Nonparametric learning of kernels in nonlocal operators

@article{Lu2022NonparametricLO,
  title={Nonparametric learning of kernels in nonlocal operators},
  author={Fei Lu and Qi An and Yue Yu},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.11006}
}
Nonlocal integral operator learning has become a popular tool for designing solution maps between function spaces, due to its efficiency in representing long-range dependence and the attractive feature of being resolution-invariant. In this work, we provide a rigorous identifiability analysis and convergence study for the learning of kernels in nonlocal operators. It is found that when the data resolution increases, the kernel learning problem becomes increasingly ill-posed, leading to diver-gent… 

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