Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems
CNNs approximate manifold functions and derivatives with rates based on intrinsic dimension.
This paper shows convolutional neural networks (CNNs) can approximate functions and their derivatives on compact Riemannian manifolds. Approximation rates depend on the manifold's intrinsic dimension and smoothness, not ambient space. Results apply to solving elliptic boundary value problems.