A brief review of Reduced Order Models using intrusive and non-intrusive techniques

TL;DR

This paper reviews various Reduced Order Models (ROMs), including intrusive and non-intrusive techniques, highlighting their applications in reducing computational costs for simulations in control and optimization tasks.

Contribution

It provides a comprehensive overview of ROM techniques such as Galerkin projection, PINN, DDNN, RBF, DMD, and GPR, along with their applications in academic and industrial contexts.

Findings

ROMs significantly reduce computational costs.

Non-intrusive methods like PINN and DMD are effective.

Preliminary industrial application shows promising results.

Abstract

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.