MODULO: A Python toolbox for data-driven modaldecomposition

Dimensionality reduction is an essential tool in processing large datasets, enabling data compression, pattern recognition, and reduced-order modeling. Many linear tools for dimensionality reduction have been developed in fluid mechanics, where they have been formulated to identify coherent structures and build reduced-order models of turbulent flows (Ranc et al., 2014). This work proposes a major upgrade of the software package MODULO (MODal mULtiscale pOd) (Ninni & Mendez, 2020), which was designed to perform Multiscale Proper Orthogonal Decomposition (mPOD) (Mendez et al., 2019). In addition to implementing the classic Fourier Transform (DFT) and Proper Orthogonal Decomposition (POD), MODULO now also allows for computing Dynamic Mode Decomposition (DMD) (Schmid, 2010) as well as the Spectral POD by Sieber et al. (2016), the Spectral POD by Towne et al. (2018) and a generalized kernel-based decomposition akin to kernel PCA (Mendez, 2023). All algorithms are wrapped in a ‘SciKit’-like Python API, which allows computing all decompositions in one line of code. Documentation, exercises, and video tutorials are also provided to offer a primer on data drive modal analysis.