  We propose the novel use of a generative adversarial network (GAN) (i) to
make predictions in time (PredGAN) and (ii) to assimilate measurements
(DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like
properties of generative models and the ability to simulate forwards and
backwards in time. GANs have received much attention recently, after achieving
excellent results for their generation of realistic-looking images. We wish to
explore how this property translates to new applications in computational
modelling and to exploit the adjoint-like properties for efficient data
assimilation. To predict the spread of COVID-19 in an idealised town, we apply
these methods to a compartmental model in epidemiology that is able to model
space and time variations. To do this, the GAN is set within a reduced-order
model (ROM), which uses a low-dimensional space for the spatial distribution of
the simulation states. Then the GAN learns the evolution of the low-dimensional
states over time. The results show that the proposed methods can accurately
predict the evolution of the high-fidelity numerical simulation, and can
efficiently assimilate observed data and determine the corresponding model
parameters.
