Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities

no code implementations • 23 Oct 2020 • Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen, Christoph Schwab

We prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in $H^1(\Omega)$ for weighted analytic function classes in certain polytopal domains $\Omega$, in space dimension $d=2, 3$.