The classical scientific approach is to identify the pertinent physics of a problem, build an appropriate model, perform some appropriate analysis, and test the model experimentally. For engineering problems, this often produces a qualitatively-accurate model but rarely produces a quantitatively-accurate model. For engineers who would like to use a model to optimize the design of a system, however, the model needs to be reliable enough to be a quantitatively-accurate representation of the physics but small enough that it can produce results on a useful timescale.
This talk explores one way to do this, illustrated by the problem of thermoacoustic instability. This is a scientific phenomenon whose physics is qualitatively well understood but for which low order models are not accurate enough to be useful for design. The aim of the talk is to show how we build a quantitatively-accurate model by assimilating tens of thousands of experimental datapoints using first and second order adjoint methods applied to the model. It will show the formal link between this technique and other well-known techniques such as the Kalman Filter and Markov Chain Monte Carlo. Finally, it will show how to determine the best model, and that this may not be the most detailed model.