Treffer: ELEMENT-WISE MULTIPLICATION OF TENSOR TRAINS.

We present the tensor train multiplication (TTM) algorithm for the elementwise mul-tiplication of two tensor trains with bond dimension X. The computational complexity and memory requirements of the TTM algorithm scale as x³ and x², respectively. This represents a significant improvement compared with the conventional approach, where the computational complexity scales as x⁴ and memory requirements scale as x³. We benchmark the TTM algorithm using flows obtained from artificial turbulence generation and numerically demonstrate its improved runtime and memory scaling compared with the conventional approach. The TTM algorithm paves the way toward GPU accelerated tensor network simulations of computational fluid dynamics problems with large bond dimensions due to its dramatic improvement in memory scaling. [ABSTRACT FROM AUTHOR]

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