This article presents an innovative open-source software named ModelFLOWs-app, 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 methods 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. These hybrid models combine experimental and numerical database, and serve as accurate alternatives to numerical simulations, effectively diminishing computational expenses, and also as tools for optimization and control. The ModelFLOWs-app software has demonstrated in a wide range of applications its great capability to develop reliable data-driven hybrid ROMs, highlighting its potential in understanding complex non-linear dynamical systems and offering valuable insights into various applications. This article presents the mathematical background, review some examples of applications and introduces a short tutorial of ModelFLOWs-app.

翻译：本文介绍了一款创新的开源软件ModelFLOWs-app，该软件采用Python编写，经创建与测试，可生成完全数据驱动的精确且鲁棒的混合降阶模型。通过以多种方式集成模态分解与深度学习方法，该软件能够揭示动态系统中的基本模式。所获知识随后被用于增强对底层物理过程的理解、从有限测量数据中重建数据库，以及预测系统动态的演化进程。这些混合模型结合了实验与数值数据库，可充当数值模拟的准确替代方案，有效降低计算成本，并可作为优化与控制工具。ModelFLOWs-app软件已在广泛的应用场景中展现出开发可靠数据驱动混合降阶模型的强大能力，突显了其在理解复杂非线性动态系统方面的潜力，并为各类应用提供了宝贵见解。本文介绍了其数学背景，回顾了一些应用实例，并提供了ModelFLOWs-app的简短教程。