Department of Mechanical and Aerospace Engineering Seminar - Predicting Turbulent Systems from Limited Measurements: Classical Methods to Machine Learning

The study of fluid mechanics is undergoing a transformation due to recent advancements in measurement techniques and computational power. As a result, data assimilation and neural networks can now be utilized to forecast increasingly complex turbulent flows. However, it remains unclear under what conditions these data-driven methods can be effective and what role classical methods can still play. This seminar will analyse three main predictive methods: linearised (low- rank approximation) models, data assimilation, and model-free neural networks. On the one hand, linearised models require little measurement data but necessitate deep understanding of system dynamics. On the other hand, model-free networks require high-resolution space-time measurement data but require minimal knowledge of system dynamics. I will demonstrate that the measurement conditions required for effective application of data-driven methods, whether model-free or model- based, are closely related to complexity measures from chaos theory. These findings can guide the systematic collection of data and selection of predictive methods for turbulence forecasting in practical systems.