  In recent years, there are numerous methods involving neural networks for
solving partial differential equations (PDEs), such as Physics informed neural
networks (PINNs), Deep Ritz method (DRM) and others. However, the optimization
problems are typically non-convex, which makes these methods lead to
unsatisfactory solutions. With weights sampled from some distribution, applying
random neural networks to solve PDEs yields least squares problems that are
easily solvable. In this paper, we focus on Barron type functions and
demonstrate the approximation, optimization and generalization of random neural
networks for solving PDEs.
