Quantics Tensor Cross Interpolation for High-Resolution Parsimonious Representations of Multivariate Functions

Area of Science:

• Computational physics
• Applied mathematics

Background:

• Multivariate functions are essential in science but pose computational challenges regarding accuracy and memory.
• Existing methods like quantics representation and tensor cross interpolation (TCI) offer partial solutions.

Purpose of the Study:

• To present a novel computational strategy, quantics TCI, that integrates the strengths of quantics representation and TCI.
• To demonstrate the efficacy of quantics TCI in a practical scientific application.

Main Methods:

• The quantics representation encodes functions as multi-index tensors, using binary representations of variables.
• Tensor cross interpolation (TCI) provides a method for parsimonious tensor approximation.
• The proposed quantics TCI strategy combines these two techniques.

Main Results:

• Quantics TCI successfully merges the benefits of quantics representation and TCI.
• The method is demonstrated to be effective for computing Brillouin zone integrals in condensed matter physics.

Conclusions:

• Quantics TCI offers a powerful new tool for the accurate and memory-efficient computation of multivariate functions.
• This method has significant potential for applications in various scientific domains, including condensed matter physics.