Fast and Accurate Proper Orthogonal Decomposition using Efficient Sampling and Iterative Techniques for Singular Value Decomposition

TL;DR

This paper introduces an efficient iterative sampling algorithm for proper orthogonal decomposition that significantly reduces computation time while maintaining high accuracy, especially for large datasets that cannot fit in memory.

Contribution

It presents a novel iterative sampling and merging approach for POD that improves computational efficiency and accuracy over traditional methods.

Findings

Achieves high-accuracy POD modes with reduced runtime.

Effectively handles large matrices that do not fit in RAM.

Provides theoretical bounds for error introduced by merging operations.

Abstract

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique is used to update the dominant POD modes in each iteration. We derive bounds for the spectral norm of the error introduced by a series of merging operations. We use an existing theorem to get an approximate measure of the quality of subspaces obtained on convergence of the iteration. Results on various datasets indicate that the POD modes and/or the subspaces are approximated with excellent accuracy with a significant runtime improvement over computing the truncated SVD. We also propose a method to compute the POD modes of large matrices that do not fit in the RAM using this iterative sampling and merging algorithms.