ModelFLOWs-app: Data-driven post-processing and reduced order modelling tools

This article presents an innovative open-source software named ModelFLOWs-app,1 written in Python, which has been created and tested to generate precise and robust hybrid reduced order models (ROMs) fully data-driven. By integrating modal decomposition and deep learning in diverse ways, the software uncovers the fundamental patterns in dynamic systems. This acquired knowledge is then employed to enrich the comprehension of the underlying physics, reconstruct databases from limited measurements, and forecast the progression of system dynamics. The hybrid ROMs produced by ModelFLOWs-app combine experimental and numerical databases, serving as highly accurate alternatives to numerical simulations. As a result, computational expenses are significantly reduced, and the models become powerful tools for optimization and control in various applications. The exceptional capability of ModelFLOWs-app in developing reliable data-driven hybrid ROMs has been demonstrated across a wide range of applications, making it a valuable resource for understanding complex nonlinear dynamical systems and providing insights in diverse domains. This article presents the mathematical background, as well as a review of some examples of applications.