Keep the physics in the model if you can: Data assimilation in Fluid Mechanics

Abstract

This talk will show how to assimilate data rigorously into physics-based models using Bayesian inference accelerated with adjoint methods. Adjoint methods are crucial because they provide the derivatives of the model's predictions with respect to the model's parameters. This (i) accelerates data assimilation and (ii) allows uncertainties to be propagated through the model such that posterior uncertainties in parameters are calculated by combining prior uncertainties with measurement uncertainties. Quantification of the uncertainties allows candidate physics-based models to be compared rigorously against each other, allowing the best model to be selected. If the physics of the problem is known, this method is almost certainly better than assimilating data into a Neural Network because physics-based models require less training data, are interpretable, and can extrapolate to situations that share the same physics. This work is inspired by [David MacKay's book](https://www.inference.org.uk/itprnn/book.pdf) on information theory, inference, and learning algorithms. I will present applications in Magnetic Resonance Imaging of flows (flow-MRI) and thermoacoustic oscillations in rockets and aicraft engines. An overview of the talk can be found on my [website](https://mpj1001.user.srcf.net/MJ_inference.html).