Recent trends in power systems and those envisioned for the next few decades push Transmission System Operators to develop probabilistic approaches to risk estimation. However, current methods to solve power flows are too slow to fully attain this objective. Thus we propose a novel artificial neural network architecture that achieves a more suitable balance between computational speed and accuracy in this context. Improving on our previous work on Graph Neural Solver for Power System [10], our architecture is based on Graph Neural Networks and allows for fast and parallel computations. It learns to perform a power flow computation by directly minimizing the violation of Kirchhoff's law at each bus during training. Unlike previous approaches, our graph neural solver learns by itself and does not try to imitate the output of a Newton-Raphson solver. It is robust to variations of injections, power grid topology, and line characteristics. We experimentally demonstrate the viability of our approach on standard IEEE power grids (case9, case14, case30 and case118) both in terms of accuracy and computational time.