Data assimilation with machine learning for dynamical systems: Modelling indoor ventilation

Data assimilation is a method of combining physical observations with prior knowledge (for instance, a computational simulation) in order to produce an improved estimate of the state of a system; that is, improved over what the physical observations or the computational simulation, alone, could offer. Recently, machine learning techniques have been deployed in order to address the significant computational burden that is associated with the procedures involved in data assimilation. In this paper we propose an approach that uses a non-intrusive reduced-order model (NIROM) as a surrogate for a high-resolution model thereby saving computational effort. The mismatch between observations and the surrogate model is propagated forwards and backwards in time in a manner similar to 4D-variational data assimilation methods. The observations and prior are reconciled in a new way which takes full advantage of the neural network used in the NIROM and also means that there is no need to form the sensitivities explicitly when propagating the mismatch. Instead, the observations are part of the input and output of the network. The key advantages of this data assimilation approach are its simplicity (as we can avoid differentiating the forward model and bypass the use of an optimisation method), and its ability to integrate with control and uncertainty quantification methodologies. Modelling the air quality in a school classroom is the test case for our demonstration. After comparing the proposed data assimilation approach with 4D Variational Data Assimilation, we investigate two scenarios. The first of these is a dual-twin type experiment, for which the proposed approach is shown to perform very well, and the second is a test case which assimilates predictions from the NIROM with observations collected from a classroom in Houndsfield Primary School.