Geodesic
Entropine-randomized forecasting of the evolution of the area of thermokarst lakes
Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 3, pp. 384-396.

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The article proposes an alternative approach to the existing one in machine learning, which is called randomized forecasting. The approach is based on a randomized parameterized model of the process under study. The structure of the general model of the evolution of the area of the thermokarst lakes is described. To model the area of the thermokarst lakes and the average annual temperature and annual precipitation that affect it, mathematical linear dynamic regression models with random parameters are used. Three types of forecasts are considered: short-term, medium-term and long-term for three permafrost zones (continuous, discontinuous and insular) on the territory of Western Siberia. All results obtained are reproducible within the mean and standard error limits. The test results show that the selected type of the model for randomized forecasting of the evolution of lake areas describes well the dependence of the area of the lakes and leads to low values of relative errors of 0.01–0.02. On the other hand, similar modeling of temperature and precipitation leads to significantly larger errors from 0.08 to 0.22. The resulting forecast of the evolution of the area of the lakes in the permafrost zone under climatic changes is characterized by standard deviations not exceeding 2–4.5 %.
Keywords: thermokarst lakes, remote sensing, information entropy, balance equations, dynamic regression, optimization, Lyapunov problem, sampling, randomized forecasting, randomized machine learning. 
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     author = {Yu. A. Dubnov and V. Yu. Polishchuk and A. Yu. Popkov and E. S. Sokol and A. V. Mel'nikov and Yu. M. Polishchuk and Yu. S. Popkov},
     title = {Entropine-randomized forecasting of the evolution of the area of thermokarst lakes},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {384--396},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_3_a11/}
}
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Yu. A. Dubnov; V. Yu. Polishchuk; A. Yu. Popkov; E. S. Sokol; A. V. Mel'nikov; Yu. M. Polishchuk; Yu. S. Popkov. Entropine-randomized forecasting of the evolution of the area of thermokarst lakes. Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 3, pp. 384-396. http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_3_a11/

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