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Mathematical models of systems with interval representation of parameters on the basis of heterogeneous neural networks. Porous catalyst

Keywords:

A. N. Vasilyev – Dr.Sc. (Eng.), Professor, Department Higher Mathematics, Applied Mathematics and Mechanics Institute, St. Petersburg State Polytechnical University. E-mail: a.n.vasilyev@gmail.com
D. A. Tarkhov – Dr.Sc. (Eng.), Professor, Department Higher Mathematics, Applied Mathematics and Mechanics Institute, St. Petersburg State Polytechnical University. E-mail: dtarkhov@gmail.com


Neural networking technique with models based on differential equations is applied to known incorrect problems which solution by routine approaches has difficulties. An approximate solution to the problem is found as output of neural network with some prescribed architecture. Network weights are determined in the process of stepwise network training grounded on some error functional minimization in general case. We consider in the three-part composition the case when system parameters are given in some variation intervals. This paper – the first part of the composition – deals with BVP for ordinary differential equation with interval parameters. Construction of robust neural network model of processes in porous catalyst is cited as an example. The similar problem in the case of interval temperature conduction factor for both classical and nonclassical statements was solved via neurocomputing on growing neural networks in other two parts of the composition. Results of neurocomputing and some corresponding figures are given. Advantages of neural network approach and some possible generalizations are mentioned.
References:

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