Our deep learning method extends considerably the capabilities of previous strategies. In particular, it delivers reliable predictions for tokamaks other than the one on which it was trained. Our approach takes advantage of high-dimensional training data to boost predictive performance while engaging supercomputing resources at the largest scale to improve accuracy and speed. Trained on experimental data from the largest tokamaks, our method can be applied to specific tasks such as prediction with long warning times. This opens up the possibility of moving from passive disruption prediction to active reactor control and optimization. These initial results illustrate the potential for deep learning to accelerate progress in fusion-energy science and, more generally, to the understanding and prediction of complex physical systems.