A GAN-based Reduced Order Model for Prediction, Data Assimilation and Uncertainty Quantification

We propose a new method in which a generative adversarial network (GAN) within a reduced-order model (ROM) framework is used for uncertainty quantification of a numerical physical simulation, considering the presence of measurements. Previously, a method has been developed which enables a GAN to perform time series prediction and data assimilation by training it with unconditional simulations of a discretised partial differential equation (PDE) model. After training, the GAN can be used to predict the spatio-temporal evolution of the physical states and observed data is assimilated. In this paper, we describe the process required in order to quantify uncertainty, during which no additional simulations of the high-fidelity numerical PDE model are required. These methods take advantage of the adjoint-like capabilities of neural networks and the ability to simulate forwards and backwards in time. We apply the proposed approach to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GAN-based ROM can efficiently quantify uncertainty and accurately match the measurements, using only few unconditional simulations of the high-fidelity numerical PDE model.