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At least 253 records · Page 14

Optimizing a magnitude-limited spectroscopic training sample for photometric classification of supernovae

ABSTRACT In preparation for photometric classification of transients from the Legacy Survey of Space and Time (LSST) we run tests with different training data sets. Using estimates of the depth to which the 4-m Multi-Object Spectroscopic Telescope (4MOST) Time Domain Extragalactic Survey (TiDES) can classify transients, we simulate a magnitude-limited sample reaching rAB ≈ 22.5 mag. We run our simulations with the software snmachine, a photometric classification pipeline using machine learning. The machine-learning algorithms struggle to classify supernovae when the training sample is magnitude limited, in contrast to representative training samples. Classification performance noticeably improves when we combine the magnitude-limited training sample with a simulated realistic sample of faint high-redshift supernovae observed from larger spectroscopic facilities; the algorithms’ range of average area under receiver operator characteristic curve (AUC) scores over 10 runs increases from 0.547–0.628 to 0.946–0.969 and purity of the classified sample reaches 95 per cent in all runs for two of the four algorithms. By creating new, artificial light curves using the augmentation software avocado, we achieve a purity in our classified sample of 95 per cent in all 10 runs performed for all machine-learning algorithms considered. We also reach a highest average AUC score of 0.986 with the artificial neural network algorithm. Having ‘true’ faint supernovae to complement our magnitude-limited sample is a crucial requirement in optimization of a 4MOST spectroscopic sample. However, our results are a proof of concept that augmentation is also necessary to achieve the best classification results.

79 ASTRONOMY AND ASTROPHYSICS↗

Neoclassical toroidal viscosity torque prediction via deep learning

GPECnet is a densely connected neural network that has been trained on GPEC data, to predict the plasma stability, neoclassical toroidal viscosity (NTV) torque, and optimized 3D coil current distributions for desired NTV torque profiles. Using NTV torque, driven by non-axisymmetric field perturbations in a tokamak, can be vital in optimizing pedestal performance by controlling the rotation profile in both the core, to ensure tearing stability, and the edge, to avoid edge localized modes (ELMs). The generalized perturbed equilibrium code (GPEC) software package can be used to calculate the plasma stability to 3D perturbations and the NTV torque profile generated by applied 3D magnetic fields. These calculations, however, involve complex integrations over space and energy distributions, which takes time to compute. Initially, GPECnet has been trained solely on data representative of the quiescent H-mode (QH) scenario, in which neutral beams are often balanced and toroidal rotation is low across the plasma profile. Lastly, this work provides the foundation for active control of the rotation shear using a combination of beams and 3D fields for robust and high performance QH mode operation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Visualization System for Evolutionary Neural Networks for Deep Learning

Deep learning is actively used in a wide range of fields for scientific discovery. To effectively apply deep learning to a particular problem, it is important to select an appropriate network architecture and other hyper-parameters (at each layer). Evolving architectures and hyper-parameters using a genetic algorithm is one current approach to search the huge space of all possible configurations to find those more optimal for the problem. However, examining an evolutionary process and tuning the genetic algorithm are challenging, pushing most users to treat the process as a black box. To address this challenge, we propose a visualization system for evolutionary neural networks for deep learning. The key feature of our visualization system is to provide a visual analytics environment for evaluating a genetic algorithm in order to improve the underlying operations to reduce time to find good solutions. Our system is able to not only visualize how a genetic algorithm traverses its search space but also allows users to examine evolving networks in-depth to get insights to improve performance through interactive visualization components.

Chae, Junghoon↗

Quantum-Assisted Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

The quantum computing community has been searching for suitable applications to demonstrate the potential of near-term quantum devices. Quantum machine learning is a potential candidate, particularly using models that cannot be efficiently simulated with classical computers [1, 2]. This work focuses on a transition phase of quantum computers where the quantum machine learning model is still simulable classically but projected not to be simulable as the size of the model grows. Ultimately quantum computers may have advantages for high-dimensional real-world problems. Due to the limited number of qubits in current noisy intermediate-scale quantum (NISQ) devices, the direct application of quantum computers in high dimensional data is not feasible. To remedy this problem, an encoder-decoder architecture can be utilized. The encoder model would transform the high-dimensional data into a compact representation, to a level that small quantum computers can be used today (or in the near future), and the decoder would take the quantum processed outputs back to the high-dimensional space. Addressing the two challenges of quantum machine learning, this work investigates a hybrid supervised generative model with a quantum Ising Born machine embedded as the latent distribution. The model contains four main parts (Figure 1.a.): (1) a U-NET architecture responsible for learning segmentation flow, (2) a Prior network responsible for learning an encoded latent distribution of the input data, (3) a Born machine which represents the latent distribution, and (4) a Posterior network in charge of learning the joint encoded latent distribution of inputs and target data. The initial model, proposed by [3], is optimized by (1) maximizing the overlap of the prior and posterior latent distributions, and (2) minimizing the segmentation loss. The proposed model is designed to be investigated in a simulation environment applied to the real-world application of wildfire segmentation. Specifically, the model is designed to solve the patchy wildfire segmentations of Moderate Resolution Imaging Spectroradiometer (MODIS) by taking the MODIS observations and using Visible Infrared Imaging Radiometer Suite’s (VIIRS) consistent wildfire product as the target. The model solves patchy wildfire segmentations and provides insight into the epistemic errors sourced from model variation. The model utilizes the Born machine as a QUBO solver to represent the latent space as a Bernoulli distribution. The proposed configuration allows the variational segmentation model to leverage the true quantum probabilistic nature and derive a more expressive latent configuration, increasing the model performance in describing wildfire segmentations. The quantum probabilistic information of the Born machine is directly incorporated in the Kullback-Leibler divergence loss in the prior and posterior distributions, forcing the Bernoulli latent distribution to maximize the overlap of input and joint input-target distributions. The proposed model is then trained and compared with a baseline only consisting of direct Bernoulli latent distribution with no Born machine representing the latent space. The models are evaluated based on the segmentation metrics, such as precision, recall, intersect of union, with uncertainty boundaries accounting for the stochastic nature of the model. Our findings show that even in low latent-dimensional space (due to the limit in computational power of the classical quantum simulator), we are able to effectively capture the latent representation and hence the model performs better than the baseline. The findings are a projection for scaling the model into higher dimensional latent space with the Born machine surpassing the baseline performance. Figure 1. Sub-figure (a) demonstrates the architecture for the training phase. The model consists of a Prior and Posterior network that encode inputs and joint input-target data into compact representations, respectively. The Born machine represents the latent distribution, and the U-NET branch learns the segmentation patterns of the data. The stochasticity is introduced to the U-NET through its last layer to create meaningful but stochastic segmentations. Sub-figure (b) represents the inference phase where the model takes the stochastic behavior from the prior network and injects that into the U-NET. Each attempt of inference will generate different but similar segmentations from the same distribution of the wildfire event. REFERENCES [1] Coyle, B., Mills, D., Danos, V., & Kashefi, E. (2020). The Born supremacy: quantum advantage and training of an Ising Born machine. npj Quantum Information, 6(1), 1-11. [2] Liu, J. G., & Wang, L. (2018). Differentiable learning of quantum circuit born machines. Physical Review A, 98(6), 062324. [3] Kohl, S., Romera-Paredes, B., Meyer, C., De Fauw, J., Ledsam, J. R., Maier-Hein, K., ... & Ronneberger, O. (2018). A probabilistic u-net for segmentation of ambiguous images. Advances in neural information processing systems, 31.

quantum machine learning↗

Simulating large one-dimensional neutral-atom quantum systems

While abstract models of quantum computation assume a closed system of two-level states, practical quantum devices inevitably couple to the environment in some way, creating sources of noise. Understanding the tolerance to noise of specific quantum algorithms run on specific devices is important for determining the feasibility of quantum computing in the current noisy intermediate-scale quantum era. Of particular interest is understanding the noise sensitivity of these devices as more qubits are added to the system. Classical simulations are a useful tool to understand the effects of this noise, but direct classical simulations of open quantum systems are burdened by an exponentially growing cost in the number of qubits and a large local Hilbert space dimension. For onedimensional, shallow circuits, using tensor networks can replace this exponential cost with a linear one and simulate far wider systems than what would normally be available. In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a purity-preserving truncation technique that compromises between the simplicity of the matrix product state and the positivity of the matrix product density operator. We apply this simulation to a near-optimized iteration of the quantum approximate optimization algorithm on a transverse field Ising model in order to investigate the influence of large system sizes on the performance of the algorithm. We find that while circuits with a large number of qubits fail more often under noise that depletes the qubit population, their outputs on a successful measurement are just as robust under Rydberg atom dissipation or qubit dephasing as smaller systems. However, such circuits might not perform as well under coherent multiqubit errors such as Rydberg atom crosstalk. We also find that the optimized parameters are especially robust to noise, suggesting that a noisier quantum system can be used to find the optimal parameters before switching to a cleaner system for measurements of observables.

Allen, James↗

Structural design options for the new 34 meter beam waveguide antenna

In addition to the successful network of 34 m High Efficiency antennas recently built by JPL, the Deep Space Network (DSN) is embarking on the construction of a 34 m high performance, research and development antenna with beam waveguide optics at the Venus site. The construction of this antenna presents many engineering challenges in the area of structural, mechanical, RF, and pointing system design. A set of functional and structural design requirements is outlined to guide analysts in the final configuration selection. Five design concepts are presented covering both the conventional center-fed beam optics as well as the nonconventional, by-pass beam configuration. The merits of each concept are discussed with an emphasis on obtaining a homologous design. The preliminary results of structural optimization efforts, currently in progress, are promising, indicating the feasibility of meeting, as a minimum, all X-band (8.4 GHz) requirements, with a goal towards meeting Ka-band (32 GHz) quality performance, at the present budget constraints.

Katow, S.↗

Analyzing inference workloads for spatiotemporal modeling

Ensuring power grid resiliency, forecasting climate conditions, and optimization of transportation infrastructure are some of the many application areas where data is collected in both space and time. Spatiotemporal modeling is about modeling those patterns for forecasting future trends and carrying out critical decision-making by leveraging machine learning/deep learning. Once trained offline, field deployment of trained models for near real-time inference could be challenging because performance can vary significantly depending on the environment, available compute resources and tolerance to ambiguity in results. Users deploying spatiotemporal models for solving complex problems can benefit from analytical studies considering a plethora of system adaptations to understand the associated performance-quality trade-offs. To facilitate the co-design of next-generation hardware architectures for field deployment of trained models, it is critical to characterize the workloads of these deep learning (DL) applications during inference and assess their computational patterns at different levels of the execution stack. In this paper, we develop several variants of deep learning applications that use spatiotemporal data from dynamical systems. We study the associated computational patterns for inference workloads at different levels, considering relevant models (Long short-term Memory, Convolutional Neural Network and Spatio-Temporal Graph Convolution Network), DL frameworks (Tensorflow and PyTorch), precision (FP16, FP32, AMP, INT16 and INT8), inference runtime (ONNX and AI Template), post-training quantization (TensorRT) and platforms (Nvidia DGX A100 and Sambanova SN10 RDU). Overall, our findings indicate that although there is potential in mixed-precision models and post-training quantization for spatiotemporal modeling, extracting efficiency from contemporary GPU systems might be challenging. Instead, co-designing custom accelerators by leveraging optimized High Level Synthesis frameworks (such as SODA High-Level Synthesizer for customized FPGA/ASIC targets) can make workload-specific adjustments to enhance the efficiency.

97 MATHEMATICS AND COMPUTING↗

Hayabusa Re-Entry: Trajectory Analysis and Observation Mission Design

On June 13th, 2010, the Hayabusa sample return capsule successfully re-entered Earth s atmosphere over the Woomera Prohibited Area in southern Australia in its quest to return fragments from the asteroid 1998 SF36 Itokawa . The sample return capsule entered at a super-orbital velocity of 12.04 km/sec (inertial), making it the second fastest human-made object to traverse the atmosphere. The NASA DC-8 airborne observatory was utilized as an instrument platform to record the luminous portion of the sample return capsule re-entry (~60 sec) with a variety of on-board spectroscopic imaging instruments. The predicted sample return capsule s entry state information at ~200 km altitude was propagated through the atmosphere to generate aerothermodynamic and trajectory data used for initial observation flight path design and planning. The DC- 8 flight path was designed by considering safety, optimal sample return capsule viewing geometry and aircraft capabilities in concert with key aerothermodynamic events along the predicted trajectory. Subsequent entry state vector updates provided by the Deep Space Network team at NASA s Jet Propulsion Laboratory were analyzed after the planned trajectory correction maneuvers to further refine the DC-8 observation flight path. Primary and alternate observation flight paths were generated during the mission planning phase which required coordination with Australian authorities for pre-mission approval. The final observation flight path was chosen based upon trade-offs between optimal viewing requirements, ground based observer locations (to facilitate post-flight trajectory reconstruction), predicted weather in the Woomera Prohibited Area and constraints imposed by flight path filing deadlines. To facilitate sample return capsule tracking by the instrument operators, a series of two racetrack flight path patterns were performed prior to the observation leg so the instruments could be pointed towards the region in the star background where the sample return capsule was expected to become visible. An overview of the design methodologies and trade-offs used in the Hayabusa re-entry observation campaign are presented.

Cassell, Alan M.↗

Sorption compressor/mechanical expander hybrid refrigeration

Experience with Deep Space Network (DSN) ground-based cryogenic refrigerators has proved the reliability of the basic two-stage Gifford-McMahon helium refrigerator. A very long life cryogenic refrigeration system appears possible by combining this expansion system or a turbo expansion system with a hydride sorption compressor in place of the usual motor driven piston compressor. To test the feasibility of this system, a commercial Gifford-McMahon refrigerator was tested using hydrogen gas as the working fluid. Although no attempt was made to optimize the system for hydrogen operation, the refrigerator developed 1.3 W at 30 K and 6.6 W at 60 K. The results of the test and of theoretical performances of the hybrid compressor coupled to these expansion systems are presented.

Jones, J. A.↗

Experimental validation of docking and capture using space robotics testbeds

This presentation describes the application of robotic and computer vision systems to validate docking and capture operations for space cargo transfer vehicles. Three applications are discussed: (1) air bearing systems in two dimensions that yield high quality free-flying, flexible, and contact dynamics; (2) validation of docking mechanisms with misalignment and target dynamics; and (3) computer vision technology for target location and real-time tracking. All the testbeds are supported by a network of engineering workstations for dynamic and controls analyses. Dynamic simulation of multibody rigid and elastic systems are performed with the TREETOPS code. MATRIXx/System-Build and PRO-MATLAB/Simulab are the tools for control design and analysis using classical and modern techniques such as H-infinity and LQG/LTR. SANDY is a general design tool to optimize numerically a multivariable robust compensator with a user-defined structure. Mathematica and Macsyma are used to derive symbolically dynamic and kinematic equations.

Spofford, John↗

Technology forecasting for space communication. Task one report: Cost and weight tradeoff studies for EOS and TDRS

Weight and cost optimized EOS communication links are determined for 2.25, 7.25, 14.5, 21, and 60 GHz systems and for a 10.6 micron homodyne detection laser system. EOS to ground links are examined for 556, 834, and 1112 km EOS orbits, with ground terminals at the Network Test and Tracking Facility and at Goldstone. Optimized 21 GHz and 10.6 micron links are also examined. For the EOS to Tracking and Data Relay Satellite to ground link, signal-to-noise ratios of the uplink and downlink are also optimized for minimum overall cost or spaceborne weight. Finally, the optimized 21 GHz EOS to ground link is determined for various precipitation rates. All system performance parameters and mission dependent constraints are presented, as are the system cost and weight functional dependencies. The features and capabilities of the computer program to perform the foregoing analyses are described.

Source record↗

A neural-network based estimator to search for primordial non-Gaussianity in Planck CMB maps

We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the SMICA map we found f{sub NL} = 33 ± 23, at 1σ confidence level, in excellent agreement with the WMAP-9yr and Planck results. In addition, for the other three Planck maps we obtain similar constraints with values in the interval f{sub NL} element of [33, 41], concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixel's noise intensities.

79 ASTRONOMY AND ASTROPHYSICS↗

Graph neural networks for CO 2 solubility predictions in Deep Eutectic Solvents

Deep Eutectic Solvents (DESs) are a promising class of solvents for CO 2 capture. DESs are complex mixtures that can be designed to optimize CO solubility and overall capture process efficiency. However, the vast design landscape of DES mixtures makes experimental investigation prohibitive; as such, there is a need for computational models that can quickly and efficiently navigate the design space and inform data collection efforts. In this work, we propose Graph Neural Network (GNN) models for predicting CO 2 solubility for DESs; the GNN leverages a mixture graph representation that captures the molecular structure of the DES components as well as their intermolecular interactions. Here, we compare the GNN framework against alternative architectures (neural networks, graph convolution networks, and random forests) and data representations (molecular fingerprints, sigma profiles, and graphs). We show that the proposed approach offers superior predictive performance; specifically, we show that solubility can be predicted reliably directly from molecular structure (without the need of using sigma profiles as proposed in previous studies). This result is important, as obtaining sigma profiles requires expensive density functional theory computations. We also explored the ability of GNNs to predict solubility for new DES mixtures and operating conditions. We found that the model extrapolates across temperature reliably. However, we also found deficiencies in the ability of the model to predict solubility for DES mixtures, pressures, and molar ratio not included in the training sets; we show that this is due to an inherent lack of chemical diversity in datasets available in the literature. The proposed computational capabilities can thus help navigate the design space of DES and inform data collection efforts. Our models, data, and benchmarks are shared as Python code implemented in Jupyter notebooks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

When in-memory computing meets spiking neural networks—A perspective on device-circuit-system-and-algorithm co-design

This review explores the intersection of bio-plausible artificial intelligence in the form of spiking neural networks (SNNs) with the analog in-memory computing (IMC) domain, highlighting their collective potential for low-power edge computing environments. Through detailed investigation at the device, circuit, and system levels, we highlight the pivotal synergies between SNNs and IMC architectures. Additionally, we emphasize the critical need for comprehensive system-level analyses, considering the inter-dependencies among algorithms, devices, circuit, and system parameters, crucial for optimal performance. An in-depth analysis leads to the identification of key system-level bottlenecks arising from device limitations, which can be addressed using SNN-specific algorithm–hardware co-design techniques. This review underscores the imperative for holistic device to system design-space co-exploration, highlighting the critical aspects of hardware and algorithm research endeavors for low-power neuromorphic solutions.

Physics↗

Image Analysis via Fuzzy-Reasoning Approach: Prototype Applications at NASA

A set of imaging techniques based on Fuzzy Reasoning (FR) approach was built for NASA at Kennedy Space Center (KSC) to perform complex real-time visual-related safety prototype tasks, such as detection and tracking of moving Foreign Objects Debris (FOD) during the NASA Space Shuttle liftoff and visual anomaly detection on slidewires used in the emergency egress system for Space Shuttle at the launch pad. The system has also proved its prospective in enhancing X-ray images used to screen hard-covered items leading to a better visualization. The system capability was used as well during the imaging analysis of the Space Shuttle Columbia accident. These FR-based imaging techniques include novel proprietary adaptive image segmentation, image edge extraction, and image enhancement. Probabilistic Neural Network (PNN) scheme available from NeuroShell(TM) Classifier and optimized via Genetic Algorithm (GA) was also used along with this set of novel imaging techniques to add powerful learning and image classification capabilities. Prototype applications built using these techniques have received NASA Space Awards, including a Board Action Award, and are currently being filed for patents by NASA; they are being offered for commercialization through the Research Triangle Institute (RTI), an internationally recognized corporation in scientific research and technology development. Companies from different fields, including security, medical, text digitalization, and aerospace, are currently in the process of licensing these technologies from NASA.

Dominguez, Jesus A.↗

Payload Performance of Third Generation TDRS and Future Services

NASA has accepted two of the 3rd generation Tracking and Data Relay Satellites, TDRS K, L, and M, designed and built by Boeing Defense, Space & Security (DSS). TDRS K, L, and M provide S-band Multiple Access (MA) service and S-band, Ku-band and Ka-band Single Access (SA) services to near Earth orbiting satellites. The TDRS KLM satellites offer improved services relative to the 1st generation TDRS spacecraft, such as: an enhanced MA service featuring increased EIRPs and G/T; and Ka-band SA capability which provides a 225 and 650 MHz return service (customer-to-TDRS direction) bandwidth and a 50 MHz forward service (TDRS-to-customer direction) bandwidth. MA services are provided through a 15 element forward phased array that forms up to two beams with onboard active beamforming and a 32 element return phased array supported by ground-based beamforming. SA services are provided through two 4.6m tri-band reflector antennas which support program track pointing and autotrack pointing. Prior to NASAs acceptance of the satellites, payload on-orbit testing was performed on each satellite to determine on-orbit compliance with design requirements. Performance parameters evaluated include: EIRP, G/T, antenna gain patterns, SA antenna autotrack performance, and radiometric tracking performance. On-orbit antenna calibration and pointing optimization was also performed on the MA and SA antennas including 24 hour duration tests to characterize and calibrate out diurnal effects. Bit-Error-Rate (BER) tests were performed to evaluate the end-to-end link BER performance of service through a TDRS K and L spacecraft. The TDRS M is planned to be launched in August 2017. This paper summarizes the results of the TDRS KL communications payload on-orbit performance verification and end-to-end service characterization and compares the results with the performance of the 2nd generation TDRS J. The paper also provides a high-level overview of an optical communications application that will augment the data rates supported by the Space Network.

RF↗

Payload Performance of TDRS KL and Future Services

NASA has accepted two of the 3nd generation Tracking and Data Relay Satellites, TDRS K, L, and M, designed and built by Boeing Defense, Space Security (DSS). TDRS K, L, and M provide S-band Multiple Access (MA) service and S-band, Ku-band and Ka-band Single Access (SA) services to near Earth orbiting satellites. The TDRS KLM satellites offer improved services relative to the 1st generation TDRS spacecraft, such as: an enhanced MA service featuring increased EIRPs and GT; and Ka-band SA capability which provides a 225 and 650 MHz return service (customer-to-TDRS direction) bandwidth and a 50 MHz forward service (TDRS-to-customer direction) bandwidth. MA services are provided through a 15 element forward phased array that forms up to two beams with onboard active beamforming and a 32 element return phased array supported by ground-based beamforming. SA services are provided through two 4.6m tri-band reflector antennas which support program track pointing and autotrack pointing. Prior to NASAs acceptance of the satellites, payload on-orbit testing was performed on each satellite to determine on-orbit compliance with design requirements. Performance parameters evaluated include: EIRP, GT, antenna gain patterns, SA antenna autotrack performance, and radiometric tracking performance. On-orbit antenna calibration and pointing optimization was also performed on the MA and SA antennas including 24 hour duration tests to characterize and calibrate out diurnal effects. Bit-Error-Rate (BER) tests were performed to evaluate the end-to-end link BER performance of service through a TDRS K and L spacecraft. The TDRS M is planned to be launched in August 2017. This paper summarizes the results of the TDRS KL communications payload on-orbit performance verification and end-to-end service characterization and compares the results with the performance of the 2nd generation TDRS J. The paper also provides a high-level overview of an optical communications application that will augment the data rates supported by the Space Network.

Laser↗

The Efficiency of Various Computers and Optimizations in Performing Finite Element Computations

With the advent of computers with many processors, it becomes unclear how to best exploit this advantage. For example, matrices can be inverted by applying several processors to each vector operation, or one processor can be applied to each matrix. The former approach has diminishing returns beyond a handful of processors, but how many processors depends on the computer architecture. Applying one processor to each matrix is feasible with enough ram memory and scratch disk space, but the speed at which this is done is found to vary by a factor of three depending on how it is done. The cost of the computer must also be taken into account. A computer with many processors and fast interprocessor communication is much more expensive than the same computer and processors with slow interprocessor communication. Consequently, for problems that require several matrices to be inverted, the best speed per dollar for computers is found to be several small workstations that are networked together, such as in a Beowulf cluster. Since these machines typically have two processors per node, each matrix is most efficiently inverted with no more than two processors assigned to it.

Marcus, Martin H.↗