We propose a neural network architecture that emulates the behavior of a physics solver that solves electricity differential equations to compute electricity flow in power grids (so-called "load flow"). Load flow computation is a well studied and understood problem, but current methods (based on Newton-Raphson) are slow. With increasing usage expectations of the current infrastructure, it is important to find methods to accelerate computations. One avenue we are pursuing in this paper is to use proxies based on "graph neural networks". In contrast with previous neural network approaches, which could only handle fixed grid topologies, our novel graph-based method, trained on data from power grids of a given size, generalizes to larger or smaller ones. We experimentally demonstrate viability of the method on randomly connected artificial grids of size 30 nodes. We achieve better accuracy than the DC-approximation (a standard benchmark linearizing physical equations) on random power grids whose size range from 10 nodes to 110 nodes, the scale of real-world power grids. Our neural network learns to solve the load flow problem without overfitting to a specific instance of the problem.