Title: Learning Lagrangian Fluid Dynamics with Graph Neural Networks. Abstract: We present a data-driven model for fluid simulation under Lagrangian representation. Our model uses graphs to describe the fluid field, where physical quantities are encoded as node and edge features. Instead of directly predicting the acceleration or position correction given the current state, we decompose the simulation scheme into separate parts - advection, collision, and pressure projection. For these different reasoning tasks, we propose two kinds of graph neural network structures, node-focused networks, and edge-focused networks. By introducing physics prior knowledge, our model can be efficient in terms of training and inference. Our tests show that the learned model can produce accurate results and remain stable in scenarios with a large amount of particles and different geometries. Unlike many previous works, further tests demonstrate that our model is able to retain many important physical properties of incompressible fluids, such as minor divergence and reasonable pressure distribution. Additionally, our model can adopt a range of time step sizes different from ones using in the training set, which indicates its robust generalization capability.