Abstract
<title>Abstract</title> <p>Scientific Machine Learning presents an appropriate way of blending mechanistic and data-driven models in the study of nonlinear dynamic systems. In the context of modeling epidemiology, the hybrid modeling approach becomes applicable particularly when there is sufficient knowledge of the mechanism from the structural point of view, but certain processes like transmission dynamics are subject to heterogeneity of contacts, change of behavior, interventions, and measurement noise. This work addresses the problem through comparison of Neural ODEs and Universal ODEs in the traditional Susceptible-Infected-Recovered model. The Neural ODE approach is regarded as a fully data-driven continuous-time model where the whole right-hand side of the system of differential equations is estimated from trajectory data. The UDE approach exploits the known structure of the SIR equations and replaces the infection part with a neural network because of uncertainty. The trajectories of the synthetic epidemiology problem are generated through the SIR equations and contaminated by Gaussian noise in order to assess the predictive abilities, robustness, and data-efficiency of the approaches. The concept of forecast breakdown point is also employed; it describes the minimal size of the training set in order to guarantee the accuracy of the prediction. The results of the numerical simulations show that the UDE approach is more robust and epidemiologically sound in its predictions than the Neural ODE approach in the case of insufficient data availability. However, although the neural ODEs have the ability to reconstruct the trajectories when there is enough information available, their forecasts are not good when there is insufficient information and a lot of noise. Due to the integration of the recovery law that is mechanistic and learning of the transmission term, the UDE model becomes more robust and computationally stable.</p>