials for impedance matching. The key steps in our approach include generating initial designs using a periodic covariance function to provide unit cells that are both periodic on the boundaries and randomly formed inside the unit cell. Furthermore, we integrated manufacturing constraints into the design process, ensuring that the structures are interconnected for fabrication. We propose two computational optimization algorithms: GenUnit, based on a non-dominated sorting genetic algorithm (NSGA-II), and MLMatch, which leverages differentiable machine learning. The two approaches are not separate contributions but complementary com- ponents of a unified framework. GenUnit requires no training data and directly interfaces with physics-based simulations, making it highly accurate but slower for large-scale exploration. In contrast, MLMatch is data-hungry during training but, once trained, enables near-instantaneous inference and broad design-space coverage. Together, they form a hybrid strategy: ML- Match rapidly explores the global design space, and GenUnit provides local refinement with high-fidelity accuracy. This balance between training cost, inference time, and precision is the motivation for including both methods in the same study. We applied this dual-algorithm framework to generate two metallic-based metamaterial designs that match the acoustic impedance of water while exhibiting a controlled gradient in stiffness (from stiff to soft). The stiffness gradient is particularly advantageous in applications where one side of the structure must interface with soft or sensitive surfaces, such as human tissue or delicate components. Here, this work paves the way for improved materials in various acoustic applications, particularly in ultrasound devices, by providing better impedance.

Metamaterial↗

Optimal Experimental Design With Fast Neural Network Surrogate Models

Designing optimal experiments minimizes the uncertainty of results and maximizes the efficient use of resources. Herein, machine learning surrogate models and the approximate coordinate exchange (ACE) algorithm are used to determine optimum experimental designs over large or arbitrarily restrictive design spaces. Optimal experimental design is particularly salient in materials science where experiments are expensive and material properties must often be inferred indirectly. The proposed framework is demonstrated by finding optimal experiments with which the hidden constituent properties of composite materials can be most efficiently inferred from observable experimental outcomes. The optimum experimental design is given by an information-theoretic criteria, which maximizes the conditional mutual information between the hidden properties and the expected experimental outcomes. To perform tractable optimization a neural network is trained as a surrogate model to mimic a physics based simulation, which can calculate the expected experimental outcome based on a candidate experimental design and sampled constituent properties. The ACE algorithm is used to optimize over large design spaces with many tests and controlled parameters where an exhaustive search would be intractable even with the surrogate model. Using this approach, optimal experimental designs that are consistent with those produced by heuristic knowledge and established best practices are found; then optimal designs in larger design spaces where heuristic knowledge is unavailable are examined.

machine learning↗

Cyberattack Detection and Mitigation on Central Volt‐VAr Using Circuit Law and Machine Learning

ABSTRACT In a distribution grid, voltage is maintained within a nominal range through a Volt‐VAr function that controls capacitor banks, reactive power of distributed energy resources (DER), and on‐load tap changers (OLTC). Availability of communications helps with the implementation of central Volt‐VAr control; however, it also opens the system to cyberattacks, causing voltage disturbances. Previous work has shown the adverse impacts of false data injection (FDI) on the central Volt‐VAr control; however, very few works have studied methods to detect and mitigate FDI on Volt‐VAr control. This paper addresses gaps in the detection and mitigation of FDI on the measurement packets of a central Volt‐VAr control. This work uses a two‐stage algorithm for cyberattack detection since the accuracy of a single‐stage machine learning (ML)–based detection method decreases while dealing with unseen data. The first stage is based on the verification of measurements against circuit laws, and the second stage utilizes a tree search algorithm and an ML method to detect the falsified data. This paper compares long short‐term memory (LSTM) and bidirectional LSTM (BiLSTM) as the employed ML algorithms. Finally, the mitigation algorithm replaces the falsified data with the estimated output of the ML algorithm. The effectiveness of the proposed method is tested for several cases using the IEEE 13‐bus test system in PSCAD software.

Beikbabaei, Milad [Bradley Department of Electrica↗

Control simulations of many-body quantum systems by a synergism of discrete real-time learning and optimal control theory

We present a self-consistent algorithm for optimal control simulations of many-body quantum systems. The algorithm features a two-step synergism that combines discrete real-time machine learning (DRTL) with Quantum Optimal Control Theory (QOCT) using the time-dependent Schrödinger equation. Specifically, in step (1), DRTL is employed to identify a compact working space (i.e., the important portion of the Hilbert space) for the time evolution of the many-body quantum system in the presence of a control field (i.e., the initial or previously updated field), and in step (2), QOCT utilizes the DRTL-determined working space to find a newly updated control field for a chosen objective. Steps 1 and 2 are iterated until a self-consistent control objective value is reached such that the resulting optimal control field yields the same targeted objective value when the corresponding working space is systematically enlarged. Furthermore, to demonstrate this two-step self-consistent DRTL-QOCT synergistic algorithm, we perform optimal control simulations of strongly interacting 1D as well as 2D Heisenberg spin systems. In both scenarios, only a single spin (at the left end site for 1D and the upper left corner site for 2D) is driven by the time-dependent control fields to create an excitation at the opposite site as the target. It is found that, starting from all spin-down zero excitation states, the synergistic method is able to identify working spaces and convergence of the desired controlled dynamics with just a few iterations of the overall algorithm. In the cases studied, the dimensionality of the working space scales only quasi-linearly with the number of spins.

Artificial neural networks↗

A Pattern Based Algorithmic Autotuner for Graph Processing on GPUs

This paper presents Gswitch, a pattern-based algorithmic autotuning system that dynamically switches to the suitable optimization variants with negligible overhead. Its novelty is a small set of algorithmic patterns that enables configurable assembling of algorithm variants. The fast transition of Gswitch is based on a machine learning model trained from 644 real graphs from the network repository. In addition, Gswitch provides succinct programming interface which hides all low-level tuning details. We evaluate Gswitch for typical graph algorithms (BFS, CC, PR, SSSP, and BC) on Nvidia Kepler and Pascal GPUs. The results show that Gswitch runs up to 10× faster than the best configuration of the state-of-the-art programmable GPU-based graph processing libraries on ten representative graphs. Gswitch wins on 92.4% cases of 644 graph data which is the largest dataset evaluation reported to date.

HPC, graph algorithms, GPUs, auto tuning↗

Designing Monte Carlo Simulation and an Optimal Machine Learning to Optimize and Model Space Missions

This paper investigates applying artificial intelligence (AI) algorithms to attitude control system of satellites to optimally tune the controller using high performance computing. This methodology is applied to the Virtual Telescope for X-ray Observation mission, which is a precise formation of two separate spacecraft observing multiple objects in the space in the X-ray domain. The mission is divided into phases based on the instrumentation and the mission goal. To reach an stable precise formation robust to stochastic slew and slew rate (i.e., Euler angles and angular velocities) in a minimal constrained time T , consumed energy of the attitude control system, denoted as E, and root-mean-square state error of attitude control system, denoted as e, are minimized. Monte-Carlo simulation is used for the sensitivity analysis of optimization and designing a controller. Deep neural networks (DNN), Gaussian processes (GP), and support vector regression (SVR) learn this optimization as a surrogate model, while their hyperparameters are optimized in a novel approach. THETA supercomputer at Argonne Leadership Computing Facility (ALCF) is used for optimizing the hyperparameters of DNN. The surrogate model meets the requirements of the mission, and it shows a better performance over the optimization and Monte-Carlo. The optimal DNN can satisfy the mission requirements e and T while reducing E for 90% compared to the other given methods.

42 ENGINEERING↗

Toward Consistent High-Fidelity Quantum Learning on Unstable Devices via Efficient In-Situ Calibration

In the near-term noisy intermediate-scale quantum (NISQ) era, high noise will significantly reduce the fidelity of quantum computing. What's worse, recent works reveal that the noise on quantum devices is not stable, that is, the noise is dynamically changing over time. This leads to an imminent challenging problem: At run-time, is there a way to efficiently achieve a consistent high-fidelity quantum system on unstable devices? To study this problem, we take quantum learning (a.k.a., variational quantum algorithm) as a vehicle, which has a wide range of applications, such as combinatorial optimization and machine learning. A straightforward approach is to optimize a variational quantum circuit (VQC) with a parameter-shift approach on the target quantum device before using it; however, the optimization has an extremely high time cost, which is not practical at run-time. To address the pressing issue, in this paper, we proposed a novel quantum pulse-based noise adaptation framework, namely QuPAD. In the proposed framework, first, we identify that the CNOT gate is the fidelity bottleneck of the conventional VQC, and we employ a more robust parameterized multi-qubit gate (i.e., Rzx gate) to replace CNOT gate. Second, by benchmarking Rzx gate with different parameters, we build a fitting function for each coupling qubit pair, such that the deviation between the theoretic output of Rzx gate and its on-device output under a given pulse amplitude and duration can be efficiently predicted. On top of this, an evolutionary algorithm is devised to identify the pulse amplitude and duration of each Rzx gate (i.e., calibration) and find the quantum circuits with high fidelity. Experiments show that the runtime on quantum devices of QuPAD with 8–10 qubits is less than 15 minutes, which is up to 270 x faster than the parameter-shift approach. In addition, compared to the vanilla VQC as a baseline, QuPAD can achieve 59.33% accuracy gain on a classification task, and average 66.34% closer to ground state energy for molecular simulation.

Hu, Zhirui↗

ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.

97 MATHEMATICS AND COMPUTING↗

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↗