Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to overcome this problem. Tensor-train decomposition of a tensor approximating the integrand is constructed and used to evaluate a multivariate quadrature formula. We show how to deal with singularities in the integration domain and conduct theoretical analysis of the integration accuracy. The reference open-source implementation is provided.

翻译：数字融合是许多科学领域出现的一个典型问题,由于象形节点数目的指数增长,无法以传统方法处理多变融合问题。我们提出了解决这一问题的方法。建造了接近正方位的数方位的电离-电离分解,用于评价多变方位方位公式。我们展示了如何处理集成域的奇点,并对集成精度进行理论分析。我们提供了参考开源实施。