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Quantics-TT approximation on a class of multivariate functions
Keywords: High dimensional problems; Multivariate functions; Quantics tensor train format
Wed, 14:25--14:50
  • Khoromskij, Boris (Scientific Computing, Max-Planck Institute for Mathematics in the Sciences, Germany)

Modern methods of rank-structured tensor decomposition allow an efficient separable approximation on a class of multivariate functions and operators, providing linear complexity scaling in the dimension. In particular, the recent quantics-TT (QTT) matrix product states technique is proved to provide the super-compressed representation of high-dimensional data with log-volume complexity. We discuss the asymptotically optimal QTT-rank bounds for a class of multivariate functions, substantiating the computational background of the idea of quantics folding to higher dimensions. The explicit QTT expansions for a family of function generated vectors/tensors will be presented. The theory is supported by numerical illustrations in electronic structure calculations, quantum molecular dynamics and stochastic PDEs.