用多尺度网络提升深度算子网络对高频函数映射的建模能力
Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions
- 在分支与主干网络中引入多尺度结构，增强高频成分捕捉能力
- 在高频波散射问题上，性能显著优于传统DeepOnet
- 适合需高精度建模振荡函数映射的研究者或工程应用
本文提出一种多尺度DeepOnet（Mscale-DeepOnet），用于缓解传统DeepOnet在学习高度振荡函数间高频映射时的谱偏差问题，应用于赫姆霍兹方程系数与其解之间的非线性映射。Mscale-DeepOnet在原始DeepOnet的分支网络和主干网络中引入多尺度神经网络，使模型能够捕捉映射及其输出中的多种高频成分。数值实验表明，在高频波散射问题中，该方法在参数量相近的情况下，相比标准DeepOnet有显著性能提升。
原文摘要 · Abstract (English)
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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