Nonparametric learning of kernels in nonlocal operators

  title={Nonparametric learning of kernels in nonlocal operators},
  author={Fei Lu and Qi An and Yue Yu},
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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