In this presentation, we propose a novel deep learning framework for surface reconstruction from unorganized point clouds by leveraging implicit surface representations via level set functions. Our method guarantees watertightness and exhibits robust adaptability to varying topologies. The core of our approach involves solving a p-Poisson equation to learn the signed distance function (SDF) with high precision, facilitated by a variable splitting strategy that introduces the SDF gradient as an auxiliary field. To further enhance the physical plausibility and stability of the reconstruction, we impose a curl-free constraint on the auxiliary variable, reflecting the irrotational property of conservative vector fields. Extensive numerical experiments demonstrate that the proposed integration of partial differential equation modeling and vector field constraints enables accurate and topologically consistent surface reconstruction, without requiring any predefined geometric priors.