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Tensor Train Multiplication

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arxiv 2410.19747 v2 pith:3TJNFJ7C submitted 2024-10-10 physics.comp-ph quant-ph

Alexios A Michailidis , Christian Fenton , Martin Kiffner This is my paper · ORCID
classification physics.comp-phquant-ph
keywords algorithmmemorytensorcomputationalmultiplicationapproachbondcompared
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We present the Tensor Train Multiplication (TTM) algorithm for the elementwise multiplication of two tensor trains with bond dimension $\chi$. The computational complexity and memory requirements of the TTM algorithm scale as $\chi^3$ and $\chi^2$, respectively. This represents a significant improvement compared with the conventional approach, where the computational complexity scales as $\chi^4$ and memory requirements scale as $\chi^3$.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 towards GPU accelerated tensor network simulations of computational fluid dynamics problems with large bond dimensions due to its dramatic improvement in memory scaling.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations

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    A lattice Boltzmann solver whose fluid state is stored as matrix product states reproduces reference LBM results for 3D Taylor-Green, aneurysm and pin-fin flows, reaching ~120x compression for translationally structured flow.

  2. Quantics Tensor Train for solving Gross-Pitaevskii equation

    cond-mat.quant-gas 2025-07 conditional novelty 6.0 of 10

    A quantics tensor train framework solves the 1D Gross-Pitaevskii equation, including multi-species and long-range interactions, with polylogarithmic scaling of storage and operations.

  3. Quantum Solvers: Predictive Aeroacoustic & Aerodynamic modeling

    quant-ph 2025-07 conditional novelty 4.0 of 10

    The paper archives a winning Airbus/BMW challenge solution that compresses CFD operators into matrix product states and quantum circuits, reporting 0.1%-accurate cylinder flow at compression greater than 10.

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