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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 127 records · Page 7

Predicting Lightning Initiation using Deep Learning

Lightning occurrence presents safety challenges to people and property. The main challenge with lightning safety is that the majority of guidance is reactive. In other words, lightning has to have already occurred nearby before a person will respond and take shelter. Further, most injuries or fatalities occur as the storm approaches, or as it's moving away, when rainfall may not be present at the time of the flash. Thus, this project develops a physically-based deep learning model to produce lightning probabilities out to 15 minutes. The deep learning model combines a Convolutional Neural Network (CNN) with a Long Short-Term Memory (LSTM) network to capture both the spatial and temporal evolution of storms to predict the probability that lightning initiation will occur in the next 15 minutes. The model combines radar reflectivity, correlation coefficient and differential reflectivity to inferred storm hydrometer type and precipitation phase, which aids in the identification of electrification processes. The model is trained with data from the Geostationary Lightning Mapper (GLM), which is a near infrared sensor onboard the GOES-R series of satellites that measures optical brightness from lightning. This presentation will provide an overview of the project.

Andrew T White↗

A Machine Learning-Based Approach to Time-Series Wave Identification in the Solar Wind

The Wind spacecraft has yielded several decades of high-resolution magnetic field data, a large fraction of which displays small-scale structures. In particular, the solar wind is full of wavelike fluctuations that appear in both the field magnitude and its components. The nature of these fluctuations can be tied to the properties of other structures in the solar wind, such as shocks, that have implications for the time evolution of the solar wind. As such, having a large collection of wave events would facilitate further study of the effects that these fluctuations have on solar wind evolution. Given the large volume of magnetic field data available, machine learning is the most practical approach to classifying the myriad small-scale structures observed. To this end, a subset of Wind data is labeled and used as a training set for a multi-branch 1D convolutional neural network aimed at classifying circularly polarized wave modes. Using this algorithm, a preliminary statistical study of one year of data is performed, yielding about 300,000 wave intervals out of about 5,000,000 solar wind intervals. The wave intervals come about more often in the fast solar wind and at higher temperatures, and the number of waves per day is highly periodic. This machine learning-based approach to wave detection has the potential to be a powerful, inexpensive way to catalog waves throughout decades of spacecraft data.

Samuel Fordin↗

Statistical Classification of Biosignature Information using Multiple Instrument Observations

The accurate identification of biosignatures (indications of life) from data taken from remote or in situ planetary exploration is one of the most important challenges in astrobiology, the interdisciplinary field examining habitability and the potential for extraterrestrial life. This study employs machine learning algorithms to optimize the identification of biosignatures, with an emphasis on those which are agnostic to a specific biochemical basis. We exploit the wealth of terrestrial data available from biogenic and abiogenic systems to enhance efficient feature prioritization. Our dataset, pulled from public databases and laboratory recorded measurements, includes elemental abundance, isotopic fractionation, and VNIR/Raman spectra The data curation process included standardization for detection limits and ranges. Subsequent feature extraction yielded detailed inputs for machine learning, including combinations of elemental content, isotopic ratios, and parameters of spectral peaks and troughs. Feature significance was evaluated across diverse machine learning methodologies, such as k-nearest neighbors, logistic regression, Random Forest, support vector machines, and Gaussian Naïve Bayes, along with a combined voting classifier. We utilized Receiver Operating Characteristic Area Under the Curve (ROC AUC) across 2,000 50% test-train splits as a robust metric of model performance. Results revealed a promising ROC AUC of 0.853 for the combined voting classifier. Removing elemental abundance data notably reduced model accuracy (13% decrease in AUC), highlighting its critical role in biosignature detection. Several other individual data features exhibited significance within their respective data types, offering additional granularity. This research fortifies the relevance of machine learning to astrobiology, potentially enhancing life detection missions by allowing algorithmic prioritization of high-interest samples for further investigation. Future work will refine data standardization, expand the dataset to include more terrestrial systems, and incorporate convolutional neural networks for spectral feature extraction. The potential for public data sharing is also under exploration, reinforcing our commitment to collective scientific advancement.

Statistical↗

Using Machine Learning to Infer Material Properties of Debris Fragments from X-ray Images in the DebriSat Project

The DebriSat project is a collaboration effort with the NASA Orbital Debris Program Office, the U.S. Space Force Space Systems Command Center, The Aerospace Corporation, and the University of Florida. To date, over 200,000 fragments from this ground-based, hypervelocity impact experiment have been collected, and processing is underway to determine their physical characteristics, such as material, shape, color, characteristic length, and average cross-sectional area. The x-ray process is primarily used to identify the location of the fragments and estimated size for extraction, so that these physical characteristics can be assessed. This paper proposes a machine learning-based approach to characterize materials from x-ray images of debris fragments embedded in soft-catch foam used in the DebriSat project. The novel methodology discussed in this paper will highlight the use of x-ray imagery data to characterize these fragments without extraction or a human-in-the-loop. Both supervised and unsupervised machine learning techniques are utilized with this approach to infer the physical parameters of the fragments embedded in the soft-catch foam panels used in the impact experiment based on x-ray images of the foam panels. Additionally, 3D reconstructions of the extracted fragments are created with images taken from two different angles using the structure from motion (SfM) method. The characteristic lengths and shape from the 3D reconstruction, alongside the physical characteristics of the debris, are used in the inference of the material type. To develop and test the approach, a dataset of x-ray images of debris fragments of varying sizes and materials is collected. Supervised learning methods such as convolutional neural networks (CNNs), support vector machines (SVM), decision trees, and random forest classifiers are used due to the high-dimensional feature spaces of the debris and nonlinear decision boundaries for material categorization. Given the limited pre-labeled data of embedded debris materials smaller than 10 mm, unsupervised machine learning techniques such as clustering algorithms and autoencoders are used, in addition to supervised learning methods. The clustering algorithms group similar fragments together based on their physical properties, and autoencoders reduce the dimensionality of the x ray images and extract relevant features. The performance of the proposed approach's is analyzed using a range of statistical methods, including confusion matrices, receiver operating characteristic curves, and precision-recall curves. The results are compared with those obtained using a baseline approach that relies on manual identification and classification of debris fragments. To evaluate the effectiveness of different machine learning methods, statistical tests such as t-tests, ANOVA, and cross-validation are performed, comparing the performance of CNNs, SVMs, clustering algorithms, and autoencoders. Additional analysis needs to be conducted to identify any sources of bias or variability that may affect the results, such as variations in imaging conditions or fragmentation patterns. Other topics explored are limitations, refinements, and the potential use of semi-supervised learning techniques, such as self-training to label unlabeled datasets and co-training using x-ray images taken from two different angles as two different models.

Saik Anam Siam↗

Predicting Patterns of Solar Energy Buildout to Identify Opportunities for Biodiversity Conservation

The construction of solar energy facilities can have positive or negative impacts on biodiversity depending on siting and associated land use transitions. We identified drivers of solar siting and quantified patterns of buildout in states surrounding the Chesapeake Bay watershed – a biodiversity hotspot with numerous ecosystem services. Using a convolutional neural network, we mapped the footprints of ground-mounted solar arrays present in satellite imagery annually from 2017 to 2021 in Delaware, Maryland, Pennsylvania, New York, Virginia, and West Virginia. As of 2021, we identified 958 solar arrays covering 52.3 km2 built primarily on previously cultivated land, while avoiding natural landcover. We fit a binomial-Weibull model to these solar timeseries data in a hierarchical, Bayesian framework to quantify the relationship between geospatial covariates and rate of solar development. Solar array construction rate increased in cultivated areas, areas of lower agricultural suitability, lower slope, lower forest cover, lower biodiversity protection, and greater distances from roads. We also estimated changes in the rate of solar construction over time and found differences among states: acceleration in Virginia and deceleration in New York. We used parameter estimates to map the relative likelihood of future solar development across the study area. This methodology can be used to anticipate where solar is likely to be built in different landscapes and how these patterns align with conservation goals. Around the Chesapeake Bay watershed, the selection of lower quality agricultural areas for solar energy minimizes removal of important habitat and provides opportunities for native plant and pollinator restoration.

Artificial Intelligence↗

Anomaly Detection for the Roman Space Telescope Wide Field Instrument’s Science Data Processing Pipeline

The Roman Space Telescope (RST) Wide Field Instrument (WFI) will be utilizing a preliminary Science Data Processing (SDP) pipeline during its Integration and Test, and to some extent during Operations, to track basic statistics and identify known features such as cosmic rays, snowballs as well as possible anomalies in raw detector data. In our detectors, these anomalies appear as jumps in the ramp of a readout and are classified as cosmic rays if they appear as a streak or snowballs if they’re more circular. The WFI employs an array of 18 H4RG-10 detectors that collect image samples. Each set of raw frames within a non-destructive exposure is packaged by the SDP pipeline into image cubes for each detector. Each cube is a time series of 4096 × 4096 accumulating pixel frames. The preliminary analysis pipeline is used to locate anomalies in these time-series accumulation frames and identify the type of anomaly, either natural phenomena or detector characteristic. To compare different methods, we’ve implemented both heuristic-based and data-driven methods to identify anomalies. For the heuristic-based approach, we identify snowballs and cosmic rays by the size and shape of outlier pixel clusters between consecutive frames. For data driven methods, we evaluated a Convolutional Neural Network (CNN) model, and more traditional methods like Principal Component Analysis (PCA). CNN is a supervised learning/classification method. Thus, we used a labeled dataset of anomalies to perform segmentation of the image and identify anomalies. We used previously identified cosmic rays and snowballs to measure the accuracy and efficiency of the mentioned approaches. In evaluating these methods, we aim to pick the best fit for the SDP pipeline’s anomaly detection in terms of both performance and runtime.

Paul Horton↗

Damage Detection of a Pressure Vessel with Smart Sensing and Deep Learning

Structural Health Monitoring plays a crucial role in ensuring the safety and reliability of critical infrastructure, including pressure vessels involved in various applications. This research reports the damage detection of a pressure box employed in space habitat that operates in harsh environment where both structural failure and bolt joint loosening may occur. These failure modes are extremely hard to model based on first principles. We explore proper sensing mechanism and the associated inverse analysis algorithm that can elucidate the health condition of the pressure box. It is identified that piezoelectric impedance based active interrogation can provide necessary information for damage detection in such a system. Concurrently, deep learning technique leveraging spatial convolutional neural network is synthesized to analyze the raw data acquired and identify different types of damage. By training the deep learning model on a dataset of healthy and various damage scenarios, we can achieve high accuracy in identifying the presence of damage and its type. This research provides a data-driven methodology for structural damage detection using deep learning and has the potential to be extended to various systems with different failure modes.

Yang Zhang↗

Soil Salinity Level Assessment and Prediction Integrating UAV-borne Hyperspectral Imaging and Machine Learning Algorithms to Combat Desertification

In response to the ongoing global food crisis, the United Nations has identified “Zero Hunger” as one of its Sustainable Development Goals. A central contributor to the crisis is the process in which agricultural lands go through desertification. Research has shown a direct correlation between soil salinity and desertification - increased salinity levels indicate a higher risk for desertification. Furthermore, researchers have explored various techniques to map soil salinity, but these methods are oftentimes inefficient and don’t address future salinity predictions. To improve desertification monitoring, soil salinity can be observed via hyperspectral imaging on unmanned aerial vehicles (UAVs) to predict the risk of agricultural desertification using artificial intelligence (AI) and machine learning (ML) techniques. A significant gap exists in past research that applies ML and imaging techniques to soil salinity: convolutional neural networks (CNNs) and regression models are rarely leveraged together, despite the efficiency and accuracy of these models. To compensate for this gap, the proposed system leverages the use of these AI and ML models to improve soil assessment and prediction techniques. This approach involves three steps - data collection, image analysis, and future prediction. Using hyperspectral cameras on UAVs to collect the data from the region, a trained CNN model will output estimated soil salinity levels at a specific time. The estimations will then be analyzed by a regression model to assess the accuracy of future soil salinity predictions. The proposed system will identify regions at risk of desertification to help farmers mitigate agricultural loss, in turn helping alleviate the food crisis.

UAV systems↗

Evaluation of Machine Learning and Deep Learning Algorithms for Fire Prediction in Southeast Asia

Vegetation fires are prevalent in South/Southeast Asian countries, making fire prediction crucial due to their potential environmental, economic, and social impacts. Accurate predictions of fires facilitate timely interventions, helping to mitigate uncontrolled fires that can lead to biodiversity loss and air quality issues. In this study, we utilize VIIRS satellite-derived fire data alongside six machine learning and deep learning models—Simple Persistence, Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), CNN-LSTM, and ConvLSTM—to determine the most effective fire prediction model, using Root Mean Square Error (RMSE) as the metric. Our results indicate that the CNN model is the most reliable in regions with spatial dependencies, such as Brunei, Indonesia, Malaysia, the Philippines, Timor-Leste, and Thailand. Conversely, the ConvLSTM model excels in countries with complex spatiotemporal dynamics like Laos, Myanmar, and Vietnam. The CNN-LSTM hybrid model also performed well in Cambodia, suggesting a need for a balanced approach in areas requiring both spatial and temporal feature extraction. Furthermore, simpler models like Persistence and MLP showed limitations in capturing dynamic patterns and temporal dependencies. Our findings highlight the importance of evaluating models before implementing any decision support systems (DSS) in fire management. By tailoring models to specific regional fire data, we can enhance prediction accuracy and responsiveness, ultimately improving fire risk management in Southeast Asia and beyond.

Deep learning↗

Towards Surrogate Modeling of Subgrid Turbulent Transport for 3D Radiative Hydrodynamic Simulations of the Quiet Sun

In this work, we investigate the use of deep learn-ing techniques as surrogate models, to enhance the estimationof effects of subgrid turbulent transport for 3D radiatuve hy-drodynamic simulations of the quiet Sun. We develop two dis-tinct 3D Convolutional Neural Networks (3DCNNs) to capturespatio-temporal dependencies in 3D velocity fields, leveragingdifferent activation functions and architectural designs. Thesemodels integrate both averaged velocity vector components andscalar features such as plasma density to enhance predictionaccuracy. Additionally, a Multilayer Perceptron (MLP) modelis employed to approximate complex nonlinear relationships,offering a comparison in performance between convolutionaland fully connected architectures. Logarithmic transformationis applied to the targets to handle heavily skewed data, im-proving model performance. All models are compared againsta physics-based Gradient Model. Results show that the 3DCNNmodels excel at approximating Reynolds stress tensors, makingthem a candidate for assisting in producing reduced resolutionsimulations, and thereby reducing computational overheadwhile maintaining higher accuracy than the baseline. Thesefindings demonstrate the potential of deep learning, particu-larly CNNs, to advance scalable and accurate simulations ofsolar dynamics, offering a promising alternative to traditionalturbulence models.

Heliophysics↗

Proactive Wildfire Management: A Remote Sensing and Multimodal CNN-MLP Architecture for Ignition Risk Forecasting

As the frequency and intensity of wildfires increase, with fire seasons now starting earlier and ending later than they have over the past decades, current monitoring systems, such as lookout towers and satellites, are hindered by cloud cover, low-resolution imagery, and static data gaps that fail to track vegetation moisture levels fast enough to catch rapid pre-ignition changes. This report proposes a Machine Learning-enabled Wildfire Ignition Prediction framework that combines satellite monitoring with dynamic and high-resolution remote sensing from Unmanned Aerial Vehicle (UAV) swarms. The method would use multispectral and thermal data from the Landsat program to create a baseline for vegetation health, calculating a two-band Enhanced Vegetation Index (EVI2) and the moisture content of the vegetation. These inputs will later be fused with microscale UAV weather data, including thermal hotspots found through thick canopies, hyperspectral chemical signatures of pre-visual combustion, and local weather streams. The multispectral satellite, multispectral Light Detection and Ranging (LiDAR), and thermal data would then be processed through a Convolutional Neural Network (CNN), alongside a Multilayer Perceptron (MLP) for the micro-weather telemetry. The outputs of these networks would be fused into a single feature representation and passed through a final prediction network to generate real-time ignition risk scores and hotspot alerts. Model performance would be assessed using standard classification metrics, including a Receiver Operating Characteristic - Area Under the Curve (ROC AUC) and F1 score. This system would allow first responders to identify high-risk zones and intervene before ignition occurs, improving emergency response time compared to current approaches.

machine learning↗

Revisiting the Ground Magnetic Field Perturbations Challenge: A Machine Learning Perspective

Forecasting ground magnetic field perturbations has been a long-standing goal of the space weather community. The availability of ground magnetic field data and its potential to be used in geomagnetically induced current studies, such as risk assessment, have resulted in several forecasting efforts over the past few decades. One particular community effort was the Geospace Environment Modeling (GEM) challenge of ground magnetic field perturbations that evaluated the predictive capacity of several empirical and first principles models at both mid- and high-latitudes in order to choose an operative model. In this work, we use three different deep learning models-a feed-forward neural network, a long short-term memory recurrent network and a convolutional neural network-to forecast the horizontal component of the ground magnetic field rate of change (dB H /dt) over 6 different ground magnetometer stations and to compare as directly as possible with the original GEM challenge. We find that, in general, the models are able to perform at similar levels to those obtained in the original challenge, although the performance depends heavily on the particular storm being evaluated. We then discuss the limitations of such a comparison on the basis that the original challenge was not designed with machine learning algorithms in mind.

Victor A. Pinto↗

Machine Learning Explainability and Transferability for Path Navigation

Deep neural networks are powerful tools for machine perception. Unfortunately their decisions are difficult to explain due to the complexity and size of the networks. Previously we have alleviated this issue by using the representational portion of a deep neural network and combining it with a k-nearest neighbor (KNN) classifier. Through inspection of the decisions made by the KNN, we can directly see the training data responsible for the decisions, allowing us to determine the quality of the overall decision and the quality of the representational layer of the deep NN. While the technique worked well, it requires tens of thousands of latent vectors to be stored for classification. In addition, it lacks the ability to show how parts of an image influence the classification decision. Here we address these issues by 1) Using a radial basis function network (RBFN) in place of the KNN allowing far fewer images to be used in deployment and 2) Using an auto encoder network for explainability. In addition to these techniques, we examine the effects of transfer learning to determine that results are robust. All results are tested on a domain where an unmanned aerial vehicle (UAV) navigates a forest trail through a single camera.

explainable machine learning↗

Presound: UAV Diagnostic System Enabled by Vibration-Based Machine Learning

A low-weight, inexpensive small unmanned aerial system (sUAS) that takes off, performs a mission, lands, and safely stows and recharges itself has myriad future applications ranging from agricultural imaging to last-mile package delivery. Likewise, Urban Air Mobility (UAM) systems will enable people to take air taxis from point to point in cities, rapidly moving commuters long distances without concern for road traffic and congestion. Fully electric aviation systems will be cleaner and quieter than ground transport. Cities could eliminate cars and buses, and convert roads to higher capacity bike and pedestrian throughways. Yet, for sUAS as well as UAM, system reliability and assurance is a limiting factor to deploying affordable autonomous flight systems. For this bright future of aviation to be realized, aircraft must be able to autonomously and accurately self-diagnose health issues both before takeoff and during flight. The GreenSight PreSound system is designed to identify defects on aircraft through intelligent analysis of vibration. It accomplishes this by measuring structural vibrations induced by the vehicle’s own propellers, and analyzing that data using a machine learning model that determines whether a defect is present. The PreSound system is designed to require no human oversight, and to operate across a wide array of vehicles through re-training of the model for each target aircraft. PreSound has been developed and seen limited early success using data collected from the GreenSight Dreamer sUAS, a 5lb quadrotor vehicle designed for aerial imaging applications. The final detection model, trained on data with props spinning at 50% throttle, achieves excellent performance with over 99% average accuracy in detecting blade damage using a single FFT vector input. It demonstrates the ability to generalize to new types of blade damage, correctly classifying a different type of blade damage with 98% accuracy. Full test pulses were classified with 100% accuracy, and in live testing, all sets of data during blade movement were classified accurately with over 95% confidence. When trained on in-flight data, the same model achieves an average accuracy of 85% in distinguishing between undamaged and blade-damaged states in flight. The authors believe that these accuracies show significant potential of this approach to expand unmanned flight safety, with significant potential benefits in accelerating Advanced Aerial Mobility (AAM) and UAM aviation applications.

UAS↗

Predicting Two-Dimensional Airfoil Performance Using Graph Neural Networks

Computer simulations require the use of meshes to simulate geometries. These meshes capture important geometric features of the design and can be used in machine learning modeling. This report explores the use of graph neural networks (GNNs) to learn features from two-dimensional (2D) airfoil designs represented as a set of nodes connected using edges. This type of network is common in aerospace applications: most geometries are represented as a mesh in order to perform analysis. The objective of this work is to use GNNs to predict the performance of 2D airfoils generated using the program XFOIL. The predicted performance parameters include bulk quantities such as coefficients of lift (C L ), drag (C d , C dp ), moment (C m ), and node-specific quantities such as coefficient of pressure (C p ). In this report, a spline convolutional graph-based neural network is compared with deep learning neural networks to predict both bulk and node-specific quantities. The findings indicate the GNNs are able to predict bulk quantities quite well; however, when the number of outputs is increased, the deep neural network (DNN) proves to be better in its prediction capability. Two different normalization strategies were compared in the training of both GNNs and DNNs: minmax and standard deviation. In both types of networks, standard deviation scaling proved to be the best.

machine learning↗

Flight Trajectory Prediction Based on Hybrid-Recurrent Networks

The development of future technologies for the National Airspace System (NAS) will be reliant on a new communications infrastructure capable of managing the limited available spectrum for communications among aircraft and ground systems. Emerging approaches to autonomous allocation of aviation spectrum mostlyrely on machine learning techniques, where 4D (longitude, latitude, altitude, time) trajectory prediction is an important data input to enable real-time resource allocation. This study explores and evaluates effective data sources and deep recurrent neural network techniques when determining flight trajectories. Specifically, data are collected and evaluated in a 100-day and 14-day period. Sources of data include NASA Sherlock Data Warehouse, MIT Lincoln Labs Corridor Integrated Weather Service (CIWS), and assorted NOAA weather datasets. Deep learning models for 4D predictions all utilize a hybrid-recurrent technique. A baseline model is considered via the convolutional-LSTM design from the existing literature. The modified design considers Gated Recurrent Units (GRU), Independently Recurrent Neural Networks (IndRNN), and stand-alone self-attention layers. Results indicatethe effectiveness of LSTM and GRUcells for state-of-the-art data processing (interpolation). Additionally, GRUs may be quickly trained with limited data, allowing for exacting improvements with optimizer selection. Attention mechanisms provide notable performance improvements to convolutional layers and may extend dimensional capabilities of a learning model. Finally, NOAA measurements provide only a supplemental value, requiring support from tailored measurements for Air Traffic Management.

Nathan Schimpf↗

Data fusion with artificial neural networks (ANN) for classification of earth surface from microwave satellite measurements

A data fusion system with artificial neural networks (ANN) is used for fast and accurate classification of five earth surface conditions and surface changes, based on seven SSMI multichannel microwave satellite measurements. The measurements include brightness temperatures at 19, 22, 37, and 85 GHz at both H and V polarizations (only V at 22 GHz). The seven channel measurements are processed through a convolution computation such that all measurements are located at same grid. Five surface classes including non-scattering surface, precipitation over land, over ocean, snow, and desert are identified from ground-truth observations. The system processes sensory data in three consecutive phases: (1) pre-processing to extract feature vectors and enhance separability among detected classes; (2) preliminary classification of Earth surface patterns using two separate and parallely acting classifiers: back-propagation neural network and binary decision tree classifiers; and (3) data fusion of results from preliminary classifiers to obtain the optimal performance in overall classification. Both the binary decision tree classifier and the fusion processing centers are implemented by neural network architectures. The fusion system configuration is a hierarchical neural network architecture, in which each functional neural net will handle different processing phases in a pipelined fashion. There is a total of around 13,500 samples for this analysis, of which 4 percent are used as the training set and 96 percent as the testing set. After training, this classification system is able to bring up the detection accuracy to 94 percent compared with 88 percent for back-propagation artificial neural networks and 80 percent for binary decision tree classifiers. The neural network data fusion classification is currently under progress to be integrated in an image processing system at NOAA and to be implemented in a prototype of a massively parallel and dynamically reconfigurable Modular Neural Ring (MNR).

Lure, Y. M. Fleming↗

Recent advances in coding theory for near error-free communications

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression.

Cheung, K.-M.↗