pyLOM: A HPC open source reduced order model suite for fluid dynamics applications

TL;DR

This paper introduces pyLOM, an open-source HPC library for fluid dynamics model order reduction, featuring scalable algorithms like POD, DMD, and SPOD optimized for supercomputers, with detailed profiling and validation.

Contribution

The paper presents pyLOM, a high-performance, scalable open-source library implementing reduced order modeling algorithms tailored for supercomputing environments.

Findings

Efficient QR factorization with binary tree communication pattern.

Strong and weak scalability with less than 10% serial part.

POD computation of large datasets in under 81 seconds using 10368 CPUs.

Abstract

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD), as well as, efficient SVD and matrix-matrix multiplication, all of them tailored for supercomputers. The library is profiled in detail under the MareNostrum IV supercomputer. The bottleneck is found to be in the QR factorization, which has been solved by an efficient binary tree communications pattern. Strong and weak scalability benchmarks reveal that the serial part (i.e., the part of the code that cannot be parallelized) of these algorithms is under 10% for the strong scaling and under 0.7% for the weak scaling. Using pyLOM, a POD of a dataset containing 1.14 x 108 gridpoints and 1808 snapshots that takes 6.3Tb of memory can be computed in 81.08 seconds using 10368 CPUs. Additioally, the algorithms are validated using the datasets of a flow around a circular cylinder at ReD = 100 and ReD = 1 x 104, as well as the flow in the Stanford diffuser at Reh = 1 x 104.