Title: Deep Semi-Supervised 3D Shape Reconstruction by Solving a Poisson Equation with Spectral Methods. Abstract: In this paper we propose a deep learning method for unsupervised 3D implicit shape reconstruction from point clouds. Our goal is to approximate 3D shapes as the iso-surface of a scalar field that is the solution of a Poisson partial differential equation. We propose neural network architecture that learns the distance field in the Fourier domain, and solve the PDE by using spectral differentiation through two novel loss functions. Our experiments show that our architecture can efficiently learn the Fourier coefficients while accurately estimating the target distance field. We train our models without any ground truth mesh, scalar distance field values, or surface normals.