350 rub
Journal Neurocomputers №9 for 2013 г.
Article in number:
Inverse mathematical physics problems solving by normalized radial basis function networks
Authors:
I.S. Kolbin - Ph.D. (Phys.-Math.), Moscow Aviation Institute (Technical University) D.L. Reviznikov - D.Sci. (Phys.-Math.), Moscow Aviation Institute (Technical University)
Abstract:
In this paper we propose the method for solving inverse problems of mathematical physics. The method is based on normalized radial basis function networks. We discuss problems of source term identification and boundary conditions identification. The coefficients of neural network model are tuned by means of unconstrained multidimensional optimization. The efficiency of suggested approach is demonstrated on representative set of stationary and non-stationary inverse problems for heat transfer equations.
Pages: 3-11
References

  1. Vasil'ev A.N., Tarxov D.A. Nejrosetevoe modelirovanie. Princzipy', algoritmy', prilozheniya. SPb.: Izd-vo Politexn. un-ta. 2009.
  2. Vasil'ev A.N., Osipov V.P., Tarxov D.A. Unificzirovanny'j proczess modelirovaniya fiziko-texnicheskix ob''ektov s raspredelenny'mi parametrami // Nauchno-texnicheskie vedomosti SPbGPU. Fiziko-matematicheskie nauki. 2010. № 3. S. 39-51.
  3. Vasil'ev A.N., Porubaev F.V., Tarxov D.A. Nejrosetevoj podxod k resheniyu nekorrektny'x zadach teploperenosa. // Nauchno-texnicheskie vedomosti SPbGPU. Informatika. Telekommunikaczii. Upravlenie. 2011. № 1. S. 133-141.
  4. Kolbin I.S., Reviznikov D.L. Reshenie zadach matematicheskoj fiziki s ispol'zovaniem normalizovanny'x radial'no-bazisny'x nejropodobny'x setej // «Nejrokomp'yutery'»: razrabotka, primenenie. 2012. № 2. S. 12-19.
  5. Kolbin I.S. Reshenie staczionarny'x zadach matematicheskoj fiziki s ispol'zovaniem normalizovanny'x radial'no-bazisny'x setej // Nauchno-texnicheskij vestnik Povolzh'ya. Kazan': Nauchno-texnicheskij vestnik Povolzh'ya. 2011. № 5. S. 178-181.
  6. Xajkin S. Nejronny'e seti: polny'j kurs. Izd-e 2-e: per. s angl. M.: Izdatel'skij dom «Vil'yams». 2006. S. 394.
  7. Bugmann G. Normalized Radial Basis Function Networks // Neurocomputing (Special Issue on Radial Basis Function Networks). 1998. V. 20. R. 97-110.
  8. Panteleev A.V., Letova T.A. Metody' optimizaczii v primerax i zadachax. M.: Vy'sshaya shkola. 2008.
  9. Hager W., Zhang H. A new conjugate gradient method with guaranteed descent and an efficient line search // SIAM Journal on Optimization. 2005. V. 16. R. 170-192.
  10. Samarskij A.A., Vabishhevich P.N. Chislenny'e metody' resheniya obratny'x zadach matematicheskoj fiziki. M.: Izd-vo LKI. 2009.
  11. Xie O., Zhao Z. Identifying an unknown source in the Poisson equation by a modified Tikhonov regularization method // International Journal of Mathematical and Computational Sciences. 2012. V. 6. R. 86-90.
  12. Huang C.H., Ozisik M.N. Inverse problem of determining heat flux in laminar flow through a parallel plate duct // Numerical Heat Transfer. Pt. A. 1992. V. 21. R. 55-70.