Construction of approximate neural network models according to heterogeneous data
Matematičeskoe modelirovanie, Tome 19 (2007) no. 12, pp. 43-51.

Voir la notice de l'article provenant de la source Math-Net.Ru

Neural network approach to the robust mathematical model construction according to heterogeneous pieces of information (equations, conditions, experimental data, etc.) is considered. The case of ordinary differential equations and the case of partial differential equations and possible generalizations as well are key problems in the paper. Some model examples are given.
@article{MM_2007_19_12_a4,
     author = {A. N. Vasilyev and D. A. Tarkhov},
     title = {Construction of approximate neural network models according to heterogeneous data},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {43--51},
     publisher = {mathdoc},
     volume = {19},
     number = {12},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_12_a4/}
}
TY  - JOUR
AU  - A. N. Vasilyev
AU  - D. A. Tarkhov
TI  - Construction of approximate neural network models according to heterogeneous data
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 43
EP  - 51
VL  - 19
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_12_a4/
LA  - ru
ID  - MM_2007_19_12_a4
ER  - 
%0 Journal Article
%A A. N. Vasilyev
%A D. A. Tarkhov
%T Construction of approximate neural network models according to heterogeneous data
%J Matematičeskoe modelirovanie
%D 2007
%P 43-51
%V 19
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2007_19_12_a4/
%G ru
%F MM_2007_19_12_a4
A. N. Vasilyev; D. A. Tarkhov. Construction of approximate neural network models according to heterogeneous data. Matematičeskoe modelirovanie, Tome 19 (2007) no. 12, pp. 43-51. http://geodesic.mathdoc.fr/item/MM_2007_19_12_a4/

[1] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, Editorial URSS, M., 2004

[2] Vasilev A. N., Tarkhov D. A., “Neirosetevoi podkhod k resheniyu nekotorykh neklassicheskikh zadach matematicheskoi fiziki”, Sbornik nauchnykh trudov VII Vserossiiskoi nauchno-tekhnicheskoi konferentsii “Neiroinformatika-2005”, Ch. 2, MIFI, M., 2005, 52–60

[3] Vasilev A. N., Tarkhov D. A., “Neirosetevaya metodologiya postroeniya priblizhennykh reshenii differentsialnykh uravnenii po eksperimentalnym dannym”, Intellektualnye i mnogoprotsessornye sistemy, Materialy mezhdunarodnoi konferentsii. T. 2, Taganrog-Donetsk-Minsk, 2005, 219–223

[4] Troitskii V. A., Optimization Approaches to Some Observation Problems for PDE, http://www.inftech.webservis.ru

[5] Tarkhov D.A., Neironnye seti: modeli i algoritmy, Radiotekhnika, M., 2005

[6] Ivakhnenko A. G., Yurachkovskii Yu. P., Modelirovanie slozhnykh sistem po eksperimentalnym dannym, Radio i svyaz, M., 1987