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Simulation of physical fields by spatial neural networks

DOI 10.18127/j19998554-201902-03

Keywords:

B. V. Khakimov – Dr.Sc. (Econ.), Assistant Member of the Federation Council (Moscow)
E-mail: bvhakimov@yandex.ru
I. M. Mikheev – Dr.Sc. (Phys.-Math.), Professor, Moscow Technical University of Communications and Informatics
E-mail: igormikheev@mail.ru


It has been proposed to use a spatial network of spline models of neurons to simulate the physical field. Each local area of the physical field with the center at the point of the network is modeled by its spline model, and the general model is obtained as gluing of local spline models of the surrounding points entering the sliding window. The weights of the surrounding points and their spline models in the sliding window are determined taking into account the distances from the center of the window and the mutual angular overlaps implemented in the “shadow method”. The results of modeling the roof and sole of oil and ore deposits show a multiple increase in the accuracy and speed of the spatial network of spline models of neurons in comparison with the triangulation method. Prospects of use of spatial networks of spline models of neurons for the solution of dynamic problems of mathematical physics have been specified.

References:
  1. Steklov V.A. Osnovnye zadachi matematicheskoj fiziki. M.: Nauka. 1983. [in Russian]
  2. Vasil'ev V.I., Tarkhov D.A., Shemyakina T.A. Nejrosetevoj podkhod k zadacham matematicheskoj fiziki. SPb.: Nestor-Istoriya. 2015. [in Russian]
  3. Khakimov B.V., Mikheev I.M. Modelirovanie fizicheskikh polej nejronnymi setyami. Sb. tezisov dokl. XVI Vserossijskoj nauch. konf. «Nejrokomp'yutery i ikh primenenie». M.: MGPPU. 2018. S. 129. [in Russian]
  4. Khakimov B.V. Modelirovanie korrelyatsionnykh zavisimostej splajnami na primerakh v geologii i ekologii. M.: MGU; SPb.: Neva. 2003. [in Russian]
May 29, 2020

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