Accurate forecasts of COVID-19 is central to resource management and building strategies to deal with the epidemic. We propose a heterogeneous infection rate model with human mobility for epidemic modeling, a preliminary version of which we have successfully used during DARPA Grand Challenge 2014. By linearizing the model and using weighted least squares, our model is able to quickly adapt to changing trends and provide extremely accurate predictions of confirmed cases at the level of countries and states of the United States. We show that during the earlier part of the epidemic, using travel data increases the predictions. Training the model to forecast also enables learning characteristics of the epidemic. In particular, we show that changes in model parameters over time can help us quantify how well a state or a country has responded to the epidemic. The variations in parameters also allow us to forecast different scenarios such as what would happen if we were to disregard social distancing suggestions.