34 citations · 162 across the 24 of their papers we have counts for
3 papers · 1 filter
On universal approximation and error bounds for Fourier Neural Operators
Nikola Kovachki, Samuel Lanthaler, Siddhartha Mishra
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are un…
On the approximation of functions by tanh neural networks
Tim De Ryck, Samuel Lanthaler, Siddhartha Mishra
We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic ta…
Error estimates for DeepOnets: A deep learning framework in infinite dimensions
Samuel Lanthaler, Siddhartha Mishra, George Em Karniadakis
DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite dimensional Banach spaces. We analyze DeepONets and prove estimates o…