Convergence rate of DeepONets for learning operators arising from advection-diffusion equations
arXiv:2102.10621
Abstract
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.
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- A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data
- Machine-learning custom-made basis functions for partial differential equations