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arxiv 2504.10932 v1 pith:4F774RDW submitted 2025-04-15 cs.LG cs.NAmath.NA

Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions

Bo Wang , Lizuo Liu , Wei Cai This is my paper
classification cs.LG cs.NAmath.NA
keywords deeponetmscale-deeponethigh-frequencymappingbiasfunctionslearningmulti-scale
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this paper, a multi-scale DeepOnet (Mscale-DeepOnet) is proposed to reduce the spectral bias of the DeepOnet in learning high-frequency mapping between highly oscillatory functions, with an application to the nonlinear mapping between the coefficient of the Helmholtz equation and its solution. The Mscale-DeepOnet introduces the multiscale neural network in the branch and trunk networks of the original DeepOnet, the resulting Mscale-DeepOnet is shown to be able to capture various high-frequency components of the mapping itself and its image. Numerical results demonstrate the substantial improvement of the Mscale-DeepOnet for the problem of wave scattering in the high-frequency regime over the normal DeepOnet with a similar number of network parameters.

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