The study of free surface fluid flows is of significant interest across various research fields, including civil, aerospace, and biomedical engineering. Among the numerical methods used to address free surface problems, the Particle Finite Element Method (PFEM) stands out as a robust and efficient approach. PFEM solves the governing equations using the standard finite element method while addressing mesh distortion through a fast and efficient remeshing procedure. In recent years, deep learning (DL) algorithms have demonstrated remarkable successes in learning from examples, and their application to datasets generated from numerical simulations could result in surrogate models able to reduce the computational cost of classical numerical methods. In the context of free surface fluid simulations, particularly noteworthy are attempts to employ Graph Neural Networks (GNNs), given their ability to process unstructured data that cannot be represented as structured grids, typical of these applications. Graph Neural Simulator (GNS) is a notable example of a GNN surrogate for particle-based simulations that learns the time update of the system. The GNS is purely particle based and therefore the graph structure must be computed at each time step during both training and prediction phases. Following this line of research, we propose NeuralPFEM (NPFEM), a GNN based approach for surrogate modelling of PFEM free surface fluid simulations. NPFEM inherits from the PFEM the hybrid nature between a particle based and a mesh based method. During training, NPFEM uses the mesh connectivity to build the graph. During prediction, it leverages PFEM’s mesh generation algorithm and particle redistribution tool to build the graph and to ensure a more homogeneous particle distribution within the domain. This allows to preserve the quality of the mesh to mitigate undesired effects like particle clustering. We evaluate the results both qualitatively and quantitatively, comparing them with those obtained both from PFEM and GNS. Moreover, we compute physical quantities out of the learned solution. In particular, the mesh structure, combined with the joint prediction of the velocity and the pressure fields, enables the calculation of forces and stresses, a first step in the direction of applying this kind of tools to Fluid-Structure Interaction (FSI) problems.