  There is an urgent need to build models to tackle Indoor Air Quality issue.
Since the model should be accurate and fast, Reduced Order Modelling technique
is used to reduce the dimensionality of the problem. The accuracy of the model,
that represent a dynamic system, is improved integrating real data coming from
sensors using Data Assimilation techniques. In this paper, we formulate a new
methodology called Latent Assimilation that combines Data Assimilation and
Machine Learning. We use a Convolutional neural network to reduce the
dimensionality of the problem, a Long-Short-Term-Memory to build a surrogate
model of the dynamic system and an Optimal Interpolated Kalman Filter to
incorporate real data. Experimental results are provided for CO2 concentration
within an indoor space. This methodology can be used for example to predict in
real-time the load of virus, such as the SARS-COV-2, in the air by linking it
to the concentration of CO2.
