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arXiv · 2303.11819

Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond

Marc K. Ritter·Yuriel Núñez Fernández·Markus Wallerberger·Jan von Delft·Hiroshi Shinaoka·Xavier Waintal
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Abstract

Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional dependence, versus parsimonious memory usage. Recently, two promising strategies have emerged for satisfying both requirements: (i) The quantics representation, which expresses functions as multi-index tensors, with each index representing one bit of a binary encoding of one of the variables; and (ii) tensor cross interpolation (TCI), which, if applicable, yields parsimonious interpolations for multi-index tensors. Here, we present a strategy, quantics TCI (QTCI), which combines the advantages of both schemes. We illustrate its potential with an application from condensed matter physics: the computation of Brillouin zone integrals.

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Marc K. Ritter, Yuriel Núñez Fernández, Markus Wallerberger, Jan von Delft, Hiroshi Shinaoka, Xavier Waintal. 2023-03-21. Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond. https://doi.org/10.1103/physrevlett.132.056501

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