Twelve climate models and observations are used to attribute the global mean surface temperature (GMST) changes from 1900 to 2014 to external climate forcings. The external forcings are decomposed into the effects of the well-mixed greenhouse gas concentration variation, the effects of anthropogenic aerosol concentration changes, and the effects of natural forcings. First, a convolutional neural network (CNN) is trained to estimate the simulated historical GMST from single-forcing experiments using outputs from the multi-model ensemble. We then use this CNN to solve the attribution problem using an original variational inversion approach. The variational inversion is first validated using historical climate simulations as pseudo-observations. Then we perform an inversion from observations. This provides a distribution of the GMST resulting from the three forcings. For 2014, inversions estimate that the greenhouse gases changes are responsible for a GMST anomaly within [0.8 $ {}^{\circ } $ C,1.9 $ {}^{\circ } $ C], while anthropogenic aerosols and natural forcings anomalies are within [−0.7 $ {}^{\circ } $ C,−0.1 $ {}^{\circ } $ C] and [−0.1 $ {}^{\circ } $ C,0.3 $ {}^{\circ } $ C], respectively. The method designed here can be adapted and extended to attribute the changes of other variables or to focus on the regional scale.