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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Modeling of Aircraft Unsteady Aerodynamic Characteristics/Part 3 - Parameters Estimated from Flight Data: Parameters Estimated from Flight Data - Part 3

A nonlinear least squares algorithm for aircraft parameter estimation from flight data was developed. The postulated model for the analysis represented longitudinal, short period motion of an aircraft. The corresponding aerodynamic model equations included indicial functions (unsteady terms) and conventional stability and control derivatives. The indicial functions were modeled as simple exponential functions. The estimation procedure was applied in five examples. Four of the examples used simulated and flight data from small amplitude maneuvers to the F-18 HARV and X-31A aircraft. In the fifth example a rapid, large amplitude maneuver of the X-31 drop model was analyzed. From data analysis of small amplitude maneuvers ft was found that the model with conventional stability and control derivatives was adequate. Also, parameter estimation from a rapid, large amplitude maneuver did not reveal any noticeable presence of unsteady aerodynamics.

Klein, Vladislav↗
DOE OSTI2025

Sensitivity of an integrated experiment to uncertainty in the high explosive equations of state

Traditionally, hydrodynamics simulations are performed with a single equation-of-state (EOS) to describe each material. These EOSs typically have a physics-informed functional form with adjustable parameters that are calibrated in order to replicate small-scale data. However, because the calibration data have uncertainty and there are typically inherent degeneracies in fitting the EOS, there are actually multiple EOSs that might be consistent with calibration data. In this work, we perform uncertainty quantification (UQ) for the reactant and product equations of state for the high explosive PBX 9501 to yield an ensemble of EOSs that match the uncertain small-scale calibration data. We then simulate an experiment of an explosively formed penetrator repeatedly with different EOSs to both validate the UQ analysis and determine the effects of EOS uncertainty on the prediction of quantities of interest in the experiment. In general, we find good agreement between the simulation predictions and the experimental measurements, and we identify an EOS variable that contributes most directly to the spread in the predictions as the EOSs are varied.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Morphological Characters Can Strongly Influence Early Animal Relationships Inferred from Phylogenomic Data Sets

There are considerable phylogenetic incongruencies between morphological and phylogenomic data for the deep evolution of animals. This has contributed to a heated debate over the earliest-branching lineage of the animal kingdom: the sister to all other Metazoa (SOM). Here, we use published phylogenomic data sets ($\sim $45,000–400,000 characters in size with $\sim $15–100 taxa) that focus on early metazoan phylogeny to evaluate the impact of incorporating morphological data sets ($\sim $15–275 characters). We additionally use small exemplar data sets to quantify how increased taxon sampling can help stabilize phylogenetic inferences. We apply a plethora of common methods, that is, likelihood models and their “equivalent” under parsimony: character weighting schemes. Our results are at odds with the typical view of phylogenomics, that is, that genomic-scale data sets will swamp out inferences from morphological data. Instead, weighting morphological data 2–10$\times $ in both likelihood and parsimony can in some cases “flip” which phylum is inferred to be the SOM. This typically results in the molecular hypothesis of Ctenophora as the SOM flipping to Porifera (or occasionally Placozoa). However, greater taxon sampling improves phylogenetic stability, with some of the larger molecular data sets ($>$200,000 characters and up to $\sim $100 taxa) showing node stability even with $\geqq100\times $ upweighting of morphological data. Accordingly, our analyses have three strong messages. 1) The assumption that genomic data will automatically “swamp out” morphological data is not always true for the SOM question. Morphological data have a strong influence in our analyses of combined data sets, even when outnumbered thousands of times by molecular data. Morphology therefore should not be counted out a priori. 2) We here quantify for the first time how the stability of the SOM node improves for several genomic data sets when the taxon sampling is increased. 3) The patterns of “flipping points” (i.e., the weighting of morphological data it takes to change the inferred SOM) carry information about the phylogenetic stability of matrices. The weighting space is an innovative way to assess comparability of data sets that could be developed into a new sensitivity analysis tool.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2002

Mars Global Surveyor Data Analysis Program. Origins of Small Volcanic Cones: Eruption Mechanisms and Implications for Water on Mars

The goal of the proposed work was to determine the origins of small volcanic cones observed in Mars Global Surveyor (MGS) data, and their implications for regolith ice stores and magma volatile contents. For this 1-year study, our approach involved a combination of: Quantitative morphologic analysis and interpretation of Mars Orbiter Camera (MOC) and Mars Orbiter Laser Altimeter (MOLA) data; Numerical modeling of eruption processes responsible for producing the observed features; Fieldwork on terrestrial analogs in Iceland. Following this approach, this study succeeded in furthering our understanding of (i) the spatial and temporal distribution of near-surface water ice, as defined by the distribution and sizes of rootless volcanic cones ("pseudocraters"), and (ii) the properties, eruption conditions, and volatile contents of magmas producing primary vent cones.

Fagents, Sarah A.↗
NASA NTRS2014

Features of Point Clouds Synthesized from Multi-View ALOS/PRISM Data and Comparisons with LiDAR Data in Forested Areas

LiDAR waveform data from airborne LiDAR scanners (ALS) e.g. the Land Vegetation and Ice Sensor (LVIS) havebeen successfully used for estimation of forest height and biomass at local scales and have become the preferredremote sensing dataset. However, regional and global applications are limited by the cost of the airborne LiDARdata acquisition and there are no available spaceborne LiDAR systems. Some researchers have demonstrated thepotential for mapping forest height using aerial or spaceborne stereo imagery with very high spatial resolutions.For stereo imageswith global coverage but coarse resolution newanalysis methods need to be used. Unlike mostresearch based on digital surface models, this study concentrated on analyzing the features of point cloud datagenerated from stereo imagery. The synthesizing of point cloud data from multi-view stereo imagery increasedthe point density of the data. The point cloud data over forested areas were analyzed and compared to small footprintLiDAR data and large-footprint LiDAR waveform data. The results showed that the synthesized point clouddata from ALOSPRISM triplets produce vertical distributions similar to LiDAR data and detected the verticalstructure of sparse and non-closed forests at 30mresolution. For dense forest canopies, the canopy could be capturedbut the ground surface could not be seen, so surface elevations from other sourceswould be needed to calculatethe height of the canopy. A canopy height map with 30 m pixels was produced by subtracting nationalelevation dataset (NED) fromthe averaged elevation of synthesized point clouds,which exhibited spatial featuresof roads, forest edges and patches. The linear regression showed that the canopy height map had a good correlationwith RH50 of LVIS data with a slope of 1.04 and R2 of 0.74 indicating that the canopy height derived fromPRISM triplets can be used to estimate forest biomass at 30 m resolution.

LiDARD↗
NASA NTRSDate not supplied

NASA Langley FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

This work summarizes the results of FUN3D analyses conducted for the 1st AIAA Stability and Control Workshop on behalf of participants from the NASA Langley Research Center. The workshop was created to establish best practices for the prediction of stability and control derivatives using computational fluid dynamics and assess the limitations of these methods when those best practices are applied. The inaugural workshop considered the ONERA version of the NASA/Boeing Common Research Model, which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel data at small sideslip angles remain unpublished and served as ‘blind’ data for computational comparisons. The present research generated workshop test case data using the NASA FUN3D code, which is a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Steady- state numerical simulations were conducted for workshop test cases investigating the following: grid convergence, Mach number effect on static stability, wind tunnel sting increments, static stability-derivative calculations, and a sideslip angle sweep. Results were generated for two series of unstructured, mixed-element grids, one set provided by the workshop and another set created using the HeldenMesh grid generation software. The results provided include total- and component-level breakdowns of the force and moment coefficients, in addition to sectional pressure distributions for the wing and tail components for comparisons to wind tunnel data.

CFD↗
NASA NTRS2007

Science Archives in the 21st Century: A NASA LAMBDA Report

Lambda is a thematic data center that focuses on serving the cosmic microwave background (CMB) research community. LAMBDA is an active archive for NASA's Cosmic Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) mission data sets. In addition, LAMBDA provides analysis software, on-line tools, relevant ancillary data and important web links. LAMBDA also tries to preserve the most important ground-based and suborbital CMB data sets. CMB data is unlike other astrophysical data, consisting of intrinsically diffuse surface brightness photometry with a signal contrast of the order 1 part in 100,000 relative to the uniform background. Because of the extremely faint signal levels, the signal-to-noise ratio is relatively low and detailed instrument-specific knowledge of the data is essential. While the number of data sets being produced is not especially large, those data sets are becoming large and complex. That tendency will increase when the many polarization experiments currently being deployed begin producing data. The LAMBDA experience supports many aspects of the NASA data archive model developed informally over the last ten years-that small focused data centers are often more effective than larger more ambitious collections, for example; that data centers are usually best run by active scientists; that it can be particularly advantageous if those scientists are leaders in the use of the archived data sets; etc. LAMBDA has done some things so well that they might provide lessons for other archives. A lot of effort has been devoted to developing a simple and consistent interface to data sets, for example; and serving all the documentation required via simple 'more' pages and longer explanatory supplements. Many of the problems faced by LAMBDA will also not surprise anyone trying to manage other space science data. These range from persuading mission scientists to provide their data as quickly as possible, to dealing with a high volume of nuisance (spam) messages. Because so many data center problems and solutions are common across individual data centers and disciplines it would be very valuable to establish some new systems of communication - such as informal email lists for administrators and developers. But resources are very limited, so new timeconsuming and inefficient mechanisms - like too-frequent and too-structured meetingsshould be avoided. Although there are great advantages to being small, agile and independent, there are also some areas where science data centers within and without NASA could be better coordinated - for the assignment of persistent identifiers; to encourage the early adoption of useful standards and technologies; etc. Some super-structure to facilitate such coordination might be beneficial as long as it doesn't begin to control the other work of the archives, and become a "methodology police". In this respect the CCSDS "Reference Model for an Open Archive Information System" is a little worrying. It may be that the closer a data center gets to following such a detailed prescription, the less effective it will become. It is much better to have an informal coordination process than a bureaucratic straight-jacket.

Butterworth, P.↗
NASA NTRS1984

A flight study of tone radiation patterns generated by inlet rods in a small turbofan engine

This paper presents a flight study of tone radiation patterns from a small turbofan engine and compares results with similar static test stand data and a recently developed radiation theory. An interaction tone was produced by a circumferential array of inlet rods placed just upstream of the fan blades. Overhead and sideline flight directivity patterns showed cut-on of a dominant single mode occurred where predicted and the absence of any other significant circumferential or radial modes. In general, good agreement was found between measured flight and static data, with small differences being attributed to inlet geometry and/or forward speed effects. Good agreement was also obtained between flight data and theory for directivity pattern shape, however, the theory consistently predicted higher values for peak radiation angle over a wide range of frequency.

Preisser, J. S.↗
NASA NTRS2017

Collaborative Data Publication Utilizing the Open Data Repository's (ODR) Data Publisher

Introduction: For small communities in diverse fields such as astrobiology, publishing and sharing data can be a difficult challenge. While large, homogenous fields often have repositories and existing data standards, small groups of independent researchers have few options for publishing standards and data that can be utilized within their community. In conjunction with teams at NASA Ames and the University of Arizona, the Open Data Repository's (ODR) Data Publisher has been conducting ongoing pilots to assess the needs of diverse research groups and to develop software to allow them to publish and share their data collaboratively. Objectives: The ODR's Data Publisher aims to provide an easy-to-use and implement software tool that will allow researchers to create and publish database templates and related data. The end product will facilitate both human-readable interfaces (web-based with embedded images, files, and charts) and machine-readable interfaces utilizing semantic standards. Characteristics: The Data Publisher software runs on the standard LAMP (Linux, Apache, MySQL, PHP) stack to provide the widest server base available. The software is based on Symfony (www.symfony.com) which provides a robust framework for creating extensible, object-oriented software in PHP. The software interface consists of a template designer where individual or master database templates can be created. A master database template can be shared by many researchers to provide a common metadata standard that will set a compatibility standard for all derivative databases. Individual researchers can then extend their instance of the template with custom fields, file storage, or visualizations that may be unique to their studies. This allows groups to create compatible databases for data discovery and sharing purposes while still providing the flexibility needed to meet the needs of scientists in rapidly evolving areas of research. Research: As part of this effort, a number of ongoing pilot and test projects are currently in progress. The Astrobiology Habitable Environments Database Working Group is developing a shared database standard using the ODR's Data Publisher and has a number of example databases where astrobiology data are shared. Soon these databases will be integrated via the template-based standard. Work with this group helps determine what data researchers in these diverse fields need to share and archive. Additionally, this pilot helps determine what standards are viable for sharing these types of data from internally developed standards to existing open standards such as the Dublin Core (http://dublincore.org) and Darwin Core (http://rs.twdg.org) metadata standards. Further studies are ongoing with the University of Arizona Department of Geosciences where a number of mineralogy databases are being constructed within the ODR Data Publisher system. Conclusions: Through the ongoing pilots and discussions with individual researchers and small research teams, a definition of the tools desired by these groups is coming into focus. As the software development moves forward, the goal is to meet the publication and collaboration needs of these scientists in an unobtrusive and functional way.

easy to use and implement software tool↗
NASA NTRS2012

NASA Tech Briefs, June 2012

Topics covered include: iGlobe Interactive Visualization and Analysis of Spatial Data; Broad-Bandwidth FPGA-Based Digital Polyphase Spectrometer; Small Aircraft Data Distribution System; Earth Science Datacasting v2.0; Algorithm for Compressing Time-Series Data; Onboard Science and Applications Algorithm for Hyperspectral Data Reduction; Sampling Technique for Robust Odorant Detection Based on MIT RealNose Data; Security Data Warehouse Application; Integrated Laser Characterization, Data Acquisition, and Command and Control Test System; Radiation-Hard SpaceWire/Gigabit Ethernet-Compatible Transponder; Hardware Implementation of Lossless Adaptive Compression of Data From a Hyperspectral Imager; High-Voltage, Low-Power BNC Feedthrough Terminator; SpaceCube Mini; Dichroic Filter for Separating W-Band and Ka-Band; Active Mirror Predictive and Requirement Verification Software (AMP-ReVS); Navigation/Prop Software Suite; Personal Computer Transport Analysis Program; Pressure Ratio to Thermal Environments; Probabilistic Fatigue Damage Program (FATIG); ASCENT Program; JPL Genesis and Rapid Intensification Processes (GRIP) Portal; Data::Downloader; Fault Tolerance Middleware for a Multi-Core System; DspaceOgreTerrain 3D Terrain Visualization Tool; Trick Simulation Environment 07; Geometric Reasoning for Automated Planning; Water Detection Based on Color Variation; Single-Layer, All-Metal Patch Antenna Element with Wide Bandwidth; Scanning Laser Infrared Molecular Spectrometer (SLIMS); Next-Generation Microshutter Arrays for Large-Format Imaging and Spectroscopy; Detection of Carbon Monoxide Using Polymer-Composite Films with a Porphyrin-Functionalized Polypyrrole; Enhanced-Adhesion Multiwalled Carbon Nanotubes on Titanium Substrates for Stray Light Control; Three-Dimensional Porous Particles Composed of Curved, Two-Dimensional, Nano-Sized Layers for Li-Ion Batteries 23 Ultra-Lightweight; and Ultra-Lightweight Nanocomposite Foams and Sandwich Structures for Space Structure Applications.

Source record↗
NASA NTRS1976

High supersonic stability and control characteristics of a 0.015-scale (remotely controlled elevon) model 44-0 space shuttle orbiter tested in the NASA/LaRC 4-foot UPWT (LEG 2) (LA75), volume 1

Wind tunnel tests are reported on a 0.015-scale SSV orbiter model with remote independently operated left and right elevon surfaces. Special attention was directed to definition of nonlinear aerodynamic characteristics by taking data at small increments. Six component aerodynamic force and moment and elevon position data were recorded for the space shuttle orbiter with various elevon, aileron rudder and speed brake deflection combinations over an angle of attack range from -4 deg to 32 deg at angles of sideslip of 0 deg and 3 deg. Additional tests were made over an angle of sideslip range from -6 deg to 8 deg at selected angles of attack. Test Mach numbers were 2.86, 2.90, 3.90 and 4.60 with Reynolds numbers held at a constant 2.0 x 1 million per foot.

Ball, J. W.↗
DOE OSTI2026

The Vera C. Rubin Observatory Data Preview 1

We present Rubin Data Preview 1 (DP1), the first data from the National Science Foundation–Department of Energy Vera C. Rubin Observatory, comprising raw and calibrated single-epoch images, coadds, difference images, detection catalogs, and ancillary data products. DP1 is based on 1792 optical–near-infrared exposures acquired over 48 distinct nights by the Rubin Commissioning Camera (LSSTComCam) on the Simonyi Survey Telescope at the Summit Facility on Cerro Pachón, Chile in late 2024. DP1 covers ∼15 deg 2 distributed across seven roughly equal-sized noncontiguous fields, each independently observed in six broad photometric bands, ugrizy. The median FWHM of the point-spread function across all bands is approximately 1"14, with the sharpest images reaching about 0." 58. The 5σ point-source depths for coadded images in the deepest field, the Extended Chandra Deep Field South, are u = 24.55, g = 26.18, r = 25.96, i = 25.71, z = 25.07, and y = 23.1. Other fields are no more than 2.2 mag shallower in any band, where they have nonzero coverage. DP1 contains approximately 2.3 million distinct astrophysical objects, of which 1.6 million are extended in at least one band in coadds, and 431 solar system objects, of which 93 are new discoveries. DP1 is approximately 3.5 TB in size and is available to Vera C. Rubin Observatory data rights holders via the Rubin Science Platform, a cloud-based environment for the analysis of petascale astronomical data. While small compared to future LSST releases, its high quality and diversity of data support a broad range of early science investigations ahead of full operations in 2026.

Ground-based astronomy↗
DOE OSTI2025

RTN-095: The Vera C. Rubin Observatory Data Preview 1

We present Rubin Data Preview 1 (DP1), the first release of data from the NSF-DOE Vera C. Rubin Observatory, consisting of raw and calibrated single-epoch images, coadds, difference images, detection catalogs, and other derived data products. DP1 is based on 1792 science-grade optical/near-infrared exposures acquired over 48 distinct nights by the Rubin Commissioning Camera, LSSTComCam, on the Simonyi Survey Telescope at the Summit Facility on Cerro Pachón, Chile during the first on-sky commissioning campaign in late 2024. DP1 covers a total of ~15 sq. deg. over seven roughly equally-sized non-contiguous fields, each independently observed in six broad photometric bands, ugrizy, spanning a range of stellar densities and latitudes and overlapping with external reference datasets. The median image quality across all bands, measured by the FWHM of the point-spread function, is approximately 1.13 arcseconds, with the sharpest images reaching about 0.65 arcseconds. DP1 contains approximately 2.3 million distinct astrophysical objects, of which 1.6 million are extended in at least one band, and 431 solar system objects, of which 93 are new discoveries. DP1 is approximately 3.5 TB in size and available to Rubin data rights holders via the Rubin Science Platform, a cloud-based environment for the analysis of petascale astronomical data. While small compared to future LSST releases, its high quality and diversity of data support a broad range of early science investigations across all four LSST themes, providing a valuable opportunity to engage with Rubin data ahead of the start of full operations in late 2025.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

Prediction of Externally Blown Flap Noise and Turbomachinery Strut Noise

Methods were developed for predicting externally blown flap (EBF) noise and turbomachinery strut noise. Noise radiated by under-the-wing and upper-surface-blowing EBF configurations is calculated as a sum of lift dipole noise, trailing edge noise, and jet quadrupole noise. Resulting predictions of amplitudes and spectra generally were in good agreement with data from small-scale models. These data cover a range of exhaust velocity, flap deflection, exhaust nozzle position, exhaust nozzle shape, and ratio of exhaust nozzle diameter to wing chord. A semi-empirical method for predicting dipole noise radiation from a strut with incident turbulence was in good agreement with data. Leading-edge regions made of perforated plate backed by a bulk acoustic absorber achieved up to 7 db reduction of strut noise caused by incident turbulence at high frequencies. Radial turbulence in a turbofan exit duct was found to have a relatively high level associated with the mean velocity defect in the rotor blade wakes. Use of these turbulence spectra and a dipole noise radiation equation gave general prediction of measured aft-radiated sound power caused by a splitter ring in a full-scale fan exit duct.

Fink, M. R.↗
NASA NTRS1980

Digital mapping of mountain snowcover under European conditions

The author has identified the following significant results. A method for monitoring the snow cover in high mountain terrain such as the Swiss Alps includes the rapid classification of multitemporal data for small watersheds with very high accuracy. In addition to LANDSAT channels 4,5,6 and 7 an artificial channel was created containing the average altitude information of each pixel and allowing a subdivision of the watershed in accordance to the requirements of the runoff model. Even in very small watersheds of about 40 sq km the results achieved from LANDSAT data are at least as accurate as the ones gained from measurements of orthophotographs.

Haefner, H.↗
NASA NTRS1994

MSFC institutional area network and ATM technology

The New Institutional Area Network (NEWIAN) at Marshall supports over 5000 end users with access to 26 file servers providing work presentation services. It is comprised of some 150 Ethernet LAN's interconnected by bridges/routers which are in turn connected to servers over two dual FDDI rings. The network supports various higher level protocols such as IP, IPX, AppleTalk (AT), and DECNet. At present IPX and AT protocols packets are routed, and IP protocol packets are bridged; however, work is in progress to route all IP packets. The impact of routing IP packets on network operation is examined. Broadband Integrated Services Data Network (BISDN), presently at various stages of development, is intended to provide voice, video, and data transfer services over a single network. BISDN will use asynchronous transfer mode (ATM) as a data transfer technique which provides for transmission, multiplexing, switching, and relaying of small size data units called cells. Limited ATM Wide Area Network (WAN) services are offered by Wiltel, AT&T, Sprint, and others. NASA is testing a pilot ATM WAN with a view to provide Program Support Communication Network services using ATM. ATM supports wide range of data rates and quality of service requirements. It is expected that ATM switches will penetrate campus networks as well. However, presently products in these areas are at various stages of development and standards are not yet complete. We examine development of ATM to help assess its role in the evolution of NEWIAN.

Amin, Ashok T.↗
DOE OSTI2022

Small Hydropower Interconnections: Analysis of Interconnection Processes

Small hydropower projects have faced the challenge of navigating the process to interconnect their generation source to electricity distribution and transmission grids. Small hydropower developers have found interconnection procedures to be opaque and ultimately result in unexpected cost surprises and long timelines. Noting these challenges, the U.S. Department of Energy Water Power Technologies Office enlisted Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) to investigate the small hydropower interconnection landscape across the United States. After reviewing the status of small hydropower (“Small Hydropower Interconnections: Small Hydropower in the United States”) and the interconnection procedures across the United States (“Small Hydropower Interconnections: State Interconnection Processes”) in the first two white papers of this series, this paper uses recent data from small hydropower interconnection applications to benchmark the efficacy of the process. Using data from interconnection queues hosted by utilities, balancing authorities, independent system operators (ISOs), and regional transmission organizations (RTOs), this paper provides context for the costs, timelines, and types of upgrades required for small hydropower projects. Interconnection applications and study reports for small hydropower projects were analyzed to collect key pieces of information about the interconnection process, timeline, costs, and type of upgrades required for interconnection. Information sourced from the reports was entered into an Interconnection Benchmarking database (IBdb), which may be found in Appendix A.1. Information from this database was used to evaluate the performance and challenges associated with interconnecting small hydropower projects. This white paper presents a description of the sources contained in the interconnection database (Section 2.0), an analysis of the interconnection timeline (Section 3.0), an evaluation the cost of interconnection upgrades (Section 4.0), and a description of the types of infrastructure upgrades (Section 5.0). The final paper in this series (“Small Hydropower Interconnections: Best Practices”) will use the analysis described here to outline best practices for interconnection processes that will help overcome barriers to future small hydropower development.

13 HYDRO ENERGY↗
DOE OSTI2020

Graph interpolating activation improves both natural and robust accuracies in data-efficient deep learning

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning (DL) research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high-dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace–Beltrami equation on a high-dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation integrates the advantages of both deep learning and manifold learning. Compared to the conventional DNNs with the softmax function as output activation, the new framework demonstrates the following major advantages: First, it is better applicable to data-efficient learning in which we train high capacity DNNs without using a large number of training data. Second, it remarkably improves both natural accuracy on the clean images and robust accuracy on the adversarial images crafted by both white-box and black-box adversarial attacks. Third, it is a natural choice for semi-supervised learning. This paper is a significant extension of our earlier work published in NeurIPS, 2018. For reproducibility, the code is available at https://github.com/BaoWangMath/DNN-DataDependentActivation .

Mathematics↗