Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

Vinicius L S Silva; Claire E Heaney; Yaqi Li; Christopher C Pain

doi:10.1007/s10915-022-02078-1

Data Assimilation Predictive GAN (DA-PredGAN) Applied to a Spatio-Temporal Compartmental Model in Epidemiology

J Sci Comput. 2023;94(1):25. doi: 10.1007/s10915-022-02078-1. Epub 2022 Dec 28.

Authors

Vinicius L S Silva^{1

2}, Claire E Heaney^{1

2}, Yaqi Li², Christopher C Pain^{1

2

3}

Affiliations

¹ Applied Modelling and Computation Group, Imperial College London, London, UK.
² Department of Earth Science and Engineering, Imperial College London, London, UK.
³ Data Assimilation Laboratory, Data Science Institute, Imperial College London, London, UK.

Abstract

We propose a novel use of generative adversarial networks (GANs) (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. We apply these methods to a compartmental model in epidemiology that is able to model space and time variations, and that mimics the spread of COVID-19 in an idealised town. To do this, the GAN is set within a reduced-order model, 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.

Keywords: COVID-19; Compartmental model; Data assimilation; Deep learning; Epidemiology; Generative adversarial networks; Reduced-order model; Spatio-temporal prediction.