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In this paper, we propose a multiscale DeepONet to represent nonlinearoperator between Banach spaces of highly oscillatory continuous functions. Themultiscale deep neural network (DNN) utilizes a multiple scaling technique toconvert high frequency function to lower frequency functions before using a DNNto learn a specific range of frequency of the function. The multi-scale conceptis integrated into the DeepONet which is based on a universal approximationtheory of nonlinear operators. The resulting multi-scale DeepONet is shown tobe effective to represent building seismic response operator which mapsoscillatory seismic excitation to the oscillatory building responses.

Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses