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In this talk, I would like to discuss the learning of a nonlinear operator for the scattering problem based on neural operator architectures. In most inverse scattering problems, the forward operator mapping from the refractive index to the far-field pattern is commonly used measurement. In many numerical methods for constructing the refractive index from the knowledge of the far-field pattern need to evaluate the forward operator, which involves solving PDEs and taking asymptotic. Such procedure is time consuming and not effective. It is therefore a favorable practice to construct a surrogate to replace this forward operator. Here we would like to demonstrate that, under certain conditions, the “parametric complexity” of neural scattering operators grows at most logarithmically with respect to the desired accuracy. This result makes the application of these neural operators rather promising in practice. This talk is based on joint works with Takashi Furuya.

More Information: https://www.math.ntu.edu.tw/~jnwang/