富里埃特征增强的多层残余堆叠网络:一种新的多尺度建模方法,用于物理信息的神经网络
Bo-Ya Hou1, Yu-Long Bai1, Xia-Ting Jing1
1College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, Gansu 730070, China.
概括
基于物理学的神经网络 (PINNs) 难以处理复杂的方程. 一个新的富里埃特征增强多层残余堆叠网络 (FRES) 提高了多尺度和高频问题的准确性和稳定性.
科学领域:
- 计算物理学的计算物理.
- 对于微分方程的机器学习.
背景情况:
- 基于物理学的神经网络 (PINNs) 显示出解决部分微分方程 (PDEs) 的前景.
- 由于光谱偏差和训练不稳定性,PINNs面临多尺度结构和高频组件的局限性.
- 对于复杂的物理现象,现有的方法往往缺乏稳定性和准确性.
研究的目的:
- 引入一个新的框架,即福里埃特征增强多层残余堆叠网络 (FRES),以克服PINN的局限性.
- 提高复杂的多尺度特征和高频解决方案组件的表示性.
- 在解决PDEs时提高准确性,推断能力和噪声稳定性.
主要方法:
- FRES使用剩余信息来指导频域建模.
- 一个动态的里埃嵌入机制可自适应地产生高频特征.
- 多层残留校正方案和频率增强的残留聚变模块逐渐减少错误,并集成功能.
- 一个可训练的频率矩阵增强了适应性.
主要成果:
- 在基准PDEs (伯格斯,施罗丁格,KdV方程) 上,FRES表现优越.
- 显著优于传统的PINNs和多尺度里埃特征方法 (MFF).
- 展示了增强的准确性,外推能力和噪声强度.
结论:
- FRES提供了一种强大而高效的解决方案,用于模拟由PDE控制的复杂物理场.
- 拟议的框架有效地解决了PINN中的光谱偏差和培训不稳定性.
- 在推进科学机器学习应用方面,FRES显示出巨大的潜力.
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