Before revision:  The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to one of lower frequency , and the compact support activation functions facilitate the separation of scales to be approximated by corresponding DNNs.
After revision:  The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to a problem of learning about lower frequency functions , and the compact support activation functions facilitate the separation of scales to be approximated by corresponding DNNs.