The mechanisms causing widespread flow acceleration of Jakobshavn Isbræ, West Greenland, remain unclear despite an abundance of observations and modeling studies. Here we simulate the glacier's evolution from 1985 to 2016 using a three-dimensional thermomechanical ice flow model. The model captures the timing and 90% of the observed changes by forcing the calving front. Basal drag in the trough is low, and lateral drag balances the ice stream's driving stress. The calving front position is the dominant control on changes of Jakobshavn Isbræ since the ice viscosity in the shear margins instantaneously drops in response to the stress perturbation caused by calving front retreat, which allows for widespread flow acceleration. Gradual shear margin warming contributes 5 to 10% to the total acceleration. Our simulations suggest that the glacier will contribute to eustatic sea level rise at a rate comparable to or higher than at present.