Algorithm for identifying parameters of production function models using a neural network

The purpose of the work is to ensure the monitoring and reliability of statistical data used for the analysis and forecasting of the production development on the basis of generalized indicators that take into account the volume of resources used and the ways of their use. An algorithm for parametric identification of production functions models from time series of statistical data using generalized regression, which provides the best estimation of the parametric optimization error by the method of least squares, is proposed. In contrast to existing assessment methods, neural networks are used to build models, which significantly expand the technical capabilities of modeling and contribute to improving the accuracy of calculations through the use of neural network technologies. It is shown that in order to solve the problems of this class, it is advisable to use generalized regression neural networks with simple training modes and high modeling accuracy. As a result, it is possible to propose an algorithm for quantitative assessment of the production functions parameters, which consists in the construction of a neural model with its subsequent use to fit the trajectory of the production model of a given structure to the obtained data by means of recurrent estimates of the vector of the desired coefficients at a given initial approximation. The proposed algorithm is demonstrated by estimating the parameters of the Cobb-Douglas production function and the discrete-dynamic model of the consumption function according to the corresponding statistical series. The calculations are performed using the functions of the Neural Networks package of the MATLAB software environment. The algorithm is applicable for quantitative estimation of the production models parameters with complex logical-probabilistic relationships, as well as for obtaining numerical values of target indicators and indicators for assessing the inland water transport development by statistical series and monitoring.

1. Kolchinskaya, E. E., and S. N. Rastvortseva. “Research of the factors of industrial growth in Russia using the production function.” Russian Journal of Economics and Law 4 (2013): 152–158.

2. Ruzanov, А.I. “Production functions and their use to describe the patterns of production.” Vestnik of Lobachevsky University of Nizhni Novgorod 5–1 (2011): 212–217.

3. Sakharov, V. V., A. A. Kuz’min, and A. A. Chertkov. Modeli i algoritmy optimizatsii tekhnologicheskikh protsessov na ob”ektakh vodnogo transporta v srede MATLAB: monografiya. SPb.: Izd-vo GUMRF im. adm. S. O. Makarova, 2015.

4. Suvorov, N. V., R. R. Akhunov, R. V. Gubarev, Е. I. Dzyuba, and F. S. Fayzullin. “Applying the CobbDouglas Production Function for Analysing the Region’s Industry.” Economy of Regions 16.1 (2020): 187–200. DOI: 10.17059/2020‑l‑14

5. Dmitrienko, D. V. Modeli i algoritmy effektivnoi ekspluatatsii ob”ektov vodnogo transporta. SPb.: Sudostroenie, 2010.

6. Kuboniva, M., M. Tabata, S. Tabata, and Yu. Khasebe. Matematicheskaya ekonomika na personal’nom komp’yutere. Edited by M. Kuboniva and E. Z. Demidenko. M.: Finansy i statistika, 1991.

7. Sidorov, А. V., S. V. Mikheev, and А. А. Osmushin. “Diagnosis of the transport infrastructure using neural networks.” Modern problems of science and education 6 (2013): 215.

8. Sazonov, A.E., and V. V. Deryabin. “Forecasting to paths of the motion ship with the help of neyronnoy network.” Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova 3(22) (2013): 7–13.

9. Deryabin, V. V. “Neural network implementation in vessel’s dead reckoning model.” Ekspluatatsiya morskogo transporta 3(65) (2011): 20–27.

10. Krotov, V. F., B. A. Lagosha, S. M. Lobanov, N. I. Danilina, and S. I. Sergeev. Osnovy teorii optimal’nogo upravleniya. M.: Vysshaya shkola, 1990.