# Parallel Tensor Compression for Large-Scale Scientific Data

arXiv: https://arxiv.org/abs/1510.06689 · HTML: https://mlsanity.com/paper/1510.06689/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2015.

## Built on by (most cited first, 4 of 4)

- [F-INR: Functional Tensor Decomposition for Implicit Neural Representations](https://mlsanity.com/paper/2503.21507/) (2025)
- [DPar2: Fast and Scalable PARAFAC2 Decomposition for Irregular Dense Tensors](https://mlsanity.com/paper/2203.12798/) (2022)
- [A rank-adaptive higher-order orthogonal iteration algorithm for truncated Tucker decomposition](https://mlsanity.com/paper/2110.12564/) (2021)
- [Multivariate Scientific Data Compression with Learned Cross-Variable Latent Decorrelation and Autoregressive Entropy Modeling](https://mlsanity.com/paper/2608.30262/) (2026)

## Abstract (arXiv)

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.