Reduced-communication parallel dynamic mode decomposition

A new reduced-communication parallel algorithm for deterministic dynamic mode decomposition of large datasets on distributed memory architectures is presented, which has notable savings in computational and communication costs. The parallel algorithm relies on horizontal-slicing and parallel Tall and Skinny QR factorisation to compress the high-dimensional snapshot data. The compressed snapshot data is used to construct the Koopman operator using an embarrassingly parallel approach, resulting in only one communication step for the entire parallel algorithm. The computation of the orthonormal matrix during the parallel QR factorisation is avoided for time-series data, leading to significant savings in computational costs. Numerical tests on highfidelity computational fluid dynamics data show that the current algorithm is up to 2.5 times faster than existing parallel approaches without sacrificing accuracy.

Automated summary

The parallel algorithm proposed in this study reduces communication costs for deterministic dynamic mode decomposition of large datasets, achieving notable savings in computational costs as well. By compressing high-dimensional snapshot data using horizontal-slicing and parallel Tall and Skinny QR factorisation, the algorithm constructs the Koopman operator with only one communication step. Additionally, avoiding the computation of the orthonormal matrix during the parallel QR factorisation results in significant computational savings, making the current algorithm up to 2.5 times faster than existing parallel approaches without sacrificing accuracy.