The use of deep learning methods for solving high-dimensional PDEs has gained significant attention recently. In the first part of this talk, I will present some theoretical analysis from the perspective of deep non-parametric estimation for the main deep solvers in the literature, namely DRMs, PINNs and WANs. In the second part of the talk, I will introduce a novel method called Gaussian Mixture Distribution-based Adaptive Sampling (GAS) for PINNs, which aims to boost their accuracy.