Abstract

Reduced order models (ROMs) are crucial for speeding up computational simulations of large-scale systems in a multi-query and real-time setting. They have found application in many scientific fields ranging from fluid dynamics and chemical engineering to structural mechanics and aerodynamics. While ROMs have been studied and used in scientific computing for more than four decades [Ben15S], the advent of modern AI has accelerated its development in recent years. ROMs typically involve an offline or training stage where expensive simulations are performed to build a surrogate model. This is followed by the online or inference stage where the ROM is systematically leveraged to speed up engineering workflows such as design optimization and uncertainty quantification.

This talk will provide an introduction to classical ROMs, covering both intrusive, physics-based approaches and non-intrusive data-driven approaches. Certification of the accuracy of ROMs is crucial as they get adopted more and more in applications. I will discuss robust ways of providing accuracy guarantees [Che20A][Che24A]. Furthermore, through relevant examples, I will demonstrate how error certificates can be leveraged to improve offline/training efficiency through active learning methods. I will also highlight some of the shortcomings of traditional ROMs and how this motivates more ML-flavoured approaches.