Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective in applications like real time control and shape optimization. This contribution aims to provide a brief overview about such a topic. We discuss both an intrusive framework based on a Galerkin projection technique and non-intrusive approaches, including Physics Informed Neural Networks (PINN), purely Data-Driven Neural Networks (DDNN), Radial Basis Functions (RBF), Dynamic Mode Decomposition (DMD) and Gaussian Process Regression (GPR). We also briefly mention geometrical parametrization and dimensionality reduction methods like Active Subspaces (AS). Then we present some results related to academic test cases as well as a preliminary investigation related to an industrial application.

翻译：降阶模型（ROMs）因其能显著降低数值模拟计算成本的能力，近年来受到科学界的广泛关注，这在实时控制和形状优化等应用中是一个关键目标。本文旨在就该主题提供一个简要概述。我们讨论了基于伽辽金投影技术的侵入式框架以及非侵入式方法，包括物理信息神经网络（PINN）、纯数据驱动神经网络（DDNN）、径向基函数（RBF）、动态模态分解（DMD）和高斯过程回归（GPR）。我们还简要提及了几何参数化和降维方法，如主动子空间（AS）。随后，我们展示了与学术测试案例相关的一些结果，以及与一个工业应用相关的初步研究。