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Developing a Framework for Effective Network Capacity Planning

As Internet traffic continues to grow exponentially, developing a clearer understanding of, and appropriately measuring, network's performance is becoming ever more critical. An important challenge faced by the Information Resources Directorate (IRD) at the Johnson Space Center in this context remains not only monitoring and maintaining a secure network, but also better understanding the capacity and future growth potential boundaries of its network. This requires capacity planning which involves modeling and simulating different network alternatives, and incorporating changes in design as technologies, components, configurations, and applications change, to determine optimal solutions in light of IRD's goals, objectives and strategies. My primary task this summer was to address this need. I evaluated network-modeling tools from OPNET Technologies Inc. and Compuware Corporation. I generated a baseline model for Building 45 using both tools by importing "real" topology/traffic information using IRD's various network management tools. I compared each tool against the other in terms of the advantages and disadvantages of both tools to accomplish IRD's goals. I also prepared step-by-step "how to design a baseline model" tutorial for both OPNET and Compuware products.

Yaprak, Ece

HURON (HUman and Robotic Optimization Network) Multi-Agent Temporal Activity Planner/Scheduler

HURON solves the problem of how to optimize a plan and schedule for assigning multiple agents to a temporal sequence of actions (e.g., science tasks). Developed as a generic planning and scheduling tool, HURON has been used to optimize space mission surface operations. The tool has also been used to analyze lunar architectures for a variety of surface operational scenarios in order to maximize return on investment and productivity. These scenarios include numerous science activities performed by a diverse set of agents: humans, teleoperated rovers, and autonomous rovers. Once given a set of agents, activities, resources, resource constraints, temporal constraints, and de pendencies, HURON computes an optimal schedule that meets a specified goal (e.g., maximum productivity or minimum time), subject to the constraints. HURON performs planning and scheduling optimization as a graph search in state-space with forward progression. Each node in the graph contains a state instance. Starting with the initial node, a graph is automatically constructed with new successive nodes of each new state to explore. The optimization uses a set of pre-conditions and post-conditions to create the children states. The Python language was adopted to not only enable more agile development, but to also allow the domain experts to easily define their optimization models. A graphical user interface was also developed to facilitate real-time search information feedback and interaction by the operator in the search optimization process. The HURON package has many potential uses in the fields of Operations Research and Management Science where this technology applies to many commercial domains requiring optimization to reduce costs. For example, optimizing a fleet of transportation truck routes, aircraft flight scheduling, and other route-planning scenarios involving multiple agent task optimization would all benefit by using HURON.

Hua, Hook

Artificial Neural Networks Applications: from Aircraft Design Optimization to Orbiting Spacecraft On-board Environment Monitoring

This paper reviews some of the recent applications of artificial neural networks taken from various works performed by the authors over the last four years at the NASA Glenn Research Center. This paper focuses mainly on two areas. First, artificial neural networks application in design and optimization of aircraft/engine propulsion systems to shorten the overall design cycle. Out of that specific application, a generic design tool was developed, which can be used for most design optimization process. Second, artificial neural networks application in monitoring the microgravity quality onboard the International Space Station, using on-board accelerometers for data acquisition. These two different applications are reviewed in this paper to show the broad applicability of artificial intelligence in various disciplines. The intent of this paper is not to give in-depth details of these two applications, but to show the need to combine different artificial intelligence techniques or algorithms in order to design an optimized or versatile system.

Jules, Kenol

The NASA Science Internet: An integrated approach to networking

An integrated approach to building a networking infrastructure is an absolute necessity for meeting the multidisciplinary science networking requirements of the Office of Space Science and Applications (OSSA) science community. These networking requirements include communication connectivity between computational resources, databases, and library systems, as well as to other scientists and researchers around the world. A consolidated networking approach allows strategic use of the existing science networking within the Federal government, and it provides networking capability that takes into consideration national and international trends towards multivendor and multiprotocol service. It also offers a practical vehicle for optimizing costs and maximizing performance. Finally, and perhaps most important to the development of high speed computing is that an integrated network constitutes a focus for phasing to the National Research and Education Network (NREN). The NASA Science Internet (NSI) program, established in mid 1988, is structured to provide just such an integrated network. A description of the NSI is presented.

Rounds, Fred

Generative AI for design of nanoporous materials: review and future prospects

Generative artificial intelligence (AI) is emerging as a powerful tool for advancing the design of nanoporous materials such as metal–organic frameworks, covalent–organic frameworks, and zeolites. These materials have potential application in important areas such as carbon capture, catalysis, gas storage, chemical separation, and drug delivery due to their modular, tunable structures, and their performance in these areas depends on precise control over their structure, chemical functionalities, and properties. Herein, we provide a review of generative AI algorithms that are emerging as powerful tools for the design of nanoporous materials, namely generative adversarial networks, variational autoencoders, diffusion models, genetic algorithms, reinforcement learning, and large language models. Some models are particularly good at generating diverse and high-quality designs, while others excel at exploring large design spaces or optimizing materials with desired properties. Certain algorithms also allow for efficient transitions between different designs, and some offer versatility in generating materials based on textual input. We discuss the advantages, limitations, and applications of these algorithms in porous material design and emphasize the future potential of integrating AI with experimental workflows to accelerate the development and validation of AI-generated materials.

36 MATERIALS SCIENCE

Electra: A Modular-Based Expansion of NASA's Supercomputing Capability

NASA has increasingly relied on high-performance computing (HPC) re- sources for computational modeling, simulation, and data analysis to meet the science and engineering goals of its missions in space exploration, aeronautics, and Earth and space science. The NASA Advanced Supercomputing (NAS) Division at Ames Research Center in Silicon Valley, Calif., hosts NASA’s premier supercomputing resources, integral to achieving and enhancing the success of the agency’s missions. NAS provides a balanced environment, funded under the High-End Computing Capability (HECC) project, comprised of world-class supercomputers, including its flagship distributed-memory cluster, Pleiades; high-speed networking; and massive data storage facilities, along with multi-disciplinary support teams for user support, code porting and optimization, and large-scale data analysis and scientific visualization. However, as scientists have increased the fidelity of their simulations and engineers are conducting larger parameter-space studies, the requirements for supercomputing resources have been growing by leaps and bounds. With the facility housing the HECC systems reaching its power and cooling capacity, NAS undertook a prototype project to investigate an alternative approach for housing supercomputers. Modular supercomputing, or container-based computing, is an innovative concept for expanding NASA’s HPC capabilities. With modular supercomputing, additional containers—similar to portable storage pods—can be connected together as needed to accommodate the agency’s ever-increasing demand for computing resources. In addition, taking advantage of the local weather permits the use of cooling technologies that would additionally save energy and reduce annual water usage. The first stage of NASA’s Modular Supercomputing Facility (MSF) prototype, which resulted in a 1,000 square-foot module on a concrete pad with room for 16 compute racks, was completed in Fall 2016 and an SGI (now HPE) computer system, named Electra, was deployed there in early 2017. Cooling is performed via an evaporative system built into the module, and preliminary experience shows a Power Usage Effectiveness (PUE) measurement of 1.03. Electra achieved over a petaflop on the LINPACK benchmark, sufficient to rank number 96 on the November 2016 TOP500 list [14]. The system consists of 1,152 InfiniBand-connected Intel Xeon Broadwell-based nodes. Its users access their files on a facility-wide file system shared by all HECC compute assets via Mellanox MetroX InfiniBand extenders, which connect the Electra fabric to Lustre routers in the primary facility over fiber-optic links about 900 feet long. The MSF prototype has exceeded expectations and is serving as a blueprint for future expansions. In the remainder of this chapter, we detail how modular data center technology can be used to expand an existing compute resource. We begin by describing NASA’s requirements for supercomputing and how resources were provided prior to the integration of the Electra module-based system.

Biswas, Rupak

A method for interference mitigation in space communications scheduling

Increases in the number of user spacecraft and data rates supported by NASA's Tracking and Data Relay Satellite System (TDRSS) in the S and Ku bands could result in communications conflicts due to mutual interference. A method to mitigate interference while minimizing unnecessary scheduling restrictions on both TDRSS network and user resources, based on consideration of all relevant communications parameters, was developed. The steps of this method calculate required separation angles at TDRS and produce interference intervals, which can be used in the production of schedules free of unacceptable interference. The method can also be used as a basis for analysis, evaluation, and optimization of user schedules with respect to communications performance. Described here are the proposed method and its potential application to scheduling in space communications. Test cases relative to planned missions, including the Earth Observing System, the Space Station Manned Base, and the Space Shuttle are discussed.

Wong, Yen F.

A method for interference mitigation in space communications scheduling

Increases in the number of user spacecraft and data rates supported by NASA's Tracking and Data Relay Satellite System (TDRSS) in the S and Ku bands could result in communications conflicts due to mutual interference. A method to mitigate interference while minimizing unnecessary scheduling restrictions on both TDRSS network and user resources, based on consideration of all relevant communications parameters, was developed. The steps of this method calculate required separation angles at TDRSS and produce interference intervals, which can be used in the production of schedules free of unacceptable interference. The method also can be used as the basis for analysis, evaluation, and optimization of user schedules with respect to communications performance. Described here are the proposed method and its potential application to scheduling in space communications. Test cases relative to planned missions, including the Earth Observing System, the Space Station Manned Base, and the Space Shuttle are discussed.

Wong, Yen F.

Enabling Future Science and Human Exploration with NASA's Next Generation near Earth and Deep Space Communications and Navigation Architecture

The National Aeronautics and Space Administration (NASA) is studying alternatives for the United States space communications architecture through the 2040 timeframe. This architecture provides communication and navigation services to both human exploration and science missions throughout the solar system. Several of NASA's key space assets are approaching their end of design life and major systems are in need of replacement. The changes envisioned in the relay satellite architecture and capabilities around both Earth and Mars are significant undertakings and occur only once or twice each generation, and therefore is referred to as NASA's next generation space communications architecture. NASA's next generation architecture will benefit from technology and services developed over recent years. These innovations will provide missions with new operations concepts, increased performance, and new business and operating models. Advancements in optical communications will enable high-speed data channels and the use of new and more complex science instruments. Modern multiple beam/multiple access technologies such as those employed on commercial high throughput satellites will enable enhanced capabilities for on-demand service, and with new protocols will help provide Internet-like connectivity for cooperative spacecraft to improve data return and coordinate joint mission objectives. On-board processing with autonomous and cognitive networking will play larger roles to help manage system complexity. Spacecraft and ground systems will coordinate among themselves to establish communications, negotiate link connectivity, and learn to share spectrum to optimize resource allocation. Spacecraft will autonomously navigate, plan trajectories, and handle off-nominal events. NASA intends to leverage the ever-expanding capabilities of the satellite communications industry and foster its continued growth. NASA's technology development will complement and extend commercial capabilities to meet unique space environment requirements and to provide capabilities that are beyond the commercial marketplace. The progress of the communications industry, including the emerging global space internet segment and its planned constellations of 100's of satellites offer additional opportunities for new capability and mission concepts. The opportunities and challenges of a future space architecture require an optimal solution encompassing a global perspective. The concepts and technologies intentionally define an architecture that applies not only to NASA, but to other U.S. government agencies, international space and government agencies, and domestic and international industries to advance the openness, interoperability, and affordability of space communications. Cooperation among the worlds space agencies, their capabilities, standards, operations, and interoperability are key to advancing humankind's understand of the universe and extending human presence into the solar system.

Communications

Enabling Future Science and Human Exploration with NASA's Next Generation Near Earth and Deep Space Communications and Navigation Architecture

The National Aeronautics and Space Administration (NASA) is studying alternatives for the United States space communications architecture through the 2040 timeframe. This architecture provides communication and navigation services to both human exploration and science missions throughout the solar system. Several of NASA's key space assets are approaching their end of design life and major systems are in need of replacement. The changes envisioned in the relay satellite architecture and capabilities around both Earth and Mars are significant undertakings and occur only once or twice each generation, and therefore is referred to as NASA's next generation space communications architecture. NASA's next generation architecture will benefit from technology and services developed over recent years. These innovations will provide missions with new operations concepts, increased performance, and new business and operating models. Advancements in optical communications will enable high-speed data channels and the use of new and more complex science instruments. Modern multiple beam/multiple access technologies such as those employed on commercial high throughput satellites will enable enhanced capabilities for on-demand service, and with new protocols will help provide Internet-like connectivity for cooperative spacecraft to improve data return and coordinate joint mission objectives. On-board processing with autonomous and cognitive networking will play larger roles to help manage system complexity. Spacecraft and ground systems will coordinate among themselves to establish communications, negotiate link connectivity, and learn to share spectrum to optimize resource allocation. Spacecraft will autonomously navigate, plan trajectories, and handle off-nominal events. NASA intends to leverage the ever-expanding capabilities of the satellite communications industry and foster its continued growth. NASA's technology development will complement and extend commercial capabilities to meet unique space environment requirements and to provide capabilities that are beyond the commercial marketplace. The progress of the communications industry, including the emerging global space internet segment and its planned constellations of 100's of satellites offer additional opportunities for new capability and mission concepts. The opportunities and challenges of a future space architecture require an optimal solution encompassing a global perspective. The concepts and technologies intentionally define an architecture that applies not only to NASA, but to other U.S. government agencies, international space and government agencies, and domestic and international industries to advance the openness, interoperability, and affordability of space communications. Cooperation among the worlds space agencies, their capabilities, standards, operations, and interoperability are key to advancing humankinds understand of the universe and extending human presence into the solar system.

deep space

Towards Rocket Engine Components with Increased Strength and Robust Operating Characteristics

High-energy rotating machines, powering liquid propellant rocket engines, are subject to various sources of high and low cycle fatigue generated by unsteady flow phenomena. Given the tremendous need for reliability in a sustainable space exploration program, a fundamental change in the design methodology for engine components is required for both launch and space based systems. A design optimization system based on neural-networks has been applied and demonstrated in the redesign of the Space Shuttle Main Engine (SSME) Low Pressure Oxidizer Turbo Pump (LPOTP) turbine nozzle. One objective of the redesign effort was to increase airfoil thickness and thus increase its strength while at the same time detuning the vane natural frequency modes from the vortex shedding frequency. The second objective was to reduce the vortex shedding amplitude. The third objective was to maintain this low shedding amplitude even in the presence of large manufacturing tolerances. All of these objectives were achieved without generating any detrimental effects on the downstream flow through the turbine, and without introducing any penalty in performance. The airfoil redesign and preliminary assessment was performed in the Exploration Technology Directorate at NASA ARC. Boeing/Rocketdyne and NASA MSFC independently performed final CFD assessments of the design. Four different CFD codes were used in this process. They include WIL DCA T/CORSAIR (NASA), FLUENT (commercial), TIDAL (Boeing Rocketdyne) and, a new family (AardvarWPhantom) of CFD analysis codes developed at NASA MSFC employing LOX fluid properties and a Generalized Equation Set formulation. Extensive aerodynamic performance analysis and stress analysis carried out at Boeing Rocketdyne and NASA MSFC indicate that the redesign objectives have been fully met. The paper presents the results of the assessment analysis and discusses the future potential of robust optimal design for rocket engine components.

Marcu, Bogdan

Space Shuttle RTOS Bayesian Network

With shrinking budgets and the requirements to increase reliability and operational life of the existing orbiter fleet, NASA has proposed various upgrades for the Space Shuttle that are consistent with national space policy. The cockpit avionics upgrade (CAU), a high priority item, has been selected as the next major upgrade. The primary functions of cockpit avionics include flight control, guidance and navigation, communication, and orbiter landing support. Secondary functions include the provision of operational services for non-avionics systems such as data handling for the payloads and caution and warning alerts to the crew. Recently, a process to selection the optimal commercial-off-the-shelf (COTS) real-time operating system (RTOS) for the CAU was conducted by United Space Alliance (USA) Corporation, which is a joint venture between Boeing and Lockheed Martin, the prime contractor for space shuttle operations. In order to independently assess the RTOS selection, NASA has used the Bayesian network-based scoring methodology described in this paper. Our two-stage methodology addresses the issue of RTOS acceptability by incorporating functional, performance and non-functional software measures related to reliability, interoperability, certifiability, efficiency, correctness, business, legal, product history, cost and life cycle. The first stage of the methodology involves obtaining scores for the various measures using a Bayesian network. The Bayesian network incorporates the causal relationships between the various and often competing measures of interest while also assisting the inherently complex decision analysis process with its ability to reason under uncertainty. The structure and selection of prior probabilities for the network is extracted from experts in the field of real-time operating systems. Scores for the various measures are computed using Bayesian probability. In the second stage, multi-criteria trade-off analyses are performed between the scores. Using a prioritization of measures from the decision-maker, trade-offs between the scores are used to rank order the available set of RTOS candidates.

Morris, A. Terry

A method for interference mitigation in space communications scheduling

Increases in the number of user spacecraft and data rates supported by NASA's Tracking and Data Relay Satellite System (TDRSS) in the S and Ku bands could result in communications conflicts due to mutual interference. More attention must be paid to this problem in terms of communications scheduling. A method based on consideration of all relevant communications parameters has been developed to mitigate interference while minimizing unnecessary scheduling restrictions on both the TDRSS network and user resources. This method calculates required separation angles at TDRS and produces potential interference intervals, which can be used in the production of schedules free of unacceptable interference. The method also can be used as the basis for analysis, evaluation, and optimization of user schedules with respect to communications performance. This paper describes the method and its proposed application to scheduling in space communications. Test cases relative to missions operating at Ku-band, including Space Shuttle, are discussed.

Wong, Yen F.

NASA's Efforts to Commercialize Communications Services for Mission in Near-Earth Space

The National Aeronautics and Space Administration (NASA) Space Communications and Navigation (SCaN)Program enables high speed, robust, secure and cost-effective space communications and navigation services to current and future science and exploration missions. Consistent with National Space Policy, NASA is pursuing the use of demonstrated commercial services for all its future near-Earth requirements through a flexible, multi-provider approach that minimizes risks to the user missions and ensures costs to user missions are reasonable. Progress toward this goal is advancing in multiple key areas including direct to Earth (DTE), space-based relay, technology investments, required spectrum regulatory changes and mission engagement and infusion. The transition to commercial DTE services is already underway, with a target for transition by 2024. The primary functions to execute SCaN’s DTE strategy include increasing commercial service allocations by leveraging current commercial network providers and enabling seamless onboarding of additional providers into the network. Furthermore, moving away from government DTE services will allow operational costs to be optimized. A more gradual approach is planned for the transition to commercial space-based relay services to allow for demonstration and operationalization of commercial services for future users by 2030. In June of 2022, six American SATCOM vendors were awarded a combined $278.5 million through Funded Space Act Agreements (FSAAs) for the first cycle of demonstration and validation activities. The end-to-end service capabilities being targeted are based on existing NASA mission operational needs. Accordingly, each company has proposed a technical approach to lower costs, increase flexibility, and improve performance for a broad range of missions. Successful user mission transition to commercial services, both DTE and space-based relay, are dependent on the technologies and capabilities that address gaps in commercial capability. NASA is investing in technology development and pursuing a new strategic approach to the creation or adoption of space communications standards to move the agency toward a commercial paradigm. Wideband and multi-lingual user terminals are being developed to bridge differences in industry services. Building on ground demonstrations completed in 2021, the Johns Hopkins Applied Physics Lab (APL) will be flight testing a multi-lingual wideband terminal (payload) and demonstrating connectivity to both government and commercial relay services. NASA holds a leadership role in multiple civil space standards bodies and international coordination groups to ensure that standards supporting interoperability are developed with defined functions, interfaces, and performance. However, to successfully meet commercialization objectives, NASA seeks to collaborate with industry, and as applicable adopt or adapt to commercially defined standards. As such, NASA joined the 3rd Generation Partnership Project (3GPP) as an official member in 2021 to advocate for the inclusion of space missions as a unique user segment in future 5G non-terrestrial networks, and to better understand the scope of 3GPP releases and implications for space users. Further, engagement in Spectrum regulatory bodies is being undertaken to augment existing space-Earth and inter-satellite frequency allocations available for both government and commercial space systems. This paper addresses the recent progress toward NASA’s commercial space communications transition objectives and how key challenges are being navigated.

Gregory W Heckler

NASA Leveraging Commercial Communication Ground Stations for Small Satellites

The Space Communications and Navigation (SCaN) program at NASA has reorganized its operations portfolio into two networks: the Deep Space Network and the new Near Space Network (NSN). With this reorganization, NASA can begin transforming to 100% direct-to-Earth commercial communications services for missions in the near-Earth region. NASA’s leveraging of commercial direct-to-Earth ground stations offers several benefits for the small satellite community, including lower cost, greater coverage, and increased technology infusion. In the fall of 2020, SCaN announced their intention to rely primarily on industry-provided communications services for missions close to Earth by 2030. Commercial services are one way to infuse new technology into the ground station network without requiring an investment from NASA. Digital Video Broadcast, Satellite Second Generation (DVB-S2) is one example of a current technology. When combined with variable coding and modulation (VCM), the system automatically optimizes the data rate based on signal performance, significantly increasing total downlink data volume without an increase in the spacecraft effective isotropic radiated power (EIRP). There are several commercial service providers, including Amazon Web Service (AWS) Ground Station (AGS) and the KSATLITE ground stations that support SmallSat missions using DVB-S2 waveforms for downlinks. This paper identifies some commercial off-the-shelf (COTS) CubeSat/SmallSat DVB-S2 X-band and Ka-band radios. Overall, NASA’s increased dependence on commercial direct-to-Earth ground stations is a significant benefit for the small satellite community.

Space Communications

Failure behavior identification for a space antenna via neural networks

By using neural networks, a method for the failure behavior identification of a space antenna model is investigated. The proposed method uses three stages. If a fault is suspected by the first stage of fault detection, a diagnostic test is performed on the antenna. The diagnostic test results are used by the second and third stages to identify which fault occurred and to diagnose the extent of the fault, respectively. The first stage uses a multilayer perceptron, the second stage uses a multilayer perceptron and neural networks trained with the quadratic optimization algorithm, a novel training procedure, and the third stage uses backpropagation trained neural networks.

Sartori, Michael A.

NASA Tech Briefs, October 2013

Topics include: A Short-Range Distance Sensor with Exceptional Linearity; Miniature Trace Gas Detector Based on Microfabricated Optical Resonators; Commercial Non-Dispersive Infrared Spectroscopy Sensors for Sub-Ambient Carbon Dioxide Detection; Fast, Large-Area, Wide-Bandgap UV Photodetector for Cherenkov Light Detection; Mission Data System Java Edition Version 7; Adaptive Distributed Environment for Procedure Training (ADEPT); LEGEND, a LEO-to-GEO Environment Debris Model; Electronics/Computers; Millimeter-Wave Localizers for Aircraft-to-Aircraft Approach Navigation; Impedance Discontinuity Reduction Between High-Speed Differential Connectors and PCB Interfaces; SpaceCube Version 1.5; High-Pressure Lightweight Thrusters; Non-Magnetic, Tough, Corrosion- and Wear-Resistant Knives From Bulk Metallic Glasses and Composites; Ambient Dried Aerogels; Applications for Gradient Metal Alloys Fabricated Using Additive Manufacturing; Passivation of Flexible YBCO Superconducting Current Lead With Amorphous SiO2 Layer; Propellant-Flow-Actuated Rocket Engine Igniter; Lightweight Liquid Helium Dewar for High-Altitude Balloon Payloads; Method to Increase Performance of Foil Bearings Through Passive Thermal Management; Unibody Composite Pressurized Structure; JWST Integrated Science Instrument Module Alignment Optimization Tool; Radar Range Sidelobe Reduction Using Adaptive Pulse Compression Technique; Digitally Calibrated TR Modules Enabling Real-Time Beamforming SweepSAR Architectures; Electro-Optic Time-to-Space Converter for Optical Detector Jitter Mitigation; Partially Transparent Petaled Mask/Occulter for Visible-Range Spectrum; Educational NASA Computational and Scientific Studies (enCOMPASS); Coarse-Grain Bandwidth Estimation Scheme for Large-Scale Network; Detection of Moving Targets Using Soliton Resonance Effect; High-Efficiency Nested Hall Thrusters for Robotic Solar System Exploration; High-Voltage Clock Driver for Photon-Counting CCD Characterization; Development of the Code RITRACKS; and Enabling Microliquid Chromatography by Microbead Packing of Microchannels.

Source record

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan