ИСТИНА

This work observes a neural network approach to the numerical integration of multiple integrals and its programming implementation as a Python programming language library “Skuld”. The approach concludes to a two-step pipeline of training a neural network model to approximate the integrand and using the model’s parameters to calculate the value of the integral numerically. While common numerical methods suffice low-dimensional integration problems, the integration of 3-, 4- and higher-dimensional integrands introduce significant computational and precision difficulties. The observed approach should solve the time-complexity of high-dimensional integration by decreasing the complexity of integration itself and performing the complex part while training the model. This can perfectly suit the cases where the same functions are integrated over varying domains, allowing the model to be trained once and reused multiple times. The work details the mathematical foundation of the approach and its software implementation: the “Skuld” library, which was validated using Genz's test functions package and was applied for calculations within the framework of a physics problem: modeling meson properties in a QCD-motivated model with separable interaction kernel for the NICA experiment.