Since the beginning of the COVID-19 pandemic in December 2019, the interest in im- proving epidemiological and statistical models has grown in an unprecedented way. It is of global interest to make better estimations and predictions of the future, in order for politics and society to decide which counter measures might be useful to successfully contain the viral spread of a potentially deadly disease. Especially promising for such tasks are methods from the area of machine learning. Not only can machine learning models handle sparse and noisy data when regressing models to real world data, but the statistical framework in which they usually are formulated make them perfect candidates for assessing possible underlying dynamics. In this project we want to evaluate this strength of machine learning by comparing two rather different state-of-the-art models which have already been successfully applied to real-world datasets of the COVID-19 pandemic . The models under investigation are the BayesFlow network, which involves an Invertible Neural Network (INN), and Gaus- sian Process Regression (GPR). Even though Gaussian Processes are, by its nature, parametric-free models and BayesFlows are simulation-based parametric models, both are formulated in the Bayesian framework of probability theory and statistics. It is this feature that make both models appealing for comparison, since both are able to yield uncertainty estimations for their respective predictions. Following this we will be taking a closer look into the classical compartment simulation of infectious diseases, namely the SIR-model and its advancements building upon. It is not only important to understand the dynamics of such a system in order to interpret the results, but also does the BayesFlow depend on the simulation as training samples
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