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NASA NTRS2009

Objectives and Progress on Ground Vibration Testing for the Ares Launch Vehicles

NASA has conducted dynamic tests on each of its major launch vehicles during the past 45 years. Each test has provided invaluable data to correlate and correct analytical models used to predict structural responses to differing dynamics for these vehicles. With both Saturn V and Space Shuttle, hardware changes were also required to the flight vehicles to ensure crew and vehicle safety. The Ares I IVGVT will undoubtedly provide similar valuable test data to support successful flights of the Constellation Program. The IVGVT will provide test determined natural frequencies, mode shapes and damping for the Ares I. This data will be used to support controls analysis by providing this test data to reduce uncertainty in the models. The value of this testing has been proven by past launch vehicle successes and failures. Performing dynamic testing on the Ares vehicles will provide confidence that the launch vehicles will be safe and successful in their missions. In addition, IVGVT will provide the following benefits for the Ares rockets: a) IVGVT data along with Ares development flights like Ares I-X, Ares I-Y, Ares I-X Prime, and Orion-1 or others will reduce the risk to the Orion-2 crew. IVGVT will permit anchoring the various analytical and operational models used in so many different aspects of Ares operations. b) IVGVT data will permit better understanding of the structural and GN&C margins of the spacecraft and may permit mass savings or expanded day-of-launch opportunities or fewer constraints to launch. c) Undoubtedly IVGVT will uncover some of the "unknown unknowns" so often seen in developing, launching, and flying new spacecraft vehicles and data from IVGVT may help prevent a loss of vehicle or crew. d) IVGVT also will be the first time Ares I flight-like hardware is transported, handled, rotated, mated, stacked, and integrated. e) Furthermore, handling and stacking the IVGVT launch vehicle stacks will be an opportunity to understand certain aspects of vehicle operability much better (for example, handling procedures, touch-labor time to accomplish tasks, access at interfaces, access to stage mating bolts, access to avionics boxes, access to the Interstage, GSE functionality, and many other important aspects of Ares I operability). All of these results will provide for better vehicle safety and better stewardship of national resources as NASA begins its next phase of human space exploration.

Tuma, Margaret L.↗

DOE OSTI2021

Beyond magnons in Nd 2 ScNbO 7 : An Ising pyrochlore antiferromagnet with all-in–all-out order and random fields

We report the low-temperature magnetic properties of Nd 3+ pyrochlore Nd 2 ScNbO 7 . Susceptibility and magnetization show an easy-axis moment, and heat capacity reveals a phase transition to long-range order at T N =371(2) mK with a fully recovered ΔS=Rln(2), 53% of it recovered for T>T N . Elastic neutron scattering shows a long-range all-in all-out magnetic order with low-Q diffuse elastic scattering. Inelastic neutron scattering shows a low-energy flat band, indicating a magnetic Hamiltonian similar to Nd 2 Zr 2 O 7 . Nuclear hyperfine excitations measured by ultra-high-resolution neutron backscattering indicate a distribution of static electronic moments below T N , which may be due to B-site disorder influencing Nd crystal electric fields. Analysis of heat-capacity data shows an unexpected T-linear or T 3/2 term which is inconsistent with conventional magnon quasiparticles, but is consistent with fractionalized spinons or gapless local spin excitations. We use legacy data to show similar behavior in Nd 2 Zr 2 O 7 . Comparing local static moments also reveals a suppression of the nuclear Schottky anomaly in temperature, evidencing a fraction of Nd sites with nearly zero static moment, consistent with exchange-disorder-induced random singlet formation. Finally, taken together, these measurements suggest an unusual fluctuating magnetic ground state which mimics a spin liquid, but may not actually be one.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2019

Improving Satellite Global Chlorophyll a [alpha] Data Products Through Algorithm Refinement and Data Recovery

A recently developed algorithm to estimate surface ocean chlorophyll a concentrations (Chl in milligrams per cubic meter), namely, the ocean color index (OCI) algorithm, has been adopted by the U.S. National Aeronautics and Space Administration to apply to all satellite ocean color sensors to produce global Chl maps. The algorithm is a hybrid between a band‐difference color index algorithm for low‐Chl waters and the traditional band‐ratio algorithms (OCx) for higher‐Chl waters. In this study, the OCI algorithm is revisited for its algorithm coefficients and for its algorithm transition between color index and OCx using a merged data set of high‐performance liquid chromatography and fluorometric Chl. Results suggest that the new OCI algorithm (OCI2) leads to lower Chl estimates than the original OCI (OCI1) for Chl less than 0.05 milligrams per cubic meter, but smoother algorithm transition for Chl between 0.25 and 0.40 milligrams per cubic meter. Evaluation using in situ data suggests that similar to OCI1, OCI2 has significantly improved image quality and cross‐sensor consistency between SeaWiFS (Sea-viewing Wide Field-of-view Sensor), MODISA (Moderate Resolution Imaging Spectroradiometer on Aqua), and VIIRS (Visible Infrared Imaging Radiometer Suite) over the OCx algorithms for oligotrophic oceans. Mean cross‐sensor difference in monthly Chl data products over global oligotrophic oceans reduced from approximately 10 percent for OCx to 1-2 percent for OCI2. More importantly, data statistics suggest that the current straylight masking scheme used to generate global Chl maps can be relaxed from 7 by 5 to 3 by 3 pixels without losing data quality in either Chl or spectral remote sensing reflectance (R (sub rs) by lambda (sensor wavelength), per steradian (sr (sup −1)) for not just oligotrophic oceans but also more productive waters. Such a relaxed masking scheme yields an average relative increase of 39 percent in data quantity for global oceans, thus making it possible to reduce data product uncertainties and fill data gaps.

Hu, Chuanmin↗

NASA NTRS1997

Dynamic Ground Effect for a Cranked Arrow Wing Airplane

Flight-determined ground effect characteristics for an F-16XL airplane are presented and correlated with wind tunnel predictions and similar flight results from other aircraft. Maneuvers were conducted at a variety of flightpath angles. Conventional ground effect flight test methods were used, with the exception that space positioning data were obtained using the differential global positioning system (DGPS). Accuracy of the DGPS was similar to that of optical tracking methods, but it was operationally more attractive. The dynamic flight determined lift and drag coefficient increments were measurably lower than steady-state wind-tunnel predictions. This relationship is consistent with the results of other aircraft for which similar data are available. Trends in the flight measured lift increments caused by ground effect as a function of flightpath angle were evident but weakly correlated. An engineering model of dynamic ground effect was developed based on linear aerodynamic theory and super-positioning of flows. This model was applied to the F-16XL data set and to previously published data for an F-15 airplane. In both cases, the model provided an engineering estimate of the ratio between the steady-state and dynamic data sets.

Curry, Robert E.↗

NASA NTRS2000

BOREAS TE-18 Landsat TM Physical Classification Image of the NSA

The BOREAS TE-18 team focused its efforts on using remotely sensed data to characterize the successional and disturbance dynamics of the boreal forest for use in carbon modeling. The objective of this classification is to provide the BOREAS investigators with a data product that characterizes the land cover of the NSA. A Landsat-5 TM image from 21-Jun-1995 was used to derive the classification. A technique was implemented that uses reflectances of various land cover types along with a geometric optical canopy model to produce spectral trajectories. These trajectories are used in a way that is similar to training data to classify the image into the different land cover classes. The data are provided in a binary, image file format. The data files are available on a CD-ROM (see document number 20010000884), or from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC).

Hall, Forrest G.↗

NASA NTRS1979

The Relationship of Red and Photographic Infrared Spectral Data to Grain Yield Variation Within a Winter Wheat Field

Two band hand-held radiometer data from a winter wheat field, collected on 21 dates during the spring growing season, were correlated within field final grain yield. Significant linear relationships were found between various combinations of the red and photographic infrared radiance data collected and the grain yield. The spectral data explained approximately 64 percent of the within field grain yield variation. This variation in grain yield could not be explained using meteorological data as these were similar for all areas of the wheat field. Most importantly, data collected early in the spring were highly correlated with grain yield, a five week time window existed from stem elongation through antheses in which the spectral data were most highly correlated with grain yield, and manifestations of wheat canopy water stress were readily apparent in the spectral data.

Tucker, C. J.↗

NASA NTRS1980

Relationship of spectral data to grain yield variation

Two-band hand-held radiometer data from a winter wheat field, collected on 21 dates during the spring growing season, were correlated with within-field final grain yield. Significant linear relationships were found between various combinations of the red and photographic infrared radiance data collected and the grain yield. The spectral data explained about 64 percent of the within-field grain yield variation. This variation in grain yield could not be explained using meteorological data as these were similar for all areas of the wheat field. Most importantly, data collected early in the spring were highly correlated with grain yield, a five-week time window existed from stem elongation through anthesis in which the spectral data were most highly correlated with grain yield, and manifestations of wheat canopy water stress were readily apparent in the spectral data.

Tucker, C. J.↗

NASA NTRS2005

Classification of Volcanic Eruptions on Io and Earth Using Low-Resolution Remote Sensing Data

Two bodies in the Solar System exhibit high-temperature active volcanism: Earth and Io. While there are important differences in the eruptions on Earth and Io, in low-spatial-resolution data (corresponding to the bulk of available and foreseeable data of Io), similar styles of effusive and explosive volcanism yield similar thermal flux densities. For example, a square metre of an active pahoehoe flow on Io looks very similar to a square metre of an active pahoehoe flow on Earth. If, from observed thermal emission as a function of wavelength and change in thermal emission with time, the eruption style of an ionian volcano can be constrained, estimates of volumetric fluxes can be made and compared with terrestrial volcanoes using techniques derived for analysing terrestrial remotely-sensed data. In this way we find that ionian volcanoes fundamentally differ from their terrestrial counterparts only in areal extent, with Io volcanoes covering larger areas, with higher volumetric flux. Io outbursts eruptions have enormous implied volumetric fluxes, and may scale with terrestrial flood basalt eruptions. Even with the low-spatial resolution data available it is possible to sometimes constrain and classify eruption style both on Io and Earth from the integrated thermal emission spectrum. Plotting 2 and 5 m fluxes reveals the evolution of individual eruptions of different styles, as well as the relative intensity of eruptions, allowing comparison to be made from individual eruptions on both planets. Analyses like this can be used for interpretation of low-resolution data until the next mission to the jovian system. For a number of Io volcanoes (including Pele, Prometheus, Amirani, Zamama, Culann, Tohil and Tvashtar) we do have high/moderate resolution imagery to aid determination of eruption mode from analyses based only on low spatial-resolution data.

Davies, A. G.↗

NASA NTRS1998

Long-Term Global Morphology of Gravity Wave Activity Using UARS Data

This is the first quarter's report on research to extract global gravity-wave data from satellite data and to model those observations synoptically. Preliminary analysis of global maps of extracted middle atmospheric temperature variance from the CRISTA instrument is presented, which appear to contain gravity-wave information. Corresponding simulations of global gravity-wave and mountain-wave activity during this mission period are described using global ray-tracing and mountain-wave models, and interesting similarities among simulated data and CRISTA data are noted. Climatological simulations of mesospheric gravity-wave activity using the HWM-03 wind-temperature climatology are also reported, for comparison with UARS MLS data. Preparatory work on modeling of gravity wave observations from space-based platforms and subsequent interpretation of the MLS gravity-wave product are also described. Preliminary interpretation and relation to the research objectives are provided, and further action for the next quarter's research is recommended.

Eckermann, Stephen D.↗

NASA NTRS1999

Inlet Flow Characteristics During Rapid Maneuvers for an F/A-18A Airplane

The F404-GE-400 engine powered F/A-18A High Alpha Research Vehicle (HARV) was used to examine the characteristics of inlet airflow during rapid aircraft maneuvers. A study of the degree of similarity between inlet data obtained during rapid aircraft maneuvers and inlet data obtained at steady aerodynamic attitudes was conducted at the maximum engine airflow of approximately 145 Ibm/sec using a computer model that was generated from inlet data obtained during steady aerodynamic maneuvers. Results show that rapid-maneuver inlet recoveries agreed very well with the recoveries obtained at equivalent stabilized angle-of-attack conditions. The peak dynamic circumferential distortion values obtained during rapid maneuvers agreed within 0.01 units of distortion over the 10 - 38 degree angle of attack range with the values obtained during steady aerodynamic maneuvers while similar agreement was found for the peak dynamic radial distortion values up to 29 degrees angle-of-attack. Exceedences of the rapid-maneuver peak dynamic circumferential distortion values relative to the peak distortion model values at steady attitudes occurred only at low or negative angles of attack and were inconsequential from an engine-stability assessment point of view. The results of this study validate the current industry practice of testing at steady aerodynamic conditions to characterize inlet recovery and peak dynamic distortion levels.

Steenken, William G.↗

NASA NTRS2011

Validation and Simulation of Ares I Scale Model Acoustic Test - 2 - Simulations at 5 Foot Elevation for Evaluation of Launch Mount Effects

The Ares I Scale Model Acoustics Test (ASMAT) is a series of live-fire tests of scaled rocket motors meant to simulate the conditions of the Ares I launch configuration. These tests have provided a well documented set of high fidelity measurements useful for validation including data taken over a range of test conditions and containing phenomena like Ignition Over-Pressure and water suppression of acoustics. Expanding from initial simulations of the ASMAT setup in a held down configuration, simulations have been performed using the Loci/CHEM computational fluid dynamics software for ASMAT tests of the vehicle at 5 ft. elevation (100 ft. real vehicle elevation) with worst case drift in the direction of the launch tower. These tests have been performed without water suppression and have compared the acoustic emissions for launch structures with and without launch mounts. In addition, simulation results have also been compared to acoustic and imagery data collected from similar live-fire tests to assess the accuracy of the simulations. Simulations have shown a marked change in the pattern of emissions after removal of the launch mount with a reduction in the overall acoustic environment experienced by the vehicle and the formation of highly directed acoustic waves moving across the platform deck. Comparisons of simulation results to live-fire test data showed good amplitude and temporal correlation and imagery comparisons over the visible and infrared wavelengths showed qualitative capture of all plume and pressure wave evolution features.

Strutzenberg, Louise L.↗

NASA NTRS2014

Criticality of Low-Energy Protons in Single-Event Effects Testing of Highly-Scaled Technologies

We report low-energy proton and low-energy alpha particle single-event effects (SEE) data on a 32 nm silicon-on-insulator (SOI) complementary metal oxide semiconductor (CMOS) latches and static random access memory (SRAM) that demonstrates the criticality of using low-energy protons for SEE testing of highly-scaled technologies. Low-energy protons produced a significantly higher fraction of multi-bit upsets relative to single-bit upsets when compared to similar alpha particle data. This difference highlights the importance of performing hardness assurance testing with protons that include energy distribution components below 2 megaelectron-volt. The importance of low-energy protons to system-level single-event performance is based on the technology under investigation as well as the target radiation environment.

random access memory↗

DOE OSTI2023

Quantifying the effect of late bombardment on terrestrial zircons

The first 500 million years of Earth history is thought to be a period of intense planetary bombardment, but the timing and flux of this meteorite bombardment is poorly understood. In particular, on the basis of an inferred lunar impact history, some workers have hypothesized a ~3.9 Ga terminal cataclysm (TC) in which there was marked increase in the impact flux affecting the Moon, the Earth and possibly other terrestrial planets. Minerals that survived this enigmatic period offer a way to test early planetary bombardment models as they may contain telltale micro- to nanoscale shock features. Here, we present results from a numerical modeling calculation that assesses the probability that a zircon residing in the crust would escape shock melting or shock deformation during a TC bombardment event. Even with conservative pressure estimates for zircon shock deformation and intermediate bombardment intensities, we find that only ~6% of ≥4.0 Ga crust would be expected to survive a 3.9 Ga cataclysm without experiencing either complete melting or zircon shock metamorphism. In this study, we couple this modeling with a search for shock effects in the oldest zircons from the Acasta Gneiss Complex, which would have been present in the Earth's crust during a putative 3.9 Ga TC. Spatially correlated electron and NanoSIMS ion microscopy of 4.02 Ga igneous zircons from Acasta reveals no evidence of ancient shock. These data, together with similar results from other Hadean zircon suites, confirm that a post-Hadean TC is unlikely to have occurred. We suggest that the dearth of pre-3.9 Ga terrestrial crust and zircons is instead best explained by endogenic processes related to the mechanisms of early crust formation. Our modeling allows us to evaluate bombardment scenarios from the terrestrial zircon record by applying probabilistic interpretations to zircon shock deformation data. This approach will be valuable for other planetary bodies, allowing broader conclusions to be drawn from geographically limited datasets.

58 GEOSCIENCES↗

DOE OSTI2022

Application of Multi-Criteria Decision Analysis Techniques for Informing Select Agent Designation and Decision Making

The Centers for Disease Control and Prevention (CDC) Select Agent Program establishes a list of biological agents and toxins that potentially threaten public health and safety, the procedures governing the possession, utilization, and transfer of those agents, and training requirements for entities working with them. Every 2 years the Program reviews the select agent list, utilizing subject matter expert (SME) assessments to rank the agents. In this study, we explore the applicability of multi-criteria decision analysis (MCDA) techniques and logic tree analysis to support the CDC Select Agent Program biennial review process, applying the approach broadly to include non-select agents to evaluate its generality. We conducted a literature search for over 70 pathogens against 15 criteria for assessing public health and bioterrorism risk and documented the findings for archiving. The most prominent data gaps were found for aerosol stability and human infectious dose by inhalation and ingestion routes. Technical review of published data and associated scoring recommendations by pathogen-specific SMEs was found to be critical for accuracy, particularly for pathogens with very few known cases, or where proxy data (e.g., from animal models or similar organisms) were used to address data gaps. Analysis of results obtained from a two-dimensional plot of weighted scores for difficulty of attack (i.e., exposure and production criteria) vs. consequences of an attack (i.e., consequence and mitigation criteria) provided greater fidelity for understanding agent placement compared to a 1-to-n ranking and was used to define a region in the upper right-hand quadrant for identifying pathogens for consideration as select agents. A sensitivity analysis varied the numerical weights attributed to various properties of the pathogens to identify potential quantitative (x and y) thresholds for classifying select agents. The results indicate while there is some clustering of agent scores to suggest thresholds, there are still pathogens that score close to any threshold, suggesting that thresholding “by eye” may not be sufficient. The sensitivity analysis indicates quantitative thresholds are plausible, and there is good agreement of the analytical results with select agent designations. A second analytical approach that applied the data using a logic tree format to rule out pathogens for consideration as select agents arrived at similar conclusions.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1992

Multifrequency data analysis software on STARLINK

Although the STARLINK project was set up to provide image processing facilities to UK astronomers, it has grown over the last 12 years to the extent that it now provides most of the data analysis facilities for UK astronomers. One aspect of the growth of the STARLINK network is that it now has to cater for astronomers working in a diverse range of wavelengths. Since a given individual may be working with data obtained in a variety of wavelengths, it is most convenient if the data can be stored in a common format and the programs that analyze the data have a similar 'look and feel'. What is known as 'STARLINK software' is obtained from many sources: STARLINK funded programmers; astronomers; foreign projects such as AIPS; generally available shareware; and commercial sources when this proves cost effective. This means that the ideal situation of a completely integrated system cannot be realized in practice. Nevertheless, many of the major packages written by STARLINK application programmers and by astronomers do use a common data format, based on the Hierarchical Data System, so that interchange of data between packages designed separately from each other is simply a matter of using the same file names. For example, as astronomer might use KAPPA to read some optical spectra off a FITS tape, then use CCDPACK to debias and flat field the data (it is easy to set up an overnight batch job to do this if there is a lot of data), then use KAPPA to have a quick look at the data and then use Figaro to reduce the spectra. It is useful to divide data analysis packages into wavelength specific packages, or even instrument specific packages, and general purpose ones. Once the instrumental signature has been removed from some data, any appropriate general purpose package can be used to analyze te data. For example, the ASTERIX package deals with x-ray data reduction, but after dealing with all of the x-ray specific processing, an astronomer may well want to find the brightness of objects in a given frame. Since ASTERIX uses the standard STARLINK data format, the astronomer can use PHOTOM or DAOPHOT 2 to measure the brightness of the objects. Although DAOPHOT was written with optical astronomy in mind, it is useful for analyzing data from several wavelengths. The ability of DAOPHOT 2 to handle non-standard point spread functions can be especially useful in many areas of astronomy.

Allan, P. M.↗

DOE OSTI2021

Comparing Satellite- and Ground-Based Observations of Cloud Occurrence Over High Southern Latitudes

The 2B-CLDCLASS-LIDAR R05 (2BCL5) and the raDAR/liDAR (DARDAR) satellite retrievals of cloud occurrence are compared as a function of altitude and latitude. The largest disparities are observed at low altitudes over high southern latitudes. These data sets are cross referenced to ground-based measurements from the Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment (AWARE) campaign at McMurdo Station, Antarctica. Compared with AWARE observations, both 2BCL5 and DARDAR underestimate cloud occurrence below 1.5 km, with 2BCL5 and DARDAR distinguishing roughly one third of cloud occurrences observed by AWARE at 0.5 km. While DARDAR identifies greater cloud occurrences than 2BCL5 below 1.5 km, cloud occurrence values for the two data sets have similar differences relative to ground-based measurements. Therefore, the DARDAR retrievals of greater cloud occurrence at low altitudes are likely due to a larger quantity of false positives associated with radar ground clutter or attenuated lidar retrievals. DARDAR cloud occurrences match better with AWARE than 2BCL5 above 5 km. However, the likely underestimation of ground-based measurements at higher altitudes suggests DARDAR may underestimate high level cloud occurrence. Finally, both data sets indicate the presence of liquid containing clouds at temperatures within the homogeneous freezing regime, despite the fact that the ECMWF-AUX data set implemented in their processing clearly indicates temperatures below -38°C. Finally, using AWARE radiosonde (ECMWF-AUX) temperature data, we find that 2BCL5 detects 13.3% (13.8%) of mixed phase clouds below -38°C, while DARDAR detects 5.7% (6.6%) of mixed phase and 1.1% (1.3%) of liquid phase clouds below -38°C.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

A deep learning-enhanced framework for multiphysics joint inversion

Joint inversion has drawn considerable attention due to the availability of multiple geophysical data sets, ever-increasing computational resources, the development of advanced algorithms, and its ability to reduce inversion uncertainty. A key issue of joint inversion is to develop effective strategies to link different geophysical data in a unified mathematical framework, in which the information obtained from different models can complement each other. We have developed a deep learning-enhanced joint inversion framework to simultaneously reconstruct different physical models by fusing different types of geophysical data. Traditionally, structure similarity constraints are pursued by joint inversion algorithms using manually crafted formulations (e.g., cross gradient). The constraint is constructed by a deep neural network (DNN) during the learning process. The framework is designed to combine the DNN and a traditional independent inversion workflow and improve the joint inversion result iteratively. The network can be easily extended to incorporate multiphysics without structural changes. Numerical experiments on the joint inversion of 2D DC resistivity data and seismic traveltime are used to validate our method. In addition, this learning-based framework demonstrates excellent generalization abilities when tested on data sets using different geologic structures. It also can handle different sensing configurations and nonconforming discretization.

Geochemistry & Geophysics↗

DOE OSTI2020

Conditional Generative Adversarial Networks for Solving Heat Transfer Problems

Generative Adversarial Networks (GANs) have been used as a deep learning approach to solving physics and engineering problems. Using deep learning for these problems is attractive in that reasonably accurate models can be inferred from only raw data, eliminating the need to define the exact physical equations governing a problem. We expand on previous work using GANs to generate steady-state solutions to the two-dimensional heat equation. Using a basic conditional GAN (cGAN), we generate accurate solutions for rectangular domains conditioned on four edge boundary conditions (MAE < 0.5%). For finding steady-state solutions over arbitrary two-dimensional domains (not constrained to rectangles), we use a cGAN designed for image-to-image translation. We train this GAN on various types of geometric domains (circles, squares, triangles, shapes with one circular or rectangular hole), achieving accurate results on test data made up of geometries similar to those in training (MAE < 1%). For both of these GANs, we experiment with different loss function terms, showing that a term using the gradients of solution images significantly improves the basic cGAN but not the image-to-image GAN. Lastly, we show that the image-to-image GAN performs poorly when applied to two-dimensional geometries that vary in structure from training data (MAE < 8% for shapes with multiple holes or different shaped holes). This demonstrates the cGAN's lack of generalizability. While the cGAN is an accurate and computationally efficient method when trained and tested on similarly structured data, it is a much less reliable method when applied to data that is slightly different in structure from the training data.

97 MATHEMATICS AND COMPUTING↗