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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Discovering hydrothermalism from Afar: In Situ methane instrumentation and change-point detection for decision-making

Seafloor hydrothermalism plays a critical role in fundamental interactions between geochemical and biological processes in the deep ocean. A significant number of hydrothermal vents are hypothesized to exist, but many of these remain undiscovered due in part to the difficulty of detecting hydrothermalism using standard sensors on rosettes towed in the water column or robotic platforms performing surveys. Here, we use in situ methane sensors to complement standard sensing technology for hydrothermalism discovery and compare sensors on a towed rosette and an autonomous underwater vehicle (AUV) during a 17 km long transect in the Northern Guaymas Basin in the Gulf of California. This transect spatially intersected with a known hydrothermally active venting site. These data show that methane signalled possible hydrothermal-activity 1.5–3 km laterally (100–150 m vertically) from a known vent. Methane as a signal for hydrothermalism performed similarly to standard turbidity sensors (plume detection 2.2–3.3 km from reference source), and more sensitively and clearly than temperature, salinity, and oxygen instruments which readily respond to physical mixing in background seawater. We additionally introduce change-point detection algorithms—streaming cross-correlation and regime identification—as a means of real-time hydrothermalism discovery and discuss related data supervision technologies that could be used in planning, executing, and monitoring explorative surveys for hydrothermalism.

58 GEOSCIENCES↗
DOE OSTI2024

An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metamaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. Here, these effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

PETSc/TAO Users Manual (Rev. 3.19)

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and opti mization that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than packages such as MATLAB or a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or lldb, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than “rolling them” yourself. For many tasks a package such as MATLAB is often the best tool; PETSc is not intended for the classes of problems for which effective MATLAB code can be written. There are several packages, built on PETSc, that may satisfy your needs without requiring directly using PETSc. We recommend reviewing these packages functionality before starting to code directly with PETSc. PETSc can be used to provide a “MPI parallel linear solver” in an otherwise sequential, or OpenMP parallel code. This approach cannot provide extremely large improvements in the application time by utilizing large numbers of MPI processes but can still improve the performance. Certainly all parts of a previously sequential code need not be parallelized but the matrix generation portion must be parallelized to expect true scalability to large numbers of MPI processes. See PCMPI for details on how to utilize the PETSc MPI linear solver server. Since PETSc is under continued development, small changes in usage and calling sequences of routines will occur. PETSc has been supported for twenty-five years; see mailing list information on our website for information on contacting support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Final Technical Report - Rapid Surface Microanalysis using a Low Temperature Plasma

This project focused on improving our current understanding and scientific knowledge in the area of plasma-surface interactions and plasma assisted material synthesis related to advanced microelectronics and nanotechnology. Current challenges include: controlling the interaction of Low Temperature Plasma (LTP) with a single layer of atoms to manufacture integrated circuits, continued miniaturization of integrated circuits, LTP processing of material surfaces and thin films to enable industrial scale fabrication of advanced microelectronics, synthesis of new materials, nanomaterials, nanotubes, and complex materials, Technology developed in this subtopic is of value to either (i) enable scans of surfaces (~1 sq. cm area) using various microscopies (electron, optical, other) at high resolution (micron or sub-micron resolution) rapidly (hours or days rather than years to complete a high-resolution scan of such a large surface area), or (ii) enable scans of surfaces (~1 sq. cm area) using various microscopies (electron, optical, other) at relatively low resolution rapidly, then apply algorithms to select spots for micron-scale imaging. Sputtering occurs when particles of a solid material are ejected from its surface by energetic particles from a plasma. While the degradation of the solid material and the subsequent deposition of the ejected material onto vulnerable surfaces are the usual subjects of sputtering studies, plasma science has yet to be combined with sputtering to create new diagnostics devices and systems. Small changes in the design of the plasma discharge device make it possible to create broad plasma beams for rapid scanning or small plasma beams to obtain the distribution of ejected elements with micron resolution. In the high-resolution use, the ion flux is extracted from the gas-discharge plasma and focused by a spherical emission surface to micron sizes onto the target specimen, providing very local sputtering and local elemental analysis. We call this “self-focusing”. The radiation from the excited and ionized sputtered atoms is recorded by a spectrometer through a window and fiberglass cable and analyzed with standard software packages used for optical glow discharge spectroscopy. Computer simulations of beam formation were used to verify and optimize the designs to be tested. A prototype was designed, constructed, and used to start experiments of beam formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Combinatorial Evaluation of Physical Feature Engineering, Classical Machine Learning, and Deep Learning Models for Synchrophasor Data at Scale

A major objective of the project was to train and evaluate the effectiveness of multiple event and anomaly detection, identification and classification deep temporal learning models for processing of real-time phasor measurement unit (PMU) data streams. A vast dataset, consisting of two years of phasor measurements from all three U.S. Interconnections, was curated and released by the Department of Energy (DOE) through Pacific Northwest National Laboratory (PNNL). The dataset also included an event log that provided event times and types (e.g. generator trips, line trips, planned service events, transformer operations, etc.). Our analysis of this dataset addressed six (6) of the eleven (11) research priorities identified in Funding Opportunity Announcement (FOA) DE-FOA-0001861 “Big Data Analysis of Synchrophasor Data” (FOA 1861). Rather than being limited to pre-determined specific algorithms, this project relied on the uniquely structured, highly performant underlying time series database capabilities of the PredictiveGrid platform to assess the vast dataset utilizing a wide variety of algorithms.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Aerosol-deep convection interaction based on joint cell-thermal tracking in Large Eddy Simulations during the TRACER campaign

In cumulus clouds, aerosol concentrations control cloud droplet concentrations, modifying cloud radiative properties, precipitation processes, and cloud electrification. However, mechanisms of aerosol-deep convection interactions are not well understood due to complex cloud dynamics and microphysics. We investigate the interaction of aerosols with isolated deep convection using Large Eddy Simulations of two cases during the TRacking Aerosol Convection interactions ExpeRiment (TRACER) near Houston, Texas, using a joint cell-thermal tracking algorithm. Cumulus thermals are droplet generators, since supersaturation and droplet nucleation coincide with thermal centers, where the strongest updrafts occur. Primary ice crystal formation does not take place inside thermals, but at layers where previous thermals detrained moisture. As subsequent thermals containing supercooled droplets penetrate these layers, hail and graupel form at or near these thermals. Higher aerosol concentrations result in higher droplet concentrations that suppress drizzle, delay warm rain processes, and transport more moisture aloft. This increases snow and ice amount, as well as graupel and hail, leading to more lightning. Polluted thermals initiate at slightly higher altitudes, and are slightly larger and faster, suggesting a weak invigoration. We also find more thermals per cell, but fewer isolated cells, since convection is more aggregated and intense, especially near the end of the 24 h simulation. Non-linear mesoscale feedback likely triggered by temperature and moisture responses to aerosol-thermal interactions causes the aggregation. Time-lagged aerosol-reinitialization experiments show that the mesoscale response is the predominant forcing for the invigoration. These changes happen within one day, on a smaller scale than previously suggested.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evaluation of global teleconnections in CMIP6 climate projections using complex networks

In climatological research, the evaluation of climate models is one of the central research subjects. As an expression of large-scale dynamical processes, global teleconnections play a major role in interannual to decadal climate variability. Their realistic representation is an indispensable requirement for the simulation of climate change, both natural and anthropogenic. Therefore, the evaluation of global teleconnections is of utmost importance when assessing the physical plausibility of climate projections. We present an application of the graph-theoretical analysis tool δ-MAPS, which constructs complex networks on the basis of spatio-temporal gridded data sets, here sea surface temperature and geopotential height at 500 hPa. Complex networks complement more traditional methods in the analysis of climate variability, like the classification of circulation regimes or empirical orthogonal functions, assuming a new non-linear perspective. While doing so, a number of technical tools and metrics, borrowed from different fields of data science, are implemented into the δ-MAPS framework in order to overcome specific challenges posed by our target problem. Those are trend empirical orthogonal functions (EOFs), distance correlation and distance multicorrelation, and the structural similarity index. δ-MAPS is a two-stage algorithm. In the first place, it assembles grid cells with highly coherent temporal evolution into so-called domains. In a second step, the teleconnections between the domains are inferred by means of the non-linear distance correlation. We construct 2 unipartite and 1 bipartite network for 22 historical CMIP6 climate projections and 2 century-long coupled reanalyses (CERA-20C and 20CRv3). Potential non-stationarity is taken into account by the use of moving time windows. The networks derived from projection data are compared to those from reanalyses. Our results indicate that no single climate projection outperforms all others in every aspect of the evaluation. But there are indeed models which tend to perform better/worse in many aspects. Differences in model performance are generally low within the geopotential height unipartite networks but higher in sea surface temperature and most pronounced in the bipartite network representing the interaction between ocean and atmosphere.

58 GEOSCIENCES↗
DOE OSTI2025

Spectroscopic Online Monitoring: Using a Multi-Track Visible Spectrometer to Facilitate a Mass Balance Study in a Simulated TALSPEAK Process

Nuclear energy is a promising low-carbon energy candidate to meet the increased demand for green energy, where the integration of fuel recycling can have significant benefits for material usage and waste reduction. Utilizing in situ monitoring tools can provide ample opportunities to better control and safeguard nuclear material recycle processes while also offering knowledge and insight into real-time solution properties. The simultaneous measurement of analytical targets in multiple process locations can enable real-time mass balance and material accountancy calculations. This is demonstrated here with a mass balance study of Nd 3+ on countercurrent aqueous/organic metal extraction within a single centrifugal contactor. The Nd 3+ concentration was simultaneously monitored at the inlets and outlets of both aqueous and organic phases using a visible absorbance detector that allowed for the simultaneous measurement of up to six locations. The Nd 3+ concentration was calculated by using chemical data science algorithms, where model training sets were collected on a single track of the detector. The discussion includes addressing the challenges of using a model collected on a single track and applying it as a model across the other tracks on the detector. Each track of the detector corresponds to one measurement location on the contactor. The difference in the integrated moles of Nd 3+ between the inlet and outlet at the end of the experiment was near zero, indicating that the mass balance of this experiment was maintained. Overall, the online spectroscopic monitoring was able to follow changing solution conditions and accurately measure the concentration of Nd 3+ in different locations within the contactor system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Deep Symbolic Optimization for Electric Component Sizing in Fixed Topology Power Converters

Power converters (PC) are a major component in any current electronic hardware device. The development and design is usually guided by expert knowledge and heavily relies on human intuition and experience. The process is a very time consuming and costly activity and it is generally hard to improve upon current designs. As a first step towards autonomous PC design, we are here proposing a new framework for the sizing of components for fixed topology PCs based on given design requirements. To this end, we developed surrogate models for rapid evaluation of new topologies and adapt the deep symbolic optimization (DSO) framework to generate new topologies guided by a reinforcement learning training signal. In an empirical evaluation, we show that our DSO based approach is able to find the optimal configuration for all investigated topologies, while reducing the learning time by at least a factor of 100 compared to popular RL algorithms.

Xue, Lincoln↗
DOE OSTI2026

How Do You Hear a Quantum Computer Whisper?

Quantum transduction is the process of upconverting microwave quantum signals into optical signals to develop quantum networks through optical fibers outside the dilution refrigerator, enabling connections between quantum technologies on the quantum internet. In this project, upconversion is achieved by directing an optical laser and the microwave quantum signal into an electro-optic bulk crystal. The crystal is housed within a Superconducting Radio Frequency (SRF) cavity designed to maximize the overlap between the microwave field and the crystal volume. In the presence of microwaves, the refractive index of the crystal changes through the Pockels effect. This change in refractive index modifies the propagation of the optical field within the crystal, allowing the quantum information carried by the microwave field to be transferred to the optical field. This study focuses on coupling laser light from suspended waveguide chips into the whispering-gallery modes (WGMs) of the crystal to enable transduction. The coupling efficiency between the optical field in the suspended waveguide and the WGM depends on the position of the laser spot on the crystal. To address this challenge, a feedback-based algorithm is being developed to fine-tune the waveguide position so that the optical signal is coupled efficiently into the crystal. After passing through the crystal, the optical signal is detected by a photodiode connected to an oscilloscope. The algorithm evaluates the coupling quality and iteratively adjusts the waveguide position to maximize coupling efficiency. The expected outcome is an automated waveguide alignment method that improves optical coupling and enables more efficient microwave-to-optical quantum transduction.

Karanastasis, Mihael [Fermilab]↗
DOE OSTI2021

Using Machine Learning to Track Objects Across Cameras

Video surveillance is one of the most important technologies used by the International Atomic Energy Agency in international safeguards. At large, complicated facilities, multiple surveillance cameras are deployed to monitor the transfer of safeguards-relevant objects across the site. During inspections, all surveillance videos are reviewed to ensure the objects are not manipulated or diverted during transfer, a laborious, time-consuming task. This work describes using deep machine learning algorithms to track objects automatically across multiple cameras, greatly improving the efficiency of the review process. The fundamental problem in this object tracking task across multiple cameras is how to associate the same object, which may show extreme intra-class variations, such as viewpoints, occlusions, and various scales, in different and even non-overlapped cameras. Object re-identification (Re-ID) in nuclear facility video surveillance is even more challenging than classic person or vehicle Re-ID problems because different instances in the same category may display an identical appearance. One observation from nuclear facility surveillance videos is that all objects must be carted (e.g., via forklift) to move. Therefore, the spatial context information of an object, which provides the feature from the carrier, is critical for the object Re-ID task. This work proposes a two-stream convolutional neural networks model that takes features of objects and their surrounding regions into account. Moreover, the custom videos usually are gleaned from different scenes from the training data, which may have extreme variations in illumination changes and/or cluttered backgrounds. Directly applying the trained model to custom videos will dramatically decrease the performance. To tackle this problem, an advanced domain adaptation technique is proposed to mitigate the gap between the data taken from different scenes. The proposed framework will track objects of interest across a nuclear complex. The resulting tracks can be used in further analyses, such as event/activity recognition, anomaly detection, etc.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2023

Optimizing cloud motion estimation on the edge with phase correlation and optical flow

Abstract. Phase correlation (PC) is a well-known method for estimating cloud motion vectors (CMVs) from infrared and visible spectrum images. Commonly, phase shift is computed in the small blocks of the images using the fast Fourier transform. In this study, we investigate the performance and the stability of the blockwise PC method by changing the block size, the frame interval, and combinations of red, green, and blue (RGB) channels from the total sky imager (TSI) at the United States Atmospheric Radiation Measurement user facility's Southern Great Plains site. We find that shorter frame intervals, followed by larger block sizes, are responsible for stable estimates of the CMV, as suggested by the higher autocorrelations. The choice of RGB channels has a limited effect on the quality of CMVs, and the red and the grayscale images are marginally more reliable than the other combinations during rapidly evolving low-level clouds. The stability of CMVs was tested at different image resolutions with an implementation of the optimized algorithm on the Sage cyberinfrastructure test bed. We find that doubling the frame rate outperforms quadrupling the image resolution in achieving CMV stability. The correlations of CMVs with the wind data are significant in the range of 0.38–0.59 with a 95 % confidence interval, despite the uncertainties and limitations of both datasets. A comparison of the PC method with constructed data and the optical flow method suggests that the post-processing of the vector field has a significant effect on the quality of the CMV. The raindrop-contaminated images can be identified by the rotation of the TSI mirror in the motion field. The results of this study are critical to optimizing algorithms for edge-computing sensor systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A Dataset of 3D Structural and Simulated Transport Properties of Complex Porous Media

Physical processes that occur within porous materials have wide-ranging applications including - but not limited to - carbon sequestration, battery technology, membranes, oil and gas, geothermal energy, nuclear waste disposal, water resource management. The equations that describe these physical processes have been studied extensively; however, approximating them numerically requires immense computational resources due to the complex behavior that arises from the geometrically-intricate solid boundary conditions in porous materials. Here, we introduce a new dataset of unprecedented scale and breadth, DRP-372: a catalog of 3D geometries, simulation results, and structural properties of samples hosted on the Digital Rocks Portal. The dataset includes 1736 flow and electrical simulation results on 217 samples, which required more than 500 core years of computation. This data can be used for many purposes, such as constructing empirical models, validating new simulation codes, and developing machine learning algorithms that closely match the extensive purely-physical simulation. This article offers a detailed description of the contents of the dataset including the data collection, simulation schemes, and data validation.

3D images↗
DOE OSTI2020

Evaluation of Methods for Causal Discovery in Hydrometeorological Systems

Understanding causal relations is of utmost importance in hydrology and climate research for systems identification, prediction, and understanding systems behavior in a changing climate. Traditionally, researchers in hydrometeorology attempted to study causal questions by conducting controlled experiments using numerical models. This approach, however, in most cases of interest provides uncertain results because the models are approximate representation of the natural system. An alternative approach that has recently drawn significant attention in several fields is to infer causal relations from purely observational data. It possesses several traits to its utility particularly in hydrometeorology due to the rapid accumulation of in situ and remotely sensed data records. The first objective of this study is to present a brief description of four causal discovery methods (Granger causality, Transfer Entropy, graph-based algorithms, and Convergent Cross Mapping) with special emphasis on the assumptions on which they are built. Second, using synthetic data generated from a hydrological model, we assess their performance in retrieving causal information taking into account sensitivity to sample size and presence of noise. Last, we use causal analysis to examine and formulate hypotheses on causal drivers of evapotranspiration in a shrubland region during summer and winter seasons. An interpretation of the hypotheses based on canopy seasonal dynamics and evapotranspiration processes is presented. It is hoped that the results presented here can be useful in guiding researchers studying hydrometeorological systems as to which causal method is most appropriate to the characteristics of the system under study.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Active sampling for neural network potentials: Accelerated simulations of shear-induced deformation in Cu–Ni multilayers

Neural network potentials (NNPs) can greatly accelerate atomistic simulations relative to ab initio methods, allowing one to sample a broader range of structural outcomes and transformation pathways. In this work, we demonstrate an active sampling algorithm that trains an NNP that is able to produce microstructural evolutions with accuracy comparable to those obtained by density functional theory, exemplified during structure optimizations for a model Cu–Ni multilayer system. We then use the NNP, in conjunction with a perturbation scheme, to stochastically sample structural and energetic changes caused by shear-induced deformation, demonstrating the range of possible intermixing and vacancy migration pathways that can be obtained as a result of the speedups provided by the NNP. The code to implement our active learning strategy and NNP-driven stochastic shear simulations is openly available at https://github.com/pnnl/Active-Sampling-for-Atomistic-Potentials .

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

Exploring Uncertainty in Moment Estimation for Small Earthquakes in Southern Nevada Using the Coda Envelope Method

Compiling source parameter estimates for small earthquakes is important both for our understanding of earthquake physics and for accurately assessing earthquake hazard. Reliable source parameter estimates are difficult to achieve for small earthquakes, in part due to our inability to accurately model the relevant physical processes at high frequencies. The coda envelope methodology developed by Mayeda and Walter (1996) and Mayeda et al. (2003) can mitigate this concern and estimate the moment of small earthquakes by determining the parameters that control the shape of the S-wave coda envelope while eliminating path effects by minimizing the scatter between seismic stations. Here, we use an open-source implementation of this technique called the Coda Calibration Tool (CCT; Barno, 2017) to calculate CCT-based moment magnitude estimates of small earthquakes (M L 0–3) in the Rock Valley, Nevada, region within the Nevada National Security Site. The Rock Valley data set is of particular interest because it allows us to explore the changes in uncertainties of the coda calibration method with earthquake size and depth. We found that a consistent linear relationship exists between the local magnitude M L and our coda-derived M w estimates for earthquakes as small as M L 0–3, but that current CCT workflows do not accurately characterize very shallow events. We also demonstrate that the epistemic uncertainty in the apparent stress value assumed by the CCT algorithm can influence magnitude estimates of small earthquakes. In conclusion, these results provide valuable insight into the seismicity of this region, and inform future analysis and modeling efforts for nuclear monitoring and seismic hazard.

58 GEOSCIENCES↗
DOE OSTI2022

Data reduction through optimized scalar quantization for more compact neural networks

Raw data generation for several existing and planned large physics experiments now exceeds TB/s rates, generating untenable data sets in very little time. Those data often demonstrate high dimensionality while containing limited information. Meanwhile, Machine Learning algorithms are now becoming an essential part of data processing and data analysis. Those algorithms can be used offline for post processing and post data analysis, or they can be used online for real time processing providing ultra low latency experiment monitoring. Both use cases would benefit from data throughput reduction while preserving relevant information: one by reducing the offline storage requirements by several orders of magnitude and the other by allowing ultra fast online inferencing with low complexity Machine Learning models. Moreover, reducing the data source throughput also reduces material cost, power and data management requirements. In this work we demonstrate optimized nonuniform scalar quantization for data source reduction. This data reduction allows lower dimensional representations while preserving the relevant information of the data, thus enabling high accuracy Tiny Machine Learning classifier models for online fast inferences. We demonstrate this approach with an initial proof of concept targeting the CookieBox, an array of electron spectrometers used for angular streaking, that was developed for LCLS-II as an online beam diagnostic tool. We used the Lloyd-Max algorithm with the CookieBox dataset to design an optimized nonuniform scalar quantizer. Optimized quantization lets us reduce input data volume by 69% with no significant impact on inference accuracy. When we tolerate a 2% loss on inference accuracy, we achieved 81% of input data reduction. Finally, the change from a 7-bit to a 3-bit input data quantization reduces our neural network size by 38%.

97 MATHEMATICS AND COMPUTING↗