An HPC Approach to Accelerate Tensor Decompositions

2026-08-25

AI Summary

本文针对高维数据处理难题，提出一种新的基于CUDA的Jacobi型张量分解算法，并在NVIDIA H100 GPU上验证其有效性及高效性。

Abstract

Quantum systems grow in complexity so rapidly that even modest models become difficult to simulate, creating a strong need for methods that can handle high-dimensional data, also known as tensors. In this work, we investigate a novel Jacobi-type tensor algorithm for tensor decomposition and develop a CUDA-based algorithm that supports tensors of arbitrary order on a single GPU. We test the implementation on NVIDIA H100 GPUs and show that the algorithm converges correctly for diagonalizable tensors up to nine dimensions, with runtime scaling in a predictable way as tensor order grows. Finally, our general algorithm outperforms the original MATLAB reference by more than two orders of magnitude.

Problem

• high-dimensional data
• tensors
• quantum systems
• simulation

Innovation

• CUDA-based algorithm
• arbitrary order tensors
• predictable runtime scaling
• two orders of magnitude performance improvement