Physics-constrained machine learning in unpredictable fluids

The ability of fluid mechanics modelling to predict the evolution of a flow is enabled by physical principles and empirical approaches. Physical principles, for example conservation laws, are extrapolative (until the assumptions upon which they hinge break down): they provide predictions on phenomena that have not been observed. Human beings are excellent at extrapolating knowledge because we are excellent at finding physical principles. Empirical modelling provides correlation functions within data. Artificial intelligence and machine learning are excellent at empirical modelling. In this talk, the complementary capabilities of both approaches will be exploited to achieve adaptive modelling and optimization of nonlinear, unsteady and uncertain flows. The focus of the talk is on computational methodologies for modelling and optimization of increasingly complex flows: (i) data assimilation with a Bayesian approach for controlling thermoacoustic oscillations in rockets/gas turbines, (ii) auto-encoders for reduced-order modelling of turbulent flows, which generalise POD/DMD methods to nonlinear dynamics; and (iii) modelling of multi-phase flows (time permitting). The flows under investigation are relevant to aerospace propulsion, with a focus on thermoacoustics, and turbulence.