Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913794969567232 |
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| author | Wang, Bo Liu, Lizuo Cai, Wei |
| author_facet | Wang, Bo Liu, Lizuo Cai, Wei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions Wang, Bo Liu, Lizuo Cai, Wei Machine Learning Numerical Analysis 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. |
| title | Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2504.10932 |