标题： 多尺度DeepOnet（Mscale-DeepOnet）用于减轻振荡函数高频算子学习中的光谱偏差 显示英文标题

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

摘要： 本文提出了一种多尺度 DeepOnet（Mscale-DeepOnet），以减少 DeepOnet 在学习高度振荡函数之间的高频映射时的谱偏倚，应用到亥姆霍兹方程系数与其解之间的非线性映射中。 Mscale-DeepOnet 在原始 DeepOnet 的分支网络和主干网络中引入了多尺度神经网络，结果表明该模型能够捕获映射本身及其像的各种高频分量。 数值结果表明，对于高频范围内的波散射问题，与具有相似网络参数数量的标准 DeepOnet 相比，Mscale-DeepOnet 显示出显著改进。 显示英文摘要

摘要： 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.