Assimptotic numerical method for multidimensional integrals of forecasting of thermokarst lakes

We develop an analytical method for the approximate calculation of multidimensional integrals, focused on solving balance equations in Randomized Machine Learning procedures. The latter are used to forecast the evolution of thermokarst lakes’ area. The method is based on the series expansion of an analytical function – the exponential – and the transformation of multidimensional integrals into the product of simple one-dimensional integrals on interval sets.