We present convergence rates of operator learning in [Chen and Chen 1995] and [Lu et al. 2020] when the operators are solution operators of differential equations. In particular , we consider solution operators of both linear and nonlinear advection-diffusion equations  .
We present convergence analysis of operator learning in [Chen and Chen 1995] and [Lu et al. 2020] , where continuous operators are approximated by a sum of products of branch and trunk networks. In this work , we consider the rates of learning solution operators from both linear and nonlinear advection-diffusion equations with or without reaction. We find that the convergence rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators .
R
rates
analysis
R
when the operators are solution operators of differential equations. In particular
, where continuous operators are approximated by a sum of products of branch and trunk networks. In this work
R
solution operators of
the rates of learning solution operators from
A
with or without reaction. We find that the convergence rates depend on the architecture of branch networks as well as the smoothness of inputs and outputs of solution operators