Station keeping is an essential maneuver for Autonomous Surface Vehicles (ASVs), mainly when used in confined spaces, to carry out surveys that require the ASV to keep its position or in collaboration with other vehicles where the relative position has an impact over the mission. However, this maneuver can become challenging for classic feedback controllers due to the need for an accurate model of the ASV dynamics and the environmental disturbances. This work proposes a Model Predictive Controller using Neural Network Simulation Error Minimization (NNSEM-MPC) to accurately predict the dynamics of the ASV under wind disturbances. The performance of the proposed scheme under wind disturbances is tested and compared against other controllers in simulation, using the Robotics Operating System (ROS) and the multipurpose simulation environment Gazebo. A set of six tests were conducted by combining two wind speeds (3 m/s and 6 m/s) and three wind directions (0$^\circ$, 90$^\circ$, and 180$^\circ$). The simulation results clearly show the advantage of the NNSEM-MPC over the following methods: backstepping controller, sliding mode controller, simplified dynamics MPC (SD-MPC), neural ordinary differential equation MPC (NODE-MPC), and knowledge-based NODE MPC (KNODE-MPC). The proposed NNSEM-MPC approach performs better than the rest in 4 out of the 6 test conditions, and it is the second best in the 2 remaining test cases, reducing the mean position and heading error by at least 31\% and 46\% respectively across all the test cases. In terms of execution speed, the proposed NNSEM-MPC is at least 36\% faster than the rest of the MPC controllers. The field experiments on two different ASV platforms showed that ASVs can effectively keep the station utilizing the proposed method, with a position error as low as $1.68$ m and a heading error as low as $6.14^{\circ}$ within time windows of at least $150$s.