Sridhar Chellappa will introduce the concept of reduced order modeling (ROM), a technique used in the field of simulation and AI to reduce the complexity of mathematical models. The seminar will cover the basics of ROM, its applications, and a lead up to more ML-flavoured approaches.AbstractReduced order models (ROMs) are crucial for speeding up computationalsimulations of large-scale systems in a multi-query and real-time setting. Theyhave found application in many scientific fields ranging from fluid dynamics andchemical engineering to structural mechanics and aerodynamics. While ROMs havebeen studied and used in scientific computing for more than four decades [Ben15S], the advent of modern AI has accelerated itsdevelopment in recent years. ROMs typically involve an offline or training stagewhere expensive simulations are performed to build a surrogate model. This isfollowed by the online or inference stage where the ROM is systematicallyleveraged to speed up engineering workflows such as design optimization anduncertainty quantification.This talk will provide an introduction to classical ROMs, covering bothintrusive, physics-based approaches and non-intrusive data-driven approaches.Certification of the accuracy of ROMs is crucial as they get adopted more andmore in applications. I will discuss robust ways of providing accuracyguarantees [Che20A][Che24A]. Furthermore, through relevant examples, I willdemonstrate how error certificates can be leveraged to improve offline/trainingefficiency through active learning methods. I will also highlight some of theshortcomings of traditional ROMs and how this motivates more ML-flavouredapproaches.
