When computations of the dynamic behavior of a digital twin includes the recursion of an internal state, data assimilation can be used to adjust the numerical values of the state. The optimal linear adjustment of this state on the basis of observations and simulations is known as a Kalman filter, in which an optimal linear gain is computed based on covariance information to minimize the variance on the state error. This paper illustrates that such covariance information can be learned and used to find an optimal trade-off between the observations and simulations for state adjustment. Although the concept of learning covariance information is well understood by the Ensemble Kalman Filter (EnKF), this paper emphasizes the underlying approach how to learn covariance information with the purpose of convergence and minimal variance of the state error. The concept is illustrated for a dynamic digital twins of a linear oscillatory mechanical system and a non-linear dynamic wildfire progression. The examples illustrate that the results on data assimilation heavily depends on the quality of the covariance information.