Abstract: An exemplary system and method using a deep neural network to predict the high-fidelity solutions of a system of differential equations is disclosed. The deep neural network requires input of at least two parts from two or more approximate solutions, each taken from low-cost numerical models that converge toward the exact solution of the differential equations. Each of the parts of the input is a local space-time patch of the corresponding low-cost numerical solution. The neural network predicts high-fidelity solutions to the system of equations as part of the exemplary method and is implemented in the exemplary system.