Among advanced manufacturing techniques for fiber-reinforced polymer-matrix composites (FRPCs) which are critical for aerospace, marine, automotive, and energy industries, frontal polymerization (FP) has been recently proposed to save orders of magnitude of time and energy. However, the cure kinetics of the matrix phase, usually a thermosetting polymer, brings difficulty to the design and control of the process. Here, we develop a deep learning model, ChemNet, to solve an inverse problem for predicting and optimizing the cure kinetics parameters of the thermosetting FRPCs for a desired fabrication strategy. ChemNet consists of a fully connected FeedForward 9 layer deep neural network trained on one million examples, and predicts activation energy and reaction enthalpy given the front characteristics such as speed and maximum temperature. ChemNet provides highly accurate predictions measured by the mean squared error (MSE) and by the maximum absolute error (MAE) metrics. ChemNet's performance on the "hidden" test data set had an MSE of 5.58 X 10(-6) and a MAE of 1 X 10(-3).