Data Assimilation Predictive GAN (DA-PredGAN): applied to determine the spread of COVID-19

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.