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.本文介绍一款采用Python语言编写的创新型开源软件ModelFLOWs-app¹，该软件经开发与测试验证，可生成精准可靠的全数据驱动混合降阶模型（reduced order models，ROM）。该软件通过多种方式融合模态分解与深度学习技术，挖掘动力学系统的内在基本规律。所习得的这些规律可用于深化对系统内在物理机制的理解、从有限测量数据中重建数据库，以及预测系统动力学的演化进程。ModelFLOWs-app生成的混合降阶模型融合实验与数值数据库，可作为数值模拟的高精度替代方案，由此大幅降低计算开销，使其成为各类应用场景中优化与控制的强力工具。ModelFLOWs-app在构建可靠全数据驱动混合降阶模型方面的卓越性能已在众多应用场景中得到验证，使其成为理解复杂非线性动力学系统的宝贵资源，并可为多领域研究提供重要见解。本文同时介绍了相关数学背景，并对部分应用案例进行了综述。