Realising reduced order models for heat transfer problems via Data Assimilation and machine learning

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The analysis of time series has received a significant boost from the field of machine learning, where for example dedicated hardware enables training of neural nets to fit the data. Often these NNs can be used as surrogates for expensive numerical or laboratory experiments. However, there are many possibilities for net topology and depth, so that the poor performance of one choice gives little indication as to what might do better, and even if the NN fit is good, it will frequently be unclear whether it can be used for parameters outside the original training set. There is however good evidence that including in the fitting process the information that (magneto-) fluid dynamics underlies the time series phenomena may lead to more comprehensible and robust models. The project will begin by using novel optimization and data assimilation software developed by Leeds and Oxford to identify and validate models of heat transport by time dependent fluid dynamical systems, taken to include idealized models of tokamak plasma. Relevant deficiencies in the software will be identified by comparison with other system identification codes, for example SINDy (Brunton et al) or reservoir computing (Pathak et al 2018). The numerical skills and data analysis experience gained should be useful in general, and in particular for the UK fusion programme.