Copper has always been used in thermoelectric applications due to its extensive properties among metals. However, it requires further improving its heat transport performance at the nanosized applications by supporting another high thermal conductivity material. Herein, copper was coated with graphene, and the neural network fitting was employed for the nonequilibrium molecular dynamics simulations of graphene-coated copper nanomaterials to predict thermal conductivity. The Langevin thermostat that was tuned with a neural network fitting, which makes up the backbone of deep learning, generated the temperature difference between the two ends of the models. The neural network fitting calibrated the Langevin thermostat damping constants that helped to control the temperatures precisely. The buffer and thermostat lengths were also analyzed, and they have considerable effects on the thermostat temperatures and a significant impact on the thermal conductivity of the graphene-coated copper. Regarding thermal conductivity, the four different shapes of vacancy defect concentrations and their locations in the graphene sheets were further investigated. The vacancy between the thermostats significantly decreases the thermal conductivity; however, the vacancy defect in thermostats does not have a similar effect. When the graphene is placed between two copper blocks, the thermal conductivity decreases drastically, and it continues to drop when the sine wave amplitude on the graphene sheet increases.