Abstract

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.

中文翻译：

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具有奇异性的多元函数的张量训练数值积分

摘要

数值积分是许多科学领域中出现的经典问题。由于正交节点的数量呈指数增长，因此经典方法无法实现多元积分。我们提出了一种方法来克服这个问题。构造逼近被积函数的张量的张量训练分解并用于评估多元求积公式。我们展示了如何处理积分域中的奇点并对积分精度进行理论分析。提供了参考开源实现。