# 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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