This paper introduces NeuralSSD, a method for reconstructing 3D implicit surfaces from point cloud data. Utilizing a neural Galerkin approach, NeuralSSD aims to produce high-quality, accurate surfaces. The method addresses limitations in existing implicit field parameterizations by proposing a novel energy equation that balances point cloud information reliability. Additionally, a new convolutional network is introduced to learn three-dimensional information, enhancing optimization results. Evaluations on datasets like ShapeNet and Matterport demonstrate that NeuralSSD achieves state-of-the-art results in surface reconstruction accuracy and generalizability.