Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions
This addresses a specific bottleneck in operator learning for high-frequency wave scattering problems, representing an incremental improvement.
The paper tackled the problem of spectral bias in DeepOnet when learning high-frequency mappings between oscillatory functions, specifically for the Helmholtz equation, and demonstrated that the proposed Mscale-DeepOnet substantially improves performance over the normal DeepOnet with similar parameters.
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.