THERMAL SCIENCE

International Scientific Journal

COMPARISON OF TWO NEURAL NETWORK APPROACHES TO MODELING PROCESSES IN A CHEMICAL REACTOR

ABSTRACT
In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the Störmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value.
KEYWORDS
PAPER SUBMITTED: 2018-09-10
PAPER REVISED: 2018-11-11
PAPER ACCEPTED: 2018-11-30
PUBLISHED ONLINE: 2019-05-05
DOI REFERENCE: https://doi.org/10.2298/TSCI19S2583S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 2, PAGES [S583 - S589]
REFERENCES
  1. Tarkhov, D. A., Vasilyev A. N., Mathematical Models of Complex Systems on the Basis of Artificial Neural Networks, Nonlinear Phenomena in Complex Systems, 17 (2014), 3, pp. 327-335
  2. Kainov, N. U., et al., Application of Neural Network Modeling to Identification and Prediction in Ecology Data Analysis for Metallurgy and Welding Industry, Nonlinear Phenomena in Complex Systems, 17 (2014), 1, pp. 57-63
  3. Budkina, E. M., et al., Neural Network Technique in Boundary Value Problems for Ordinary Differential Equations, Lecture Notes in Computer Science, 9719 (2016), July, pp. 277-283
  4. Gorbachenko, V. I., et al., Neural Network Technique in Some Inverse Problems of Mathematical Physics, Lecture Notes in Computer Science, 9719 (2016), July, pp. 310-316
  5. Shemyakina, T. A., et al., Neural Network Technique for Processes Modeling in Porous Catalyst and Chemical Reactor, Lecture Notes in Computer Science, 9719 (2016), July, pp. 547-554
  6. Lazovskaya, T. V., et al., Parametric Neural Network Modeling in Engineering, Recent Patents on Engineering, 11 (2017), 1, pp. 10-15
  7. Lozhkin, V., et al., Differential Neural Network Approach in Information Process for Prediction of Roadside Air Pollution by Peat Fire, Proceedings, IOP Conf. Series: Materials Science and Engineering, Kazan, Russia, 2016, Vol. 158
  8. Neha, Y., et al., An Introduction to Neural Network Methods for Differential Equations, Springer, New York, London, 2015, p. 115
  9. Lazovskaya, T. V., Tarkhov, D. A., Multilayer Neural Network Models Based on Grid Methods, Proceedings, IOP Conf. Series: Materials Science and Engineering, Kazan, Russia, 2016, Vol. 158
  10. Vasilyev, A. N., et al., Approximate Analytical Solutions of Ordinary Differential Equations (in Russian), Proceedings, Selected Papers of the XI International Scientific-Practical Conference Modern Information Technologies and IT-Education (SITITO 2016), Moscow, Russia, 2016, рp. 393-400
  11. Lazovskaya, T. V., et al., Multi-Layer Solution of Heat Equation, Advances, in: Neural Computation, Machine Learning and Cognitive Research, (Eds. Kryzhanovski, B., et al.), Springer, Moskow, Russia, 2017, Oct., pp. 18-19
  12. Hairer, E., et al., Solving Ordinary Differential Equations I: Nonstiff Problem, Springer-Verlag, Berlin, 1987, p. 480
  13. Na, T. Y. Computational Methods in Engineering Boundary Value, Academic Press, Dearborn, Mich., USA, 1979, p. 296
  14. Hall, A. R., Wolfhard, H. G., Multiple Reaction Zones in low Pressure Flames with Ethyl and Methyl Nitrate, Methyl Nitrate and Nitromethane, Proceedings, VI Symp. (Intern.) on Combustion, New York, USA, 1957, pp. 190-199
  15. Bush, W. B., Fendell, F. E., Asymptotic Analysis of Laminar Flame Propagation for General Lewis Numbers, Comb Sci. Techn., 1 (1970), 6, pp. 421-428
  16. Fendell, F. E., Asymptotic Analysis of Premixed Burning with Large Activation Energy, J. Fluid Mech., 56 (1972), 1, pp. 81-95

© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence