Black box approximation in the tensor train format initialized by ANOVA decomposition

Understand

Surrogate models can reduce computational costs for multivariable functions with an unknown internal structure (black boxes).

• In a discrete formulation, surrogate modeling is equivalent to restoring a multidimensional array (tensor) from a small part of its elements.
• The alternating least squares (ALS) algorithm in the tensor train (TT) format is a widely used approach to effectively solve this problem in the case of non-adaptive tensor recovery from a given training set (i.e., tensor completion problem).
• TT-ALS allows obtaining a low-parametric representation of the tensor, which is free from the curse of dimensionality and can be used for fast computation of the values at arbitrary tensor indices or efficient implementation of algebra operations with the black box (integration, etc.).