论文标题
多尺度的深神经网络（MSCALEDNN），用于在复杂域中求解泊松玻璃到泊松方程
Multi-scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
论文作者
论文摘要
在本文中，我们使用频域中的径向缩放和激活功能具有紧凑的支持，提出了多尺度的深神经网络（MSCALEDNNS）。径向尺度将PDE解决方案高频内容物的近似问题转换为学习较低频率功能的问题，而紧凑的支持激活函数有助于通过相应的DNN近似目标函数的频率内容分离。结果，MSCALEDNNS在多个尺度上实现了快速均匀的收敛。所提出的MSCALEDNN被证明优于传统的完全连接的DNN，并且是一种有效的无网格数值方法，用于用于与复杂和奇异域相比频率丰富的泊松 - 波尔兹曼方程。
In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to a problem of learning about lower frequency functions, and the compact support activation functions facilitate the separation of frequency contents of the target function to be approximated by corresponding DNNs. As a result, the MscaleDNNs achieve fast uniform convergence over multiple scales. The proposed MscaleDNNs are shown to be superior to traditional fully connected DNNs and be an effective mesh-less numerical method for Poisson-Boltzmann equations with ample frequency contents over complex and singular domains.
