Neural network dynamic

Feedback Dynamics. In assuming the counteractive rule, the optical feedback system automatically updates the illumination pattern. The feedback is implemented with a discrete form of recurrent neural network dynamics known as Hopfield-Tank model [8] yi t + At) = 1 — where Wij is the... 

The local dynamics of tire systems considered tluis far has been eitlier steady or oscillatory. However, we may consider reaction-diffusion media where tire local reaction rates give rise to chaotic temporal behaviour of tire sort discussed earlier. Diffusional coupling of such local chaotic elements can lead to new types of spatio-temporal periodic and chaotic states. It is possible to find phase-synchronized states in such systems where tire amplitude varies chaotically from site to site in tire medium whilst a suitably defined phase is synclironized tliroughout tire medium 51. Such phase synclironization may play a role in layered neural networks and perceptive processes in mammals. Somewhat suriDrisingly, even when tire local dynamics is chaotic, tire system may support spiral waves... 

In previous chapters, we have examined a variety of generalized CA models, including reversible CA, coupled-map lattices, reaction-diffusion models, random Boolean networks, structurally dynamic CA and lattice gases. This chapter covers an important field that overlaps with CA neural networks. Beginning with a short historical survey, chapter 10 discusses zissociative memory and the Hopfield model, stocheistic nets, Boltzman machines, and multi-layered perceptrons. 

Hypercubes and other new computer architectures (e.g., systems based on simulations of neural networks) represent exciting new tools for chemical engineers. A wide variety of applications central to the concerns of chemical engineers (e.g., fluid dynamics and heat flow) have already been converted to run on these architectures. The new computer designs promise to move the field of chemical engineering substantially away from its dependence on simplified models toward computer simulations and calculations that more closely represent the incredible complexity of the real world. 

Narendra, K. S., and Parthasarathy, K., Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Networks 1, (1990). 

Vaidyanathan, R., and Venkatasubramanian, V., Process fault detection and diagnosis using neural networks II. Dynamic processes. AIChE Ann. Meet., Chicago, IL (1990). 

Rost, B., Casadio, R., and Fariselli, P. (1996). Refining neural network predictions for helical transmembrane proteins by dynamic programming. Intell. Syst. Mol. Biol. 4, 192-200. 

Robert Hecht-Nielsen, the inventor of one of the first commercial neurocomputers, defined [17] a neural network as a computing system made up of a number of simple, highly interconnected processing elements, which process information by its dynamic state response to external inputs. ... 

Thangavel P, Murali K, Lakshmanan M. 2000 Dynamics of certain Chaotic delayed cellular neural networks. In Nonlinear dynamics Integrability and chaos. M Daniel, KM Tamizhmani, R Sahadevan (Eds). Narosa Publishing House, New Delhi, pp 227-286. 

Kosko B 1992 Neural Networks and Fuzzy Systems A Dynamical Systems Approach to Machine Intelligence. Prentice-Hall, A Simon Schuster Company, Englewood Cliffs, New Jersey. 

Gross GW, Kowalski J (1991) Experimental and theoretical analysis of random nerve cell network dynamics. In Antognetti P and Milutinovic V. (eds) Neural Networks Concepts, Applications, and Implementations. Englewood City, New Jersey, Prentice-Hall, p 47... 

Using the model, Barolo et al. (1998) further studied the dynamic behaviour of the column and interactions of different design and operating parameters on the column operability and productivity were established. See the original reference for further details. The optimisation study carried out by Greaves et al (2003) using a Neural Network based dynamic model is presented in Chapter 12. 

In Mujtaba and Hussain (1998), the detailed dynamic model was assumed to be the exact representation of the process while the difference in predictions of the process behaviour using a simple model and the detailed model was assumed to be the dynamic process-model mismatches. Theses dynamic mismatches were modelled using neural network techniques and were coupled with the simple model... 

Dynamic sets of process-model mismatches data is generated for a wide range of the optimisation variables (z). These data are then used to train the neural network. The trained network predicts the process-model mismatches for any set of values of z at discrete-time intervals. During the solution of the dynamic optimisation problem, the model has to be integrated many times, each time using a different set of z. The estimated process-model mismatch profiles at discrete-time intervals are then added to the simple dynamic model during the optimisation process. To achieve this, the discrete process-model mismatches are converted to continuous function of time using linear interpolation technique so that they can easily be added to the model (to make the hybrid model) within the optimisation routine. One of the important features of the framework is that it allows the use of discrete process data in a continuous model to predict discrete and/or continuous mismatch profiles. 

In Greaves et al. (2001) and Greaves (2003), instead of using a rigorous model (as in the methodology described above), an actual pilot plant batch distillation column is used. The differences in predictions between the actual plant and the simple model (Type III and also in Mujtaba, 1997) are defined as the dynamic process-model mismatches. The mismatches are modelled using neural network techniques as described in earlier sections and are incorporated in the simple model to develop the hybrid model that represents the predictions of the actual column. 

The four experiments done previously with Rnp (= 0.5, 1, 3, 4) were used to train the neural network and the experiment with / exp = 2 was used to validate the system. Dynamic models of process-model mismatches for three state variables (i.e. X) of the system are considered here. They are the instant distillate composition (xD), accumulated distillate composition (xa) and the amount of distillate (Ha). The inputs and outputs of the network are as in Figure 12.2. A multilayered feed forward network, which is trained with the back propagation method using a momentum term as well as an adaptive learning rate to speed up the rate of convergence, is used in this work. The error between the actual mismatch (obtained from simulation and experiments) and that predicted by the network is used as the error signal to train the network as described earlier. 

Neural Network based hybrid dynamic modelling and optimisation methods for conventional and unconventional column configurations... 

Milton, J., VanDerHeiden, U., Longtin, A., and Mackey, M., Complex dynamics and noise in simple neural networks with delayed mixed feedback, Biomedica Biochimica Acta, Vol. 49, No. 8-9, 1990, pp. 697-707. 

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