PhD Seminar Series: “Between order and randomness: the challenge of modeling a complex world”

Abstract: 

As engineers, we are often faced with challenging phenomena which require modeling. Our task is to reduce their complexity into tractable mathematical or computational representations which provide predictive skill at a reasonable cost. But this common problem of engineering practice brings with it a profound dichotomy: if simplicity comes at a cost in predictive skill, how much of the inherent complexity of a phenomenon can we discard and still be successful? This fundamental question connects engineering with the principle driving science: Occam’s Razor. This axiom states that models should be free of unnecessary elements, urging the engineer to find optimal solutions in the trade-off between model complexity and predictive skill. In this talk, we will review these ideas with focus on the problem of forecasting in complex systems such as turbulence. We will see how the intuitive notion of complexity–something between strict order and complete randomness–can be suitably defined using information theory and used to design a robust implementation
of Occam’s Razor. This framework is applied to the problem of extreme-event prediction in turbulence to show that there is a lower bound to the simplest model that can be constructed to make successful predictions. It will be argued that this limit is directly imposed by the fundamental complexity of turbulence, which appears as a key aspect in the design of predictive models. From a general engineering perspective, these results show that some measure of complexity is necessary to know what to expect when constructing models, particularly in the context of data-driven, physics-agnostic methods.