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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 505 records · Page 28

Perspectives on Designer Photocathodes for X-ray Free-Electron Lasers: Influencing Emission Properties with Heterostructures and Nanoengineered Electronic States

Here, the development of photoemission electron sources to specifically address the competing andnincreasingly stringent requirements of advanced light sources such as X-ray Free Electron Lasers (XFELs) motivates a comprehensive material-centric approach that integrates predictive compu- tational physics models, advanced nano-synthesis methods, and sophisticated surface science char- acterization with in situ correlated study of photoemission performance and properties. Related efforts in material science are adopting various forms of nanostructure (such as compositionally graded stoichiometry in heterostructured architectures, and quantum features) allowing for tailored electronic structure to control and enhance opto-electronic properties. These methods influence the mechanisms of photoemission (absorption, transport, and emission) but have not, as yet, been systematically considered for use in photocathode applications. Recent results and near-term op- portunities are described to exploit controlled functionality of nanomaterials for photoemission. An overview of the requirements and status is provided.

47 OTHER INSTRUMENTATION↗

Localized Radial Basis Functions for Radiation Transport in Slab Geometry

Meshing the spatial domain for the neutron transport equation can be computationally expensive and labor-intensive. Mesh-free methods, such as radial basis function (RBF) approximations, may alleviate these concerns by using a pointwise solution of the transport equation instead of the standard volume-integrated solution using cells or elements. This allows for the use of any geometric description that can provide the material at solution points and the boundary normal directions for boundary points. RBFs give spectral convergence when used to solve differential equations, but only if they are infinitely smooth. This occurs when the RBFs are effectively flat, creating an ill-conditioned, dense system of equations. One simple way to alleviate this issue is to use localized RBFs. Global RBFs have been applied previously to the monoenergetic radiative transport equation in X-Y geometry using source iteration. In this summary, localized RBFs are applied to the multigroup neutron transport equation in slab geometry using Krylov iteration. The results show agreement with benchmark solutions, provided the coefficients for the RBF basis are properly chosen. (authors)

97 MATHEMATICS AND COMPUTING↗

Integrated quantum optical phase sensor in thin film lithium niobate

Abstract The quantum noise of light, attributed to the random arrival time of photons from a coherent light source, fundamentally limits optical phase sensors. An engineered source of squeezed states suppresses this noise and allows phase detection sensitivity beyond the quantum noise limit (QNL). We need ways to use quantum light within deployable quantum sensors. Here we present a photonic integrated circuit in thin-film lithium niobate that meets these requirements. We use the second-order nonlinearity to produce a squeezed state at the same frequency as the pump light and realize circuit control and sensing with electro-optics. Using 26.2 milliwatts of optical power, we measure (2.7 ± 0.2)% squeezing and apply it to increase the signal-to-noise ratio of phase measurement. We anticipate that photonic systems like this, which operate with low power and integrate all of the needed functionality on a single die, will open new opportunities for quantum optical sensing.

47 OTHER INSTRUMENTATION↗

A Transparent Translation from Legacy System Model into Common Information Model

Advances in the smart grid are forcing utilities toward better monitoring, control, and analysis of distribution systems, and require extensive cyber-based, intelligent systems and applications to realize various functionalities. The ability of systems, or components within systems, to interact and exchange services or information with each other is the key to the success of smart grid technologies, and it requires efficient information exchanging and data sharing infrastructure. The Common Information Model (CIM) is a standard that allows different applications to exchange information about an electrical system, and it has become a widely accepted solution for information exchange among different platforms and applications. However, most existing legacy systems were developed using their own languages rather than CIM. Integrating such legacy systems is a challenge for utilities, and the appropriate use of the integrated legacy systems is even more intricate. Thus, this paper describes an approach and open-source tool developed to translate legacy system models into CIM format. The developed tool was tested for a commercial distribution management system and simulation results have proved its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Addressing Experimental Challenges in Probing Dark Energy with Accuracy and Precision with the Rubin Observatory Legacy Survey of Space & Time (LSST)

With support from this award, the Stanford group under the leadership of PI Patricia Burchat focused on pixel-level algorithms that are key to the investigation of dark energy with the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). The work was carried out through strong engagement in the DOE-supported LSST Dark Energy Science Collaboration (DESC), for which the PI served as Deputy Spokesperson (07/2019 - 07/2021) and Technical Coordinator (07/2021 - 07/2023). Members of the Burchat group are Full DESC members and are among scientists who have been accepted to join the Rubin Observatory System Integration, Test, and Commissioning (SIT-Com) effort. The specific intellectual focus of the group was the optimization of gravitational lensing as a probe of the evolution of the distribution of dark matter in space and time to learn about the nature of dark energy. The Stanford group pursued an integrated research program to understand in detail, and then remediate or calibrate, systematic effects that could limit the sensitivity of the LSST to cosmic shear as a dark energy probe -- particularly those related to our understanding of the atmospheric point spread function (PSF), challenges associated with blended galaxy images, and impacts of residual camera artifacts. Key to this work was developing, enhancing, and validating the fidelity of simulations that play a key role in the development of our understanding of subtle systematic biases and then using these simulations to develop techniques to characterize and mitigate biases, and associated algorithms for implementation in the LSST or DESC science pipelines. The group’s work included contributions to the open-source GalSim simulation package, which is widely used in the community; simulations and studies of spatial correlations of atmospheric PSFs; studies of temporal correlations of the atmospheric PSF; impacts of chromatic PSFs on cosmic shear calibration; continued studies of anisotropic Gaussian process interpolation of PSF models across the focal plane; and measuring and mitigating impacts of residual camera artifacts on cosmic shear. A primary impact of this work is that it increases the scientific discovery potential of the DOE and NSF investments in the Rubin Observatory Legacy Survey of Space \& Time, by addressing challenges in interpreting astronomical images through more accurate descriptions of the blurring of images due to the atmosphere. Specifically, this work impacts our ability to understand the fundamental nature of dark energy.

Burchat, Patricia Rose↗

From Modular ADMS to Plug-and-Play Ops: Distribution Grid Operations with Platform-Level Orchestration to Enable Ambitious App Hosting

The core function of the distribution grid is to provide electricity to consumers affordably, reliably, and securely. In pursuing these core objectives, distribution utilities are accountable to customers, regulators, and in some cases, shareholders. Other third parties such as aggregators and microgrids can also have a stake in the smooth operation of the grid. Each of these stakeholders has economic, business, and/or governance objectives that inform their expectations of the distribution grid. This multi-objective, multi-stakeholder environment creates tension that must be reconciled to successfully design and operate the distribution grid. Innovative companies are competing to bring high-tech solutions to electric utilities and their customers that address each of these objectives. Many developers of advanced distribution management systems (ADMS) and distributed energy resource management systems (DERMS) have adopted a modular architecture that allows grid operators to select functions and features according to their individual system needs. A modular platform also allows the solution provider to develop and integrate specific new product modules; however, the need to pursue multiple objectives with a fixed set of controllable devices makes integration expensive whether it is done at the product development stage or the deployment stage. This cost creates a significant barrier to adoption and can lengthen the product to market time of new solutions. To fundamentally address the complexity of system integration for distribution grid operations, the U.S. Department of Energy Office of Electricity has funded the GridAPPS-D project at PNNL, which streamlines integration by contributing to standards development, defining system architecture, applying advanced mathematics, and developing open-source software to demonstrate the concept of an open data-integration platform for distribution operations. The open data-integration platform concept enables system operators and solution providers to deploy ambitious, best-of-breed applications (or apps) without continually reengineering for integration. Ambitious apps developed by different solution providers will inevitably attempt to achieve different control objectives with the same set of controllable devices. If the open platform itself can resolve these conflicts in a way that achieves the best available outcomes for all apps, doesn’t restrict the ambitious design of apps, and ensures safe and secure operations, apps will be able to plug-and-play with the platform at the same time as other ambitious apps. In this paper, we describe a framework called App Deconfliction that empowers a platform to assign setpoints to controllable devices based on the values preferred by different apps (and even external stakeholder entities like customers or aggregators). The App Deconfliction framework is compatible with several methods for determining setpoint values. We present two methods based on game theory that provide a subtle built-in incentive structure for developers to adapt their apps to the fact that they will be operating in a moderated multi-app environment and to favor device setpoints that have the most effect on their objectives over those that have the least effect. Our simulation-based demonstrations have shown that game-theory-based deconfliction can lead to a 7% improvement in control space utilization compared to design-based methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Computational models of direct and indirect X‐ray breast imaging detectors for in silico trials

Abstract Background To facilitate in silico studies that investigate digital mammography (DM) and breast tomosynthesis (DBT), models replicating the variety in imaging performance of the DM and DBT systems, observed across manufacturers are needed. Purpose The main purpose of this work is to develop generic physics models for direct and indirect detector technology used in commercially available systems, with the goal of making them available open source to manufacturers to further tweak and develop the exact in silico replicas of their systems. Methods We recently reported on an in silico version of the SIEMENS Mammomat Inspiration DM/DBT system using an open‐source GPU‐accelerated Monte Carlo x‐ray imaging simulation code (MC‐GPU). We build on the previous version of the MC‐GPU codes to mimic the imaging performances of two other Food and Drug Administration (FDA)‐approved DM/DBT systems, such as Hologic Selenia Dimensions (HSD) and the General Electric Senographe Pristina (GSP) systems. In this work, we developed a hybrid technique to model the optical spread and signal crosstalk observed in the GSP and HSD systems. MC simulations are used to track each x‐ray photon till its first interaction within the x‐ray detector. On the other hand, the signal spread in the x‐ray detectors is modeled using previously developed analytical equations. This approach allows us to preserve the modeling accuracy offered by MC methods in the patient body, while speeding up secondary carrier transport (either electron–hole pairs or optical photons) using analytical equations in the detector. The analytical optical spread model for the indirect detector includes the depth‐dependent spread and collection of optical photons and relies on a pre‐computed set of point response functions that describe the optical spread as a function of depth. To understand the capabilities of the computational x‐ray detector models, we compared image quality metrics like modulation transfer function (MTF), normalized noise power spectrum (NNPS), and detective quantum efficiency (DQE), simulated with our models against measured data. Please note that the purpose of these comparisons with measured data would be to gauge if the model developed as part of this work could replicate commercially used direct and indirect technology in general and not to achieve perfect fits with measured data. Results We found that the simulated image quality metrics such as MTF, NNPS, and DQE were in reasonable agreement with experimental data. To demonstrate the imaging performance of the three DM/DBT systems, we integrated the detector models with the VICTRE pipeline and simulated DM images of a fatty breast model containing a spiculated mass and a calcium oxalate cluster. In general, we found that the images generated using the indirect model appeared more blurred with a different noise texture and contrast as compared to the systems with direct detectors. Conclusions We have presented computational models of three commercially available FDA‐approved DM/DBT systems, which implement both direct and indirect detector technology. The updated versions of the MC‐GPU codes that can be used to replicate three systems are available in open source format through GitHub.

Sengupta, Aunnasha↗

Toward High-Voltage Cathodes for Zinc-Ion Batteries: Discovery Pipeline and Material Design Rules

Efficient energy storage systems are crucial to address the intermittency of renewable energy sources. As multivalent batteries, Zn-ion batteries (ZIBs), while inherently low voltage, offer a promising low-cost alternative to Li-ion batteries due to the viable use of zinc as the anode. However, to maximize the potential impact of ZIBs, rechargeable cathodes with improved Zn diffusion are needed. To better understand the chemical and structural factors influencing Zn-ion mobility within battery electrode materials, we employ a high-throughput computational screening approach to systematically evaluate candidate intercalation hosts for ZIB cathodes, expanding the chemical search space on empty intercalation hosts that do not contain Zn. We leverage a high-throughput screening funnel to identify promising cathodes in ZIBs, integrating screening criteria with density functional theory (DFT)-based calculations of Zn2+ intercalation and diffusion inside the host materials. Using these data, we identify the design principles that favor Zn-ion mobility in candidate cathode materials. Building on previous work on divalent-ion cathodes, this study broadens the chemical space for next-generation multivalent energy storage systems.

electrodes↗

Direct Deposition of Crystalline Ta 3 N 5 Thin Films on FTO for PEC Water Splitting

Tantalum Nitride is a promising photoanode material for solar water splitting, but the further study and practical use is constrained by the harsh conditions of the synthesis from Ta metal. Here we report the direct deposition of crystalline Ta 3 N 5 on FTO substrate via a custom-built ALD system. A combination of TaCl 5 (Ta-precursor) and ammonia (N-source) were sequentially pulsed into the ALD reactor with the substrate heated to 550 °C to deposit compact and thin films of Ta 3 N 5 with controllable thicknesses on FTO substrates. Importantly, it is shown that the FTO is chemically and structurally stable under the reducing conditions of ammonia at 550 °C. These electrodes produced an exceptional photocurrent onset potential of ~ 0.3 V vs. RHE with a maximum photocurrent of ~ 2.4 mA cm -2 at 1.23 V vs RHE. Results of photoelectrochemical investigations as a function of film thickness and illumination direction reveal that the performance of Ta 3 N 5 is controlled by a hole diffusion length of ~50 nm. These results are crucial for the successful integration of Ta 3 N 5 in efficient unassisted water splitting applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurement of the ionization response of amorphous selenium with 122 keV γ rays

In this work, we performed a measurement of the ionization response of 200 μm-thick amorphous selenium (aSe) layers under drift electric fields of up to 50 V/μm. The aSe target was exposed to ionizing radiation from a 57 Co radioactive source and the ionization pulses were recorded with high resolution. Using the spectral line from the photoabsorption of 122 keV γ rays, we measured the charge yield in aSe and the line width as a function of drift electric field. From a detailed microphysics simulation of charge generation and recombination in aSe, we conclude that the strong dependence of recombination on the ionization track density provides the dominant contribution to the energy resolution in aSe. These results provide valuable input to estimate the sensitivity of a proposed next-generation search for the neutrinoless ββ decay of 82 Se that aims to employ imaging sensors with an active layer of aSe. We estimate the RMS line width of the integrated ionization signal from neutrinoless ββ decay events (of deposited energy 3 MeV) to be 2.0% for a drift field of 50 V/μm. The energy resolution can be improved to 1% by correcting for the charge yield as a function of ionization density along the imaged electron tracks.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Toward quantum networking with frequency-bin qudits

Quantum networking holds tremendous promise in transforming computation and communication. Entangled-photon sources are critical for quantum repeaters and networking, while photonic integrated circuits are vital for miniaturization and scalability. In this talk, we focus on generating and manipulating frequency-bin entangled states within integrated platforms. We encode quantum information as a coherent superposition of multiple optical frequencies; this approach is favorable due to its amenability to high-dimensional entanglement and compatibility with fiber transmission. We successfully generate and measure the density matrix of biphoton frequency combs from integrated silicon nitride microrings, fully reconstructing the state in an 8 × 8 two-qudit Hilbert space, the highest so far for frequency bins. Moreover, we employ Vernier electro-optic phase modulation methods to perform time-resolved measurements of biphoton correlation functions. Currently, we are exploring bidirectional pumping of microrings to generate indistinguishable entangled pairs in both directions, aiming to demonstrate key networking operations such as entanglement swapping and Greenberger–Horne–Zeilinger state generation in the frequency domain.

Myilswamy, Karthik V.↗

Unified feature association networks through integration of transcriptomic and proteomic data

High-throughput multi-omics studies and corresponding network analyses of multi-omic data have rapidly expanded their impact over the last 10 years. As biological features of different types (e.g. transcripts, proteins, metabolites) interact within cellular systems, the greatest amount of knowledge can be gained from networks that incorporate multiple types of -omic data. However, biological and technical sources of variation diminish the ability to detect cross-type associations, yielding networks dominated by communities comprised of nodes of the same type. We describe here network building methods that can maximize edges between nodes of different data types leading to integrated networks. We systematically rank several network inference methods and demonstrate that, in many cases, using a random forest method, GENIE3, produces the most integrated networks. This increase in integration does not come at the cost of accuracy as GENIE3 produces networks of approximately the same quality as the other network inference methods tested here. Using GENIE3, we also infer networks representing antibody-mediated Dengue virus cell invasion and receptor-mediated Dengue virus invasion. A number of functional pathways showed centrality differences between the two networks including genes responding to both GM-CSF and IL-4, which had a higher centrality value in an antibody-mediated vs. receptor-mediated Dengue network. Because a biological system involves the interplay of many different types of molecules, incorporating multiple data types into networks will improve their use as models of biological systems. The methods explored here are some of the first to specifically highlight and address the challenges associated with how such multi-omic networks can be assembled and how the greatest number of interactions can be inferred from different data types. The resulting networks can lead to the discovery of new host response patterns and interactions during viral infection, generate new hypotheses of pathogenic mechanisms and confirm disease associated mechanisms of disease.

59 BASIC BIOLOGICAL SCIENCES↗

Characterizing Organic Aerosol Processes and Climatically Relevant Properties via Advanced and Integrated Analyses of Aerosol Mass Spectrometry Datasets from DOE Campaigns and ACRF Measurements. Final report for DE-SC0007178

Organic aerosols (OA) are an important but poorly characterized component of the earth’s climate system. Enormous complexities commonly associated with OA composition and life cycle processes have significantly complicated the simulation and quantification of aerosol effects. To unravel these complexities and improve understanding of the properties, sources, formation, evolution processes, and radiative properties of atmospheric OA, we propose to perform advanced and integrated analyses of multiple DOE aerosol mass spectrometry datasets, including two high-resolution time-of-flight aerosol mass spectrometer (HR-AMS) datasets from intensive field campaigns on the aerosol life cycle and the Aerosol Chemical Speciation Monitor (ACSM) datasets from long-term routine measurement programs at ACRF sites. In this project, we will focus on 1) characterizing the chemical (i.e., composition, organic elemental ratios), physical (i.e., size distribution and volatility), and radiative (i.e., sub- and super-saturated growth) properties of organic aerosols, 2) examining the correlations of these properties with different source and process regimes (e.g., primary, secondary, urban, biogenic, biomass burning, marine, or mixtures), 3) quantifying the evolutions of these properties as a function of photochemical processing, 4) identifying and characterizing special cases for important processes such as SOA formation and new particle formation and growth, and 5) correlating size-resolved aerosol chemistry with measurements of radiative properties of aerosols to determine the climatically relevant properties of OA and characterize the relationship between these properties and processes of atmospheric aerosol organics. Our primary goal is to improve a process-level understanding of the life cycle of organic aerosols in the Earth’s atmosphere. We will also aim at bridging between observations and models via synthesizing and translating the results and insights generated from this research into data products and formulations that may be directly used to inform, improve, and evaluate regional and global models. In addition, we will continue our current very active collaborations with several modeling groups to enhance the use and interpretation of our data products. Overall, this research will contribute new data to improve quantification of the aerosol’s effects on climate and thus the achievement of ASR’s science goal of – “improving the fidelity and predictive capability of global climate models”.

54 ENVIRONMENTAL SCIENCES↗

A Novel Design for Switchable Grid-Following and Grid-Forming Control

This paper presents the design of a novel grid- forming (GFM) control structure adapted from a typical grid- following (GFL) control structure with minimal edits, thereby enabling a switchable control structure for voltage sourced converters (VSCs) to operate in either GFL or GFM mode by simply switching a flag manually. The VSC is shown to be able to operate in the GFL control mode synchronizing to the main grid through a phase-locked-loop (PLL) and operate as a GFM controller with power-based synchronization for both grid-connected and islanded conditions. To guarantee smooth operation, the control schemes and the mode switching logic have been carefully designed and examined via a series of experiments. Here, the experiment results show that the switchable control structure can fulfill the desired control and operation functions and enable smooth transition between control modes.

14 SOLAR ENERGY↗

Fast Photoactuation Driven by Supramolecular Polymers Integrated into Covalent Networks

Abstract The design of robotic soft matter capable of emulating the complex movements of living organisms such as mechanical actuation, shape transformation, and autonomous translation remains a grand challenge in soft materials science. Functionalized hydrogels are excellent candidates for such materials since they can operate in water and are highly responsive to their environment, but their response times can be slow. This work investigates fast photoactuation of hybrid bonding hydrogels composed of peptide amphiphile (PA) supramolecular nanofibers bonded covalently to merocyanine‐based (MCH + ) photoresponsive networks. By incorporating ionizable acrylic acid (AA) co‐monomers in these networks, photoactuation at nearly neutral pH is observed, which in turn enables a new mechanism to accelerate the response by triggering the bundling of supramolecular nanofibers by rapid proton exchange reactions. Furthermore, this rapid response and its consequent large shape transformations lead to hydrogels capable of spontaneously tracking external light sources inspired by pedicellariae, defensive organs present in echinoderms like the starfish and the sea urchin. This work suggests that hybrid bonding polymers (HBPs), which leverage the interplay between supramolecular assemblies and covalent networks, offer novel strategies to design rapidly actuating soft robotic materials.

Cezan, S. Doruk↗

Calibration and Initial Results of Space Radiation Dosimetry Using the iMESA-R

The integrated Miniaturized Electrostatic Analyzer-Reflight (iMESA-R) is a space weather instrument designed to measure plasma density, temperature, and spacecraft charging, along with total ionizing dose and dose rate. A constellation consisting of five nearly identical instruments has been designed and developed to act as science payloads hosted on-board Department of Defense satellites operating in low-Earth orbit. To validate the dosimetry component of the iMESA-R, a radiation test study was performed to calibrate the dosimeter and ascertain the attenuation due to the instrument aluminum housing. An 80 curie Cobalt-60 radioisotope source emitting beta, X-ray, and gamma ray radiation decay products was used to calibrate the dosimeter response as a function of distance and instrument shielding. We present results of the calibration study along with initial on-orbit data presented from the first operational iMESA-R hosted on-board Space Test Program Satellite 5 in a polar Earth orbit. The initial on-orbit data demonstrate the ability to map the radiation environment, particularly the South Atlantic Anomaly and the auroral regions using total ionizing dose rate due to electrons of E > 1.5 MeV and protons of E > 25 MeV.

79 ASTRONOMY AND ASTROPHYSICS↗

Deriving the Contribution of Blazars to the Fermi -LAT Extragalactic γ -ray Background at E > 10 GeV with Efficiency Corrections and Photon Statistics

Here, the Fermi Large Area Telescope (LAT) Collaboration has recently released the Third Catalog of Hard Fermi -LAT Sources (3FHL), which contains 1556 sources detected above 10 GeV with seven years of Pass 8 data. Building upon the 3FHL results, we investigate the flux distribution of sources at high Galactic latitudes ($|b| \gt 20^\circ $), which are mostly blazars. We use two complementary techniques: (1) a source-detection efficiency correction method and (2) an analysis of pixel photon count statistics with the one-point probability distribution function (1pPDF). With the first method, using realistic Monte Carlo simulations of the γ-ray sky, we calculate the efficiency of the LAT to detect point sources. This enables us to find the intrinsic source-count distribution at photon fluxes down to 7.5 × 10 –12 ph cm –2 s –1 . With this method, we detect a flux break at (3.5 ± 0.4) × 10 –11 ph cm –2 s –1 with a significance of at least 5.4σ. The power-law indexes of the source-count distribution above and below the break are 2.09 ± 0.04 and 1.07 ± 0.27, respectively. This result is confirmed with the 1pPDF method, which has a sensitivity reach of ~10 –11 ph cm –2 s –1 . Integrating the derived source-count distribution above the sensitivity of our analysis, we find that (42 ± 8)% of the extragalactic γ-ray background originates from blazars.

79 ASTRONOMY AND ASTROPHYSICS↗

hls4ml: A Flexible, Open-Source Platform for Deep Learning Acceleration on Reconfigurable Hardware

We present hls4ml, a free and open-source platform that translates machine learning (ML) models from modern deep learning frameworks into high-level synthesis (HLS) code that can be integrated into full designs for field-programmable gate arrays (FPGAs) or application-specific integrated circuits (ASICs). With its flexible and modular design, hls4ml supports a large number of deep learning frameworks and can target HLS compilers from several vendors, including Vitis HLS, Intel oneAPI and Catapult HLS. Together with a wider eco-system for software-hardware co-design, hls4ml has enabled the acceleration of ML inference in a wide range of commercial and scientific applications where low latency, resource usage, and power consumption are critical. In this paper, we describe the structure and functionality of the hls4ml platform. The overarching design considerations for the generated HLS code are discussed, together with selected performance results.

FOS: Computer and information sciences↗