Parallel Tensor Compression for Large-Scale Scientific Data

TL;DR

This paper introduces a distributed-memory parallel Tucker decomposition method for compressing massive scientific data represented as tensors, achieving high compression ratios with negligible accuracy loss on real-world datasets.

Contribution

It presents the first distributed-memory parallel implementation of Tucker decomposition tailored for large-scale scientific data, with optimized data distribution avoiding data redistribution.

Findings

Achieves compression ratios up to 5000 with minimal accuracy loss.

Demonstrates scalable parallel performance on real-world datasets.

Provides analysis of computation and communication costs.

Abstract

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8~TB of data, assuming double precision. By viewing the data as a dense five-way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 5000 on real-world data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed-memory parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. We provide accompanying analysis of the computation and communication costs of the algorithms. To demonstrate the compression and accuracy of the method, we apply our approach to real-world data sets from combustion science simulations. We also provide detailed performance results, including parallel performance in both weak and strong scaling experiments.