  Solving the Schr\"odinger equation is key to many quantum mechanical
properties. However, an analytical solution is only tractable for
single-electron systems. Recently, neural networks succeeded at modeling wave
functions of many-electron systems. Together with the variational Monte-Carlo
(VMC) framework, this led to solutions on par with the best known classical
methods. Still, these neural methods require tremendous amounts of
computational resources as one has to train a separate model for each molecular
geometry. In this work, we combine a Graph Neural Network (GNN) with a neural
wave function to simultaneously solve the Schr\"odinger equation for multiple
geometries via VMC. This enables us to model continuous subsets of the
potential energy surface with a single training pass. Compared to existing
state-of-the-art networks, our Potential Energy Surface Network PESNet speeds
up training for multiple geometries by up to 40 times while matching or
surpassing their accuracy. This may open the path to accurate and orders of
magnitude cheaper quantum mechanical calculations.
