  The recent COVID-19 pandemic has thrown the importance of accurately
forecasting contagion dynamics and learning infection parameters into sharp
focus. At the same time, effective policy-making requires knowledge of the
uncertainty on such predictions, in order, for instance, to be able to ready
hospitals and intensive care units for a worst-case scenario without needlessly
wasting resources. In this work, we apply a novel and powerful computational
method to the problem of learning probability densities on contagion parameters
and providing uncertainty quantification for pandemic projections. Using a
neural network, we calibrate an ODE model to data of the spread of COVID-19 in
Berlin in 2020, achieving both a significantly more accurate calibration and
prediction than Markov-Chain Monte Carlo (MCMC)-based sampling schemes. The
uncertainties on our predictions provide meaningful confidence intervals e.g.
on infection figures and hospitalisation rates, while training and running the
neural scheme takes minutes where MCMC takes hours. We show convergence of our
method to the true posterior on a simplified SIR model of epidemics, and also
demonstrate our method's learning capabilities on a reduced dataset, where a
complex model is learned from a small number of compartments for which data is
available.
