Before revision:  This papershows that gradient descent can identify a global minimizer of the optimization problem with a well-controlled generalization error in the case of two-layer neural networks in the over-parameterization regime (i. e., the network width is sufficiently large).
After revision:  This papershows that gradient descent can identify a global minimizer of the least-squares optimization for solving second-order linear PDEs with two-layer neural networks in the over-parameterization regime (i. e., the network width is sufficiently large).