A brief review of reduced order models using intrusive and non‐intrusive techniques

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 a classic intrusive framework based on a Galerkin projection technique and hybrid/non-intrusive approaches, including Physics Informed Neural Networks (PINN), purely Data-Driven Neural Networks (NN), 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 (ASs). Then we test the performance of such approaches in terms of efficiency and accuracy against three academic test cases, the lid driven cavity, the flow past a cylinder and the geometrically parametrized Stanford Bunny. Moreover, we also briefly present some preliminary results related to a more complex case involving an industrial application.