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At least 307 records · Page 17

Micro- and Nano-techniques for the Study of Fission Product Precipitation in SiC Layer

The complexity of fission product distribution and composition within the SiC layer of tristructural isotropic (TRISO) coated particles, irradiation effects on the SiC structure as well as the variable nature of metallic fission product release, has led to the exploration of multiple micro- and nano-characterization techniques. The fine scale of the fission product precipitates necessitates unique learnings and application of electron microscopic techniques with irradiated fuel during the Advanced Gas Reactor (AGR)-1 experiment analysis. A summarized discussion on the specific advanced techniques with associated method development for TRISO coated particles is provided followed by the down selected techniques currently considered to provide the highest impact. Techniques considered are electron probe micro-analyzer (EPMA), scanning transmission electron microscopy (STEM), and Precession electron diffraction (PED). SiC grain boundary characteristics are evaluated due to the mobility of specific fission products through grain boundaries. PED was performed for understanding the role of grain boundary character on fission product transport. One set of comparative analyses between AGR-1 and AGR-2 particles leads to a finding that the AGR-1, high-Ag-retention particle, had statistically more coincidence site lattice (CSL)-related grain boundaries (but fewer low-angle grain boundaries), compared to the AGR-2 particle. This implies that CSL-related grain boundaries may have a direct influence on Ag retention. However, precipitates were found on a relatively small fraction of CSL-related grain boundaries in both particles. In another set of comparison between AGR-1 and AGR-2 particles that were subjected to safety testing, there is significant differences in average SiC grain boundary distributions, but the fission product distributions on these grain boundaries are very similar.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Examples of X-Ray Characterization Techniques in Energy Storage Research

Lithium-ion batteries have revolutionized the portable electronics and transportation sectors. Their performance is often critically dependent on the crystal structures of the anode and cathode electrode materials, which must enable the transport and reversible storage of lithium ions into and out of the lattice. Because lithium is a low-Z element, characterization of materials for lithium-ion batteries can be particularly challenging. Regardless, X-ray techniques enable analysis of material structures to better understand how battery materials perform and degrade, particularly when combined with other materials characterization and electrochemical characterization techniques. While X-ray techniques are most often used in battery research for phase identification of crystal structures, X-ray characterization techniques are also used for a wide variety of other purposes. I will discuss several examples from my research with various collaborators on several projects that highlight the impact that X-ray characterization techniques can have on battery research. The first example will focus on low-temperature microwave-assisted solvothermal synthesis of vanadium-doped LiFePO4 cathode materials for lithium-ion batteries. (1,2) Through a combination of electrochemical and materials characterization, we determined that low temperature synthesis resulted in metastable phases that enabled incorporation of higher dopant levels than resulting from high-temperature synthesis of thermodynamically stable phases. Rietveld refinement of X-ray diffraction data enabled understanding of how lattice parameters changed with doping levels and synthesis temperature. X-ray absorption near edge spectroscopy enabled understanding of the vanadium and iron oxidation states to confirm how vacancies in the structure caused by doping were charge compensated. This was important to understand because the literature suggests doping can improve LiFePO4 electrical conductivity, which improves battery charge and discharge rates. The second example will focus on understanding residual strain in lithium metal anodes. Lithium-ion batteries typically use graphite anodes, but the charge-storage capacity can be theoretically improved ~10x by using lithium metal as the anode material instead. However, lithium anodes suffer from growth of high-aspect-ratio features, such as dendrites, that can pierce nanoporous polymer separators and lead to short circuits and fires. External pressure is commonly applied to cells to enable better morphological control. We hypothesized that applied pressure may promote strain and possibly work hardening during electrochemical cycling, which motivated us to look for evidence of residual strain in lithium metal cycled under applied pressure using X-ray diffraction and sin2(..psi..) analysis. We found that lithium electrodeposited under high pressure exhibited in-plane compressive strain and that that lithium electrodeposited under low pressure did not. (3) The residual strain that accompanies electrodeposition under high pressure may lead to work hardening, which may explain how a soft metal like lithium can puncture separators and why higher pressure does not always decrease short circuits. (4-6) References: 1) Harrison, K. L.; Manthiram, A. Microwave-Assisted Solvothermal Synthesis and Characterization of Metastable LiFe1- x (VO) x PO4 Cathodes. Inorganic chemistry 2011, 50(8), 3613-3620. 2) Harrison, K. L.; Bridges, C. A.; Paranthaman, M. P.; Segre, C. U.; Katsoudas, J.; Maroni, V. A.; Idrobo, J. C.; Goodenough, J. B.; Manthiram, A. Temperature Dependence of Aliovalent-Vanadium Doping in LiFePO4 Cathodes. Chemistry of Materials 2013, 25(5), 768-781. 3) Rodriguez, M. A.; Harrison, K. L.; Goriparti, S.; Griego, J. J.; Boyce, B. L.; Perdue, B. R. Use of a Be-Dome Holder for Texture and Strain Characterization of Li Metal Thin Films via Sin2 (..psi..) Methodology. Powder Diffraction 2020, 35(2), 89-97. 4) Jungjohann, K. L.; Gannon, R. N.; Goriparti, S.; Randolph, S. J.; Merrill, L. C.; Johnson, D. C.; Zavadil, K. R.; Harris, S. J.; Harrison, K. L. Cryogenic Laser Ablation Reveals Short-Circuit Mechanism in Lithium Metal Batteries. ACS Energy Letters 2021, 6(6), 2138-2144. 5) Harrison, K. L.; Merrill, L. C.; Long, D. M.; Randolph, S. J.; Goriparti, S.; Christian, J.; Warren, B.; Roberts, S. A.; Harris, S. J.; Perry, D. L. Cryogenic Electron Microscopy Reveals That Applied Pressure Promotes Short Circuits in Li Batteries. Iscience 2021, 24(12). 6) Harrison, K. L.; Goriparti, S.; Merrill, L. C.; Long, D. M.; Warren, B.; Roberts, S. A.; Perdue, B. R.; Casias, Z.; Cuillier, P.; Boyce, B. L. Effects of Applied Interfacial Pressure on Li-Metal Cycling Performance and Morphology in 4 M LiFSI in DME. ACS Applied Materials & Interfaces 2021, 13(27), 31668-31679.

batteries↗

Advanced Laboratory and Field Arrays: Evaluating Sampling Techniques for MHK Biological Monitoring (Task 6)

The overall goal of the task was to identify cost effective biological sampling techniques for MHK environmental monitoring. Protected, demersal, and pelagic fish and selected nektonic invertebrates were surveyed using capture and remote sensing techniques at the PacWave sites. The performance of capture and remote sensing monitoring techniques were evaluated and generic nekton monitoring indices were developed for MHK technologies and sites. In parallel to data collections at the PacWave site, the ability of regression models to characterize, detect, and predict change in acoustic data was evaluated using acoustic data collected in Admiralty Inlet, WA, during a biological monitoring study of the proposed SnoPud tidal turbine project site. Expected outcomes of these efforts included an evaluation of instrumentation and techniques used to monitor biological variability; identification of data streams that can be used to detect and quantify change; and sampling requirements to ensure detection of change in monitored variables.

13 HYDRO ENERGY↗

Hydro-mechanical coupled modeling of hydraulic fracturing using the mesh fragmentation technique

The inclusion of special interface elements between standard finite elements is becoming a common technique to model discontinuities in porous media using the finite element method (FEM). Recently, it was proved that high aspect ratio (HAR) elements can reproduce very satisfactorily the main features of behavior observed in a single hydraulically-induced fracture. In this paper, the mesh fragmentation technique (MFT) is proposed to extend the application of HAR elements to simulate more general problems involving the formation of hydraulic fractures in rocks by introducing this type of element in-between the standard FE of a typical mesh. The proposed framework makes use of standard FE techniques. Therefore, it is relatively easy to upgrade an existing FE program for continuous porous media to deal with evolving discontinuities. The proposed approach is verified and validated against available analytical and numerical solutions. The crack patterns predicted by the MFT are also compared with the ones observed in the laboratory. The formation of multiple fractures is also analyzed. In all cases, the proposed technique was able to properly capture the main features of rock behavior subjected to hydraulic fracturing.

58 GEOSCIENCES↗

A scoping review of non-destructive testing (NDT) techniques in building performance diagnostic inspections

Understanding building envelope thermodynamics is an essential foundation of building sciences, mainly due to the envelope’s role as a boundary layer for exterior environments, as well as a container and regulator of internal microclimates. This paper presents a scoping literature review of select Non-destructive Testing (NDT) techniques for building envelope scanning and surveying for thermodynamic diagnostics. The investigation focuses specifically on reviewing six NDT techniques: Ground Penetrating Radar (GPR), Light Detection and Ranging (LiDAR)/Laser Scanning, Thermography, Ultrasound, Close-Range Photogrammetry and Through Wall Imaging Radar (TWIR). The aim is to identify knowledge gaps in terms of their use in accurately characterizing envelope compositions for further integration in Building Energy Modeling (BEM). Each technique was evaluated according to set categories imbibed from the American Society of Heating, Refrigerating, and Air Conditioning Engineering (ASHRAE) Standard 211P that showcase the technique’s ability to extract various relevant information. A framework is then developed to inform users on how to use hybrid NDT-based workflows applied in building envelope energy audits. The study concludes by discussing possibilities of utilizing NDT in large-scale audit automation, BEM integration, and developing built environment policies focusing on increasing existing building performance through retrofitting design.

36 MATERIALS SCIENCE↗

Internal defect detection and characterization of samarium-cobalt sintered magnets by ultrasonic testing technique

Excessive quantities of samarium-cobalt (Sm-Co) magnet material are being scrapped needlessly due to a lack of understanding of inhomogeneity distribution and unacceptable internal defects. If there is a way to identify, locate, characterize and when needed separate the defective portions of magnet material, utilization can be increased and product quality improved. Further, the magnets’ magnetic and mechanical performance can be improved by reducing the occurrence of internal defects. This paper reports on a cost-effective and efficient nondestructive evaluation method based on an ultrasonic testing (UT) technique applied for detecting and characterizing internal defects in Sm-Co sintered magnets. Applying the UT technique will allow users to comprehensively analyze internal defects, such as inclusions, porosity, microcracks, and other structural irregularities, check for homogeneity and anomalous regions and give the locations of these internal anomalies and defects within the Sm-Co sintered magnets. The UT technique can also be applied to other rare-earth permanent magnets, such as sintered or die-upset neodymium-iron-boron (Nd-Fe-B) magnets. The UT technique can effectively guide quality control and acceptable product selection, in addition to optimizing the magnet alloy design and production processes. Therefore, it can facilitate the improvement of magnet manufacturing efficiency and machinability, reduce scrap, prolong service life, increase the use of what would be post-production waste, and enhance product reuse and recycling at end-of-life disposition.

36 MATERIALS SCIENCE↗

Utilization of Data Augmentation Techniques in Automated Inspection Systems for Defect Detection in Metals With Limited Data

Accurate identification of defects on metal surfaces is of great interest to many industry sectors, such as the automotive and aerospace industries. In contrast to conventional manual inspection techniques, recent automated inspection systems employ deep learning models trained to detect defects rapidly and precisely. The development of these models often requires a substantial image dataset to acquire adequate knowledge of defect features and enhance their predictive accuracy. When data is limited, augmentation techniques are often used to improve the precision and accuracy of defect detection systems. This study examined the prediction performance of two object detection models, namely Faster Region‐based Convolutional Neural Network (Faster R‐CNN) and You Only Look Once version 8 (YOLOv8), to identify dent defects in limited images of cast iron cylinder head surfaces. The original image set contains 46 images with 563 dents. To overcome limited data availability, common image augmentation techniques along with a copy‐paste method were applied. Results show that standard augmentation improved YOLOv8 accuracy by 8.00% and average precision (AP) by 3.00%. On the other hand, the copy‐paste technique achieved a 20.00% increase in accuracy and a 1% increase in AP with just 200 synthetic dents. Furthermore, these results provide support for using the copy‐paste augmentation strategy to enhance defect detection performance, with a limited dataset, contributing to more accurate defect identification in remanufacturing processes.

36 MATERIALS SCIENCE↗

Crack detection in fuel cell electrodes using a spatial filtering technique for overcoming noisy backgrounds

Image processing is a powerful tool that allows for rapid and automated data parsing in settings that occupy large variable spaces and require large data sets. Feature detection on difficultly discerned backgrounds is a subset of image processing that facilitates the extraction of quantitative metrics from otherwise subjective data. Crack detection and quantification is an important capability in polymer electrolyte membrane fuel cell quality control, failure analysis, and optimization. This work presents a technique to perform crack detection and quantification which overcomes challenges faced by commonly used image segmentation techniques. We demonstrate the use of a geometrically filtered noise‐level detection technique to select a binary threshold value from which we then quantify how cracked a sample is. Furthermore, we demonstrate the accuracy of our technique using programmatically generated test images of known crack amounts and their performance on real‐world fuel cell catalyst layer samples.

30 DIRECT ENERGY CONVERSION↗

Development of a Time-Height Profile Assimilation Technique for Large-Eddy Simulation

Mesoscale-to-microscale coupling (MMC) aims to address the limited scope of traditional large-eddy simulations by driving the microscale flow with information concerning large-scale weather patterns provided by mesoscale models. We present a new offline MMC technique for horizontally homogeneous microscale flow conditions, in which internal forcing terms are computed based on mesoscale time–height profiles of mean-flow quantities. The advantage of such an approach is that it can be used to drive a microscale simulation with either mesoscale or observational data, and that it does not rely on specific terms in the mesoscale budget equations, which are typically not part of the default output of a mesoscale solver. The performance of the proposed profile assimilation technique is assessed based on the simulation of a typical diurnal cycle over the Scaled Wind Farm Technology site in west Texas. Results indicate that simple data assimilation techniques lead to unphysically high levels of shear and turbulence caused by the algorithm’s inability to cope with inaccuracies in the mesoscale time–height profiles. Modifying the algorithm to account for vertical coherence in the mesoscale source terms gives the microscale solver a greater ability to correct the provided mesoscale time–height profiles, leading to improved predictions of shear and turbulence statistics. The resulting turbulence statistics are in good agreement with meteorological tower observations and simulation results obtained with state-of-the-art coupling techniques using mesoscale budget components.

data assimilation↗

A Review of the Influence of Processing Parameters on ODS Steels Produced via Additive Manufacturing Techniques

Abstract This paper reviews current observations regarding processing conditions for oxide dispersion-strengthened steels consolidated through additive manufacturing techniques. Variations in ODS steels observed across process parameters include changes in grain size, grain texture, oxide size, density of oxides, porosity, melt pool characteristics, and mechanical properties. These properties were then compared across techniques to understand which techniques and processing conditions lead to the highest strength, ductility, and oxide density. Current literature suggests that a mix of grain types, in the form of either morphology or phase, can significantly increase the strength of printed ODS steels. Meanwhile, the most ductile samples, regardless of consolidation technique or matrix material, were made from feedstock with oxide additions located on the powder surface. Reported grain and oxide sizes were plotted against the ratio of laser power to scan speed, volumetric energy density, and normalized enthalpy. No strong correlation between these values and microstructural features was observed. The plots that were made suggest that a larger data set, more in-depth representative equations, and more defined material properties as a function of specific feedstock used are necessary to determine a value that can be correlated to the printed ODS steel microstructure.

deJong, Matthew↗

Improved sampling technique to collect natural gas from hydrate-bearing pressure cores

High quality gas compositional data are an important factor in interpreting the genetic source of natural gas hosted in hydrate-bearing sediments and other subsurface systems. In order to accurately characterize the composition of gas samples degassed from hydrate-bearing pressure cores, one must use a reproducible sampling technique that minimizes artifacts of the sampling process. Herein, we review sediment core degassing techniques and compare data obtained from a commonly used degassing approach, which we term the standard quantitative degassing (SQD) technique, to our newly developed modified quantitative degassing (MQD) method designed to minimize atmospheric contamination and gas-water interactions. The SQD method allows sample gas to interact with water in a bubbling chamber, which we hypothesize could alter the gas composition following mixing with water or dissolved gases in the bubbling chamber. Whereas, the MQD method allows for the collection of sample gas prior to the bubbling chamber. To compare the SQD and MQD methods, we performed a side-by-side comparison of noble (He, Ne, Ar, Kr, and Xe), major (H 2 , N 2 , O 2 , and CO 2 ), and hydrocarbon (CH 4 , C 2 H 6 , C 3 H 8 , i-C 4 H 10 , C 4 H 10 , i-C 5 H 12 , C 5 H 12 ) gas concentrations and select isotopic compositions obtained using both sample collection techniques. Gas samples were collected from hydrate-bearing pressure cores recovered and maintained under hydrate stable conditions from the northern Gulf of Mexico during the UT-GOM 2 -1 Expedition. The MQD method displayed significantly lower concentrations of atmospheric gases, higher proportions of hydrocarbon gases, lower ratios of C 1 /C 2 + , and heavier stable carbon and hydrogen isotopes of methane than the SQD method. These results demonstrate that the MQD method reduced air contamination and minimized alteration of the hydrocarbon gases. Finally, we conclude this method may be important for future work that seeks to determine the composition of natural gas from pressure cores using quantitative degassing experiments, especially those seeking to measure major (e.g., N 2 ) and noble gases.

58 GEOSCIENCES↗

On The Use of Sectional Techniques for the Solution of Depolymerization Population Balances: Results on a Discrete-Continuous Mesh

To study the discrete bond-breaking phenomena of depolymerization, the use of a fully continuous Population Balance Equation (PBE) is inadequate to embody all the inherent characteristics of the process, thus resulting in the need for a discrete-continuous mesh. In this work, the performance of the three most state-of-the-art sectional techniques, i.e. the fixed pivot technique (FPT), cell average technique (CAT) and finite volume scheme (FVS) in approximating discrete depolymerization using discrete-continuous PBEs was extensively compared and evaluated. The solutions from these three methods show different accuracy depending on the breakage mechanisms. For chain-end scission, the FPT and the CAT satisfactorily predict the population densities and moments whereas the FVS fails to predict the population densities but preserves the zeroth and the first moments. In the application of a discrete-continuous model, we identified a previously-not-reported issue of a precipitous drop in the number density at the boundary of discrete and continuous region specifically for chain-end scission. We successfully fixed this problem by employing the alterations proposed in this paper, to the particle allocation functions at the boundary points. For random scission, all three sectional techniques predict the population densities and moments to a high degree of accuracy, even at a very coarse mesh, through the use of our new stoichiometric kernel which is able to closely approximate the inherently discrete bond-breaking depolymerization process. The assessments in this present work intends to provide a clear-cut direction to efficient and economical modelling of depolymerization processes.

Ahamed, Firnaaz↗

Exploratory analysis of machine learning techniques in the Nevada geothermal play fairway analysis

Play fairway analysis (PFA) is commonly used to generate geothermal potential maps and guide exploration studies, with a particular focus on locating and characterizing blind geothermal systems. This study evaluates the application of machine learning techniques to PFA in the Great Basin region of Nevada. Following the evaluation of various techniques, we identified two approaches to PFA that produced promising results, 1) supervised Bayesian probabilistic neural networks to generate geothermal potential maps with confidence intervals, and 2) unsupervised principal component analysis paired with k-means clustering to generate both cluster maps to help identify spatial patterns, as well as new combined feature inputs. We applied these techniques to perform a comparative analysis between two principal sets of geological and geophysical features related to permeability and heat and a set of positive (known geothermal resources) and negative training sites (known drill sites with unsuitable geothermal conditions). We found that these methods constrain previously unrecognized feature controls on geothermal favorability, many of which are spatially organized within the extent of cluster groups and the major structural-hydrologic domains of the study area. Furthermore, we utilized exploratory unsupervised modeling to highlight spatial relationships between input data and predictive output results of our supervised modeling. As a result, we demonstrate how our models compare to the previous Nevada PFA and how the rapid insights these machine learning techniques offer may support future assessments of both known and undiscovered blind geothermal systems in the Great Basin region of Nevada and beyond.

15 GEOTHERMAL ENERGY↗

Growth interface study of CdTeSe crystals grown by the THM technique

The Traveling Heater Method (THM) is a widely accepted technique to grow high-quality detector grade CdTe and CdZnTe ingots, especially for X-ray and gamma-ray detector applications. Unlike melt-growth techniques, the growth interface for ingots produced by the THM technique consists of two different compounds, viz. the solidified region (just below the interface) consists of the compound to be grown (e.g., CdZnTe for CdZnTe growth), while the molten zone just above the growth interface consists of Te-rich CdZnTe. Thus, optimization of the growth parameters is critical to obtain a clean growth interface with the required shape and presence of minimal Te-rich inclusions. Here, in this study, CdTeSe ingots were grown employing the THM technique to investigate the growth interface. Both macroscopic and microscopic behavior of the interface were studied. The study revealed that a microscopically smooth growth interface can be achieved by optimizing the growth parameters, which is essential for obtaining high-quality, inclusion-free ingots.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

An overview of HR-EBSD techniques for mapping local stress and dislocations in crystalline materials at sub-micron resolution

High resolution electron backscatter diffraction (HR-EBSD) is a technique used to map elastic strain, crystallographic orientation and dislocation density in a scanning electron microscope. Here, this review covers the background and mathematics of this technique, contextualizing it within the broader landscape of EBSD techniques and other materials characterization methods. Several case studies are presented showing the application of HR-EBSD to the study of plasticity in metals, failure analysis in microelectronics and defect quantification in thin films. This is intended to be a comprehensive resource for researchers developing this technique as well as an introduction to those wishing to apply it.

Ruggles, Timothy J. [Sandia National Laboratories ↗

Toward reducing uncertainty quantification costs in DEM models of particulate flow: Testing simple, sensitivity-based, forward uncertainty propagation techniques

The performance of two conceptually-simple uncertainty quantification techniques are tested against the rigorous nested-loop sampling technique of Roy and Oberkampf (Comput Methods Appl Mech Eng, 200: 2131–2144, 2011) (herein called full-sampling) using two very small-scale DEM-based models of particulate flow (one gas-solid flow and one granular flow). The first simplified forward uncertainty propagation technique, reduced-sampling, uses a sensitivity analysis to eliminate uncertain inputs that have little impact on the model output prior to nested-loop sampling. The second technique, boundary-sampling, uses a sensitivity analysis to inform the selection of two bounding cases for each key model output. In conclusion, the uncertainties in the model outputs obtained via the reduced- and boundary-sampling methods agree well with those from full-sampling for both the gas-solid and granular flow models while yielding computational savings of 65–75% (reduced sampling) and 94–97% (boundary sampling).

42 ENGINEERING↗

Review of heat transfer enhancement techniques for single phase flows

The thermal energy exchange between a flowing fluid and its confining channel is a ubiquitous process in modern society. To enhance the fluid-to-wall or wall-to-fluid heat transfer, several techniques have been developed to maximize the contact area between the fluid and the inner wall and/or disrupt the flow to enhance circulation or induce turbulence. Deployment of channels having features capable of enhancing heat transfer enables the reduction of heat exchanger size while maintaining performance. Reduction in equipment size is critical due to the ability to minimize the required volume of costly working fluids and to mitigate potential safety concerns associated with total system fluid volume. Here, a comprehensive review of single-phase heat transfer enhancement techniques is presented. The article provides a thorough comparison by analyzing the heat transfer rate, pressure drop, and other operational aspects. Single-phase heat transfer enhancement methods are divided into active and passive techniques. Active methods such as electrohydrodynamic (EHD), magnetohydrodynamics (MHD), or mechanical motion require external power to create enhancement. Passive methods such as dimples, fins, or tape inserts do not require external input and rely only on surface modification. Although active methods are more expensive and difficult to implement compared to passive techniques, it enables active control of heat transfer augmentation. Finally, this review develops and summarizes key learning data for design optimization enabled by additive manufacturing and machine learning algorithms, helping to inform these next-generation heat exchanger design methodologies for a plethora of modern applications such as electrification of vehicles, computing, and classical industries.

42 ENGINEERING↗

A survey of techniques for optimizing transformer inference

Recent years have seen a phenomenal rise in the performance and applications of transformer neural networks. The family of transformer networks, including Bidirectional Encoder Representations from Transformer (BERT), Generative Pretrained Transformer (GPT) and Vision Transformer (ViT), have shown their effectiveness across Natural Language Processing (NLP) and Computer Vision (CV) domains. Transformer-based networks such as ChatGPT have impacted the lives of common men. However, the quest for high predictive performance has led to an exponential increase in transformers' memory and compute footprint. Researchers have proposed techniques to optimize transformer inference at all levels of abstraction. Further, this paper presents a comprehensive survey of techniques for optimizing the inference phase of transformer networks. We survey techniques such as knowledge distillation, pruning, quantization, neural architecture search and lightweight network design at the algorithmic level. We further review hardware-level optimization techniques and the design of novel hardware accelerators for transformers. We summarize the quantitative results on the number of parameters/FLOPs and the accuracy of several models/techniques to showcase the tradeoff exercised by them. We also outline future directions in this rapidly evolving field of research. We believe that this survey will educate both novice and seasoned researchers and also spark a plethora of research efforts in this field.

97 MATHEMATICS AND COMPUTING↗