Mathematics is closely related to the theory and algorithms of AI and machine learning. In this talk, we investigate how deep neural networks (DNNs) can be used in the forward-inverse problems of PDEs. We develop a loss function that guides neural networks to find solutions of PDEs more efficiently. Second, we look into real-world implications of a rapidly-responsive COVID-19 spread model via deep learning. The methodology could also be employed for short-term prediction of COVID-19, which could help the government prepare for a new outbreak.