Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910380505169920 |
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| author | Ritter, Marc K. Fernández, Yuriel Núñez Wallerberger, Markus von Delft, Jan Shinaoka, Hiroshi Waintal, Xavier |
| author_facet | Ritter, Marc K. Fernández, Yuriel Núñez Wallerberger, Markus von Delft, Jan Shinaoka, Hiroshi Waintal, Xavier |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11819 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond Ritter, Marc K. Fernández, Yuriel Núñez Wallerberger, Markus von Delft, Jan Shinaoka, Hiroshi Waintal, Xavier Computational Physics Strongly Correlated Electrons Quantum Physics 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. |
| title | Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond |
| topic | Computational Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2303.11819 |