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DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗

NASA NTRS2005

Training Software in Artificial-Intelligence Computing Techniques

The Artificial Intelligence (AI) Toolkit is a computer program for training scientists, engineers, and university students in three soft-computing techniques (fuzzy logic, neural networks, and genetic algorithms) used in artificial-intelligence applications. The program promotes an easily understandable tutorial interface, including an interactive graphical component through which the user can gain hands-on experience in soft-computing techniques applied to realistic example problems. The tutorial provides step-by-step instructions on the workings of soft-computing technology, whereas the hands-on examples allow interaction and reinforcement of the techniques explained throughout the tutorial. In the fuzzy-logic example, a user can interact with a robot and an obstacle course to verify how fuzzy logic is used to command a rover traverse from an arbitrary start to the goal location. For the genetic algorithm example, the problem is to determine the minimum-length path for visiting a user-chosen set of planets in the solar system. For the neural-network example, the problem is to decide, on the basis of input data on physical characteristics, whether a person is a man, woman, or child. The AI Toolkit is compatible with the Windows 95,98, ME, NT 4.0, 2000, and XP operating systems. A computer having a processor speed of at least 300 MHz, and random-access memory of at least 56MB is recommended for optimal performance. The program can be run on a slower computer having less memory, but some functions may not be executed properly.

Howard, Ayanna↗

NASA NTRS2006

Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks

Genetic and evolutionary algorithms have been applied to solve numerous problems in engineering design where they have been used primarily as optimization procedures. These methods have an advantage over conventional gradient-based search procedures became they are capable of finding global optima of multi-modal functions and searching design spaces with disjoint feasible regions. They are also robust in the presence of noisy data. Another desirable feature of these methods is that they can efficiently use distributed and parallel computing resources since multiple function evaluations (flow simulations in aerodynamics design) can be performed simultaneously and independently on ultiple processors. For these reasons genetic and evolutionary algorithms are being used more frequently in design optimization. Examples include airfoil and wing design and compressor and turbine airfoil design. They are also finding increasing use in multiple-objective and multidisciplinary optimization. This lecture will focus on an evolutionary method that is a relatively new member to the general class of evolutionary methods called differential evolution (DE). This method is easy to use and program and it requires relatively few user-specified constants. These constants are easily determined for a wide class of problems. Fine-tuning the constants will off course yield the solution to the optimization problem at hand more rapidly. DE can be efficiently implemented on parallel computers and can be used for continuous, discrete and mixed discrete/continuous optimization problems. It does not require the objective function to be continuous and is noise tolerant. DE and applications to single and multiple-objective optimization will be included in the presentation and lecture notes. A method for aerodynamic design optimization that is based on neural networks will also be included as a part of this lecture. The method offers advantages over traditional optimization methods. It is more flexible than other methods in dealing with design in the context of both steady and unsteady flows, partial and complete data sets, combined experimental and numerical data, inclusion of various constraints and rules of thumb, and other issues that characterize the aerodynamic design process. Neural networks provide a natural framework within which a succession of numerical solutions of increasing fidelity, incorporating more realistic flow physics, can be represented and utilized for optimization. Neural networks also offer an excellent framework for multiple-objective and multi-disciplinary design optimization. Simulation tools from various disciplines can be integrated within this framework and rapid trade-off studies involving one or many disciplines can be performed. The prospect of combining neural network based optimization methods and evolutionary algorithms to obtain a hybrid method with the best properties of both methods will be included in this presentation. Achieving solution diversity and accurate convergence to the exact Pareto front in multiple objective optimization usually requires a significant computational effort with evolutionary algorithms. In this lecture we will also explore the possibility of using neural networks to obtain estimates of the Pareto optimal front using non-dominated solutions generated by DE as training data. Neural network estimators have the potential advantage of reducing the number of function evaluations required to obtain solution accuracy and diversity, thus reducing cost to design.

Rai, Man Mohan↗

NASA NTRS2005

Hot Chips and Hot Interconnects for High End Computing Systems

I will discuss several processors: 1. The Cray proprietary processor used in the Cray X1; 2. The IBM Power 3 and Power 4 used in an IBM SP 3 and IBM SP 4 systems; 3. The Intel Itanium and Xeon, used in the SGI Altix systems and clusters respectively; 4. IBM System-on-a-Chip used in IBM BlueGene/L; 5. HP Alpha EV68 processor used in DOE ASCI Q cluster; 6. SPARC64 V processor, which is used in the Fujitsu PRIMEPOWER HPC2500; 7. An NEC proprietary processor, which is used in NEC SX-6/7; 8. Power 4+ processor, which is used in Hitachi SR11000; 9. NEC proprietary processor, which is used in Earth Simulator. The IBM POWER5 and Red Storm Computing Systems will also be discussed. The architectures of these processors will first be presented, followed by interconnection networks and a description of high-end computer systems based on these processors and networks. The performance of various hardware/programming model combinations will then be compared, based on latest NAS Parallel Benchmark results (MPI, OpenMP/HPF and hybrid (MPI + OpenMP). The tutorial will conclude with a discussion of general trends in the field of high performance computing, (quantum computing, DNA computing, cellular engineering, and neural networks).

Saini, Subhash↗

NASA NTRSDate not supplied

SWIPE: Spectral Water Inversion Processor and Emulator

Degradation of Earth’s inland water resources due to anthropogenic perturbations and climate anomalies at both local and global scales continues to place human health at substantial risk. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This presentation will be discussing the progress made developing SWIPE: Spectral Water Inversion Processor and Emulator. SWIPE is a platform for advanced modeling of coastal and inland aquatic habitats. The goal is create a comprehensive and cohesive system to leverage recent advancements in computation and machine learning to develop a synthetic training ground for sensitivity studies and algorithm development. The four principal facets of SWIPE include: 1. Advanced two-layer coated sphere bio-optical modeling and GPU radiative transfer modeling, 2. Big Data involving massive synthetic spectral libraries of optical properties of various global aquatic particles, surface reflectance, and top-of-atmosphere reflectance, all at hyperspectral resolution leveraging high-end computing systems at NASA Ames Research Center, 3. Deep Learning for algorithm development for water quality inversion of concentrations of common biogeophysical variables as well as optics, full uncertainty characterization by water type, and forward emulation, and lastly, 4. Image Processing for application of developed retrieval algorithms for both hyperspectral and multispectral sensors with experimental corrections for global adjacency, noise, sunglint, and benthic reflectance. This presentation will demonstrate the Equivalent Algal Populations (EAP) two-layer coated sphere scattering model which has been used develop spectral libraries of hyperspectral inherent optical properties of roughly 80 species of phytoplankton, covering 15 different classes and nine taxonomic functional types. The EAP model was also used to derive spectral properties of 10 different non-algal particle functional types. Examples of how the SMART-G (Speed-up Monte-carlo Advanced Radiative Transfer using GPU) radiative transfer code is used to model optically complex aquatic signals will be presented and discussed in the context of creating a massive synthetic database which can leverage the full power of next generation machine learning techniques and high end computing for water quality inversion. We will discuss our active investigation in things like appropriate model architectures, dimensionality reduction techniques such as PCA and autoencoders, uncertainty quantification and abstaining, and which variables actually benefit most from hyperspectral information versus multispectral resolution. We are also curious about questions relating to cost/benefit analysis in terms of computation resources, neural network complexity, and data volumes. Answers to these questions will hopefully elaborate on cost efficiency for potential future sensor design considerations.

SWIPE↗

DOE OSTI2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

King, Andrew D. [D-Wave Quantum Inc., Burnaby, BC ↗

NASA NTRS1997

Vigilante: Ultrafast Smart Sensor for Target Recognition and Precision Tracking in a Simulated CMD Scenario

VIGILANTE is an ultrafast smart sensor testbed for generic Automatic Target Recognition (ATR) applications with a series of capability demonstration focussed on cruise missile defense (CMD). VIGILANTE's sensor/processor architecture is based on next-generation UV/visible/IR sensors and a tera-operations per second sugar-cube processor, as well as supporting airborne vehicle. Excellent results of efficient ATR methodologies that use an eigenvectors/neural network combination and feature-based precision tracking have been demonstrated in the laboratory environment.

TARGET RECOGNITION↗

NASA NTRS1990

Photonic processing at NASA Ames Research Center

The Photonic Processing group is engaged in applied research on optical processors in support of the Ames vision to lead the development of autonomous intelligent systems. Optical processors, in conjunction with numeric and symbolic processors, are needed to provide the powerful processing capability that is required for many future agency missions. The research program emphasizes application of analog optical processing, where free-space propagation between components allows natural implementations of algorithms requiring a large degree of parallel computation. Special consideration is given in the Ames program to the integration of optical processors into larger, heterogeneous computational systems. Demonstration of the effective integration of optical processors within a broader knowledge-based system is essential to evaluate their potential for dependable operation in an autonomous environment such as space. The Ames Photonics program is currently addressing several areas of interest. One of the efforts is to develop an optical correlator system with two programmable spatial light modulators (SLMs) to perform distortion invariant pattern recognition. Another area of research is optical neural networks, also for use in distortion-invariant pattern recognition.

Ochoa, Ellen↗

NASA NTRS2002

Implementation of Adaptive Digital Controllers on Programmable Logic Devices

Much has been made of the capabilities of Field Programmable Gate Arrays (FPGA's) in the hardware implementation of fast digital signal processing functions. Such capability also makes an FPGA a suitable platform for the digital implementation of closed loop controllers. Other researchers have implemented a variety of closed-loop digital controllers on FPGA's. Some of these controllers include the widely used Proportional-Integral-Derivative (PID) controller, state space controllers, neural network and fuzzy logic based controllers. There are myriad advantages to utilizing an FPGA for discrete-time control functions which include the capability for reconfiguration when SRAM- based FPGA's are employed, fast parallel implementation of multiple control loops and implementations that can meet space level radiation tolerance requirements in a compact form-factor. Generally, a software implementation on a Digital Signal Processor (DSP) device or microcontroller is used to implement digital controllers. At Marshall Space Flight Center, the Control Electronics Group has been studying adaptive discrete-time control of motor driven actuator systems using DSP devices. While small form factor, commercial DSP devices are now available with event capture, data conversion, Pulse Width Modulated (PWM) outputs and communication peripherals, these devices are not currently available in designs and packages which meet space level radiation requirements. In general, very few DSP devices are produced that are designed to meet any level of radiation tolerance or hardness. An alternative is required for compact implementation of such functionality to withstand the harsh environment encountered on spacemap. The goal of this effort is to create a fully digital, flight ready controller design that utilizes an FPGA for implementation of signal conditioning for control feedback signals, generation of commands to the controlled system, and hardware insertion of adaptive-control algorithm approaches. Radiation tolerant FPGA's are a feasible option for reaching this goal.

Gwaltney, David A.↗

NASA NTRS1990

An adaptive holographic implementation of a neural network

A holographic implementation for neural networks is proposed and demonstrated as an alternative to the optical matrix-vector multiplier architecture. In comparison, the holographic architecture makes more efficient use of the system space-bandwidth product for certain types of neural networks. The principal network component is a thermoplastic hologram, used to provide both interconnection weights and beam direction. Given the updatable nature of this type of hologram, adaptivity or network learning is possible in the optical system. Two networks with fixed weights are experimentally implemented and verified, and for one of these examples the advantage of the holographic implementation with respect to the matrix-vector processor is demonstrated.

Downie, John D.↗

NASA NTRS2002

Implementation of Adaptive Digital Controllers on Programmable Logic Devices

Much has been made of the capabilities of FPGA's (Field Programmable Gate Arrays) in the hardware implementation of fast digital signal processing. Such capability also makes an FPGA a suitable platform for the digital implementation of closed loop controllers. Other researchers have implemented a variety of closed-loop digital controllers on FPGA's. Some of these controllers include the widely used proportional-integral-derivative (PID) controller, state space controllers, neural network and fuzzy logic based controllers. There are myriad advantages to utilizing an FPGA for discrete-time control functions which include the capability for reconfiguration when SRAM-based FPGA's are employed, fast parallel implementation of multiple control loops and implementations that can meet space level radiation tolerance requirements in a compact form-factor. Generally, a software implementation on a DSP (Digital Signal Processor) or microcontroller is used to implement digital controllers. At Marshall Space Flight Center, the Control Electronics Group has been studying adaptive discrete-time control of motor driven actuator systems using digital signal processor (DSP) devices. While small form factor, commercial DSP devices are now available with event capture, data conversion, pulse width modulated (PWM) outputs and communication peripherals, these devices are not currently available in designs and packages which meet space level radiation requirements. In general, very few DSP devices are produced that are designed to meet any level of radiation tolerance or hardness. The goal of this effort is to create a fully digital, flight ready controller design that utilizes an FPGA for implementation of signal conditioning for control feedback signals, generation of commands to the controlled system, and hardware insertion of adaptive control algorithm approaches. An alternative is required for compact implementation of such functionality to withstand the harsh environment encountered on spacecraft. Radiation tolerant FPGA's are a feasible option for reaching this goal.

Gwaltney, David A.↗

NASA NTRS2003

Use of Soft Computing Technologies For Rocket Engine Control

The problem to be addressed in this paper is to explore how the use of Soft Computing Technologies (SCT) could be employed to further improve overall engine system reliability and performance. Specifically, this will be presented by enhancing rocket engine control and engine health management (EHM) using SCT coupled with conventional control technologies, and sound software engineering practices used in Marshall s Flight Software Group. The principle goals are to improve software management, software development time and maintenance, processor execution, fault tolerance and mitigation, and nonlinear control in power level transitions. The intent is not to discuss any shortcomings of existing engine control and EHM methodologies, but to provide alternative design choices for control, EHM, implementation, performance, and sustaining engineering. The approaches outlined in this paper will require knowledge in the fields of rocket engine propulsion, software engineering for embedded systems, and soft computing technologies (i.e., neural networks, fuzzy logic, and Bayesian belief networks), much of which is presented in this paper. The first targeted demonstration rocket engine platform is the MC-1 (formerly FASTRAC Engine) which is simulated with hardware and software in the Marshall Avionics & Software Testbed laboratory that

Trevino, Luis C.↗

NASA NTRS2001

Use of Soft Computing Technologies for a Qualitative and Reliable Engine Control System for Propulsion Systems

The problem to be addressed in this paper is to explore how the use of Soft Computing Technologies (SCT) could be employed to improve overall vehicle system safety, reliability, and rocket engine performance by development of a qualitative and reliable engine control system (QRECS). Specifically, this will be addressed by enhancing rocket engine control using SCT, innovative data mining tools, and sound software engineering practices used in Marshall's Flight Software Group (FSG). The principle goals for addressing the issue of quality are to improve software management, software development time, software maintenance, processor execution, fault tolerance and mitigation, and nonlinear control in power level transitions. The intent is not to discuss any shortcomings of existing engine control methodologies, but to provide alternative design choices for control, implementation, performance, and sustaining engineering, all relative to addressing the issue of reliability. The approaches outlined in this paper will require knowledge in the fields of rocket engine propulsion (system level), software engineering for embedded flight software systems, and soft computing technologies (i.e., neural networks, fuzzy logic, data mining, and Bayesian belief networks); some of which are briefed in this paper. For this effort, the targeted demonstration rocket engine testbed is the MC-1 engine (formerly FASTRAC) which is simulated with hardware and software in the Marshall Avionics & Software Testbed (MAST) laboratory that currently resides at NASA's Marshall Space Flight Center, building 4476, and is managed by the Avionics Department. A brief plan of action for design, development, implementation, and testing a Phase One effort for QRECS is given, along with expected results. Phase One will focus on development of a Smart Start Engine Module and a Mainstage Engine Module for proper engine start and mainstage engine operations. The overall intent is to demonstrate that by employing soft computing technologies, the quality and reliability of the overall scheme to engine controller development is further improved and vehicle safety is further insured. The final product that this paper proposes is an approach to development of an alternative low cost engine controller that would be capable of performing in unique vision spacecraft vehicles requiring low cost advanced avionics architectures for autonomous operations from engine pre-start to engine shutdown.

Trevino, Luis↗

NASA NTRS1989

Parallel asynchronous systems and image processing algorithms

A new hardware approach to implementation of image processing algorithms is described. The approach is based on silicon devices which would permit an independent analog processing channel to be dedicated to evey pixel. A laminar architecture consisting of a stack of planar arrays of the device would form a two-dimensional array processor with a 2-D array of inputs located directly behind a focal plane detector array. A 2-D image data stream would propagate in neuronlike asynchronous pulse coded form through the laminar processor. Such systems would integrate image acquisition and image processing. Acquisition and processing would be performed concurrently as in natural vision systems. The research is aimed at implementation of algorithms, such as the intensity dependent summation algorithm and pyramid processing structures, which are motivated by the operation of natural vision systems. Implementation of natural vision algorithms would benefit from the use of neuronlike information coding and the laminar, 2-D parallel, vision system type architecture. Besides providing a neural network framework for implementation of natural vision algorithms, a 2-D parallel approach could eliminate the serial bottleneck of conventional processing systems. Conversion to serial format would occur only after raw intensity data has been substantially processed. An interesting challenge arises from the fact that the mathematical formulation of natural vision algorithms does not specify the means of implementation, so that hardware implementation poses intriguing questions involving vision science.

Coon, D. D.↗

NASA NTRS1991

Satellite communications for the next generation telecommunication services and networks

Satellite communications can play an important role in provisioning the next-generation telecommunication services and networks, provided the protocols specifying these services and networks are satellite-compatible and the satellite subnetworks, consisting of earth stations interconnected by the processor and the switch on board the satellite, interwork effectively with the terrestrial networks. The specific parameters and procedures of frame relay and broadband integrated services digital network (B-ISDN) protocols which are impacted by a satellite delay. Congestion and resource management functions for frame relay and B-ISDN are discussed in detail, describing the division of these functions between earth stations and on board the satellite. Specific onboard and ground functions are identified as potential candidates for their implementation via neural network technology.

Chitre, D. M.↗

NASA NTRS1993

Visual information processing II; Proceedings of the Meeting, Orlando, FL, Apr. 14-16, 1993

Various papers on visual information processing are presented. Individual topics addressed include: aliasing as noise, satellite image processing using a hammering neural network, edge-detetion method using visual perception, adaptive vector median filters, design of a reading test for low-vision image warping, spatial transformation architectures, automatic image-enhancement method, redundancy reduction in image coding, lossless gray-scale image compression by predictive GDF, information efficiency in visual communication, optimizing JPEG quantization matrices for different applications, use of forward error correction to maintain image fidelity, effect of peanoscanning on image compression. Also discussed are: computer vision for autonomous robotics in space, optical processor for zero-crossing edge detection, fractal-based image edge detection, simulation of the neon spreading effect by bandpass filtering, wavelet transform (WT) on parallel SIMD architectures, nonseparable 2D wavelet image representation, adaptive image halftoning based on WT, wavelet analysis of global warming, use of the WT for signal detection, perfect reconstruction two-channel rational filter banks, N-wavelet coding for pattern classification, simulation of image of natural objects, number-theoretic coding for iconic systems.

Huck, Friedrich O.↗

NASA NTRS1996

Development of a Computer Architecture to Support the Optical Plume Anomaly Detection (OPAD) System

The NASA OPAD spectrometer system relies heavily on extensive software which repetitively extracts spectral information from the engine plume and reports the amounts of metals which are present in the plume. The development of this software is at a sufficiently advanced stage where it can be used in actual engine tests to provide valuable data on engine operation and health. This activity will continue and, in addition, the OPAD system is planned to be used in flight aboard space vehicles. The two implementations, test-stand and in-flight, may have some differing requirements. For example, the data stored during a test-stand experiment are much more extensive than in the in-flight case. In both cases though, the majority of the requirements are similar. New data from the spectrograph is generated at a rate of once every 0.5 sec or faster. All processing must be completed within this period of time to maintain real-time performance. Every 0.5 sec, the OPAD system must report the amounts of specific metals within the engine plume, given the spectral data. At present, the software in the OPAD system performs this function by solving the inverse problem. It uses powerful physics-based computational models (the SPECTRA code), which receive amounts of metals as inputs to produce the spectral data that would have been observed, had the same metal amounts been present in the engine plume. During the experiment, for every spectrum that is observed, an initial approximation is performed using neural networks to establish an initial metal composition which approximates as accurately as possible the real one. Then, using optimization techniques, the SPECTRA code is repetitively used to produce a fit to the data, by adjusting the metal input amounts until the produced spectrum matches the observed one to within a given level of tolerance. This iterative solution to the original problem of determining the metal composition in the plume requires a relatively long period of time to execute the software in a modern single-processor workstation, and therefore real-time operation is currently not possible. A different number of iterations may be required to perform spectral data fitting per spectral sample. Yet, the OPAD system must be designed to maintain real-time performance in all cases. Although faster single-processor workstations are available for execution of the fitting and SPECTRA software, this option is unattractive due to the excessive cost associated with very fast workstations and also due to the fact that such hardware is not easily expandable to accommodate future versions of the software which may require more processing power. Initial research has already demonstrated that the OPAD software can take advantage of a parallel computer architecture to achieve the necessary speedup. Current work has improved the software by converting it into a form which is easily parallelizable. Timing experiments have been performed to establish the computational complexity and execution speed of major components of the software. This work provides the foundation of future work which will create a fully parallel version of the software executing in a shared-memory multiprocessor system.

Katsinis, Constantine↗

NASA NTRS1995

Neural node network and model, and method of teaching same

The present invention is a fully connected feed forward network that includes at least one hidden layer 16. The hidden layer 16 includes nodes 20 in which the output of the node is fed back to that node as an input with a unit delay produced by a delay device 24 occurring in the feedback path 22 (local feedback). Each node within each layer also receives a delayed output (crosstalk) produced by a delay unit 36 from all the other nodes within the same layer 16. The node performs a transfer function operation based on the inputs from the previous layer and the delayed outputs. The network can be implemented as analog or digital or within a general purpose processor. Two teaching methods can be used: (1) back propagation of weight calculation that includes the local feedback and the crosstalk or (2) more preferably a feed forward gradient decent which immediately follows the output computations and which also includes the local feedback and the crosstalk. Subsequent to the gradient propagation, the weights can be normalized, thereby preventing convergence to a local optimum. Education of the network can be incremental both on and off-line. An educated network is suitable for modeling and controlling dynamic nonlinear systems and time series systems and predicting the outputs as well as hidden states and parameters. The educated network can also be further educated during on-line processing.

Parlos, Alexander G.↗