High-accuracy, high-efficiency physics-based fluid-solid interaction is essential for reality modeling and computer animation in online games or real-time Virtual Reality (VR) systems. However, the large-scale simulation of incompressible fluid and its interaction with the surrounding solid environment is either time-consuming or suffering from the reduced time/space resolution due to the complicated iterative nature pertinent to numerical computations of involved Partial Differential Equations (PDEs). In recent years, we have witnessed significant growth in exploring a different, alternative data-driven approach to addressing some of the existing technical challenges in conventional model-centric graphics and animation methods. This paper showcases some of our exploratory efforts in this direction. One technical concern of our research is to address the central key challenge of how to best construct the numerical solver effectively and how to best integrate spatiotemporal/dimensional neural networks with the available MPM's pressure solvers. In particular, we devise the MPMNet, a hybrid data-driven framework supporting the popular and powerful Material Point Method (MPM), to combine the comprehensive properties of MPM in numerically handling physical behaviors ranging from fluid to deformable solids and the high efficiency of data-driven models. At the architectural level, our MPMNet comprises three primary components: A data processing module to describe the physical properties by way of the input fields; A deep neural network group to learn the spatiotemporal features; And an iterative refinement process to continue to reduce possible numerical errors. The goal of these special technical developments is to aim at involved numerical acceleration while preserving physical accuracy, realizing efficient and accurate fluid-solid interactions in a data-driven fashion. The extensive experimental results verify that our MPMNet can tremendously speed up the computation compared with the popular numerical methods as the complexity of interaction scenes increases while better retaining the numerical accuracy.