加博尔增强的物理信息神经网络用于快速模拟声波场
Mohammad Mahdi Abedi1, David Pardo2, Tariq Alkhalifah3
1Basque Center for Applied Mathematics, Bilbao, Spain.
概括
物理信息神经网络 (PINNs) 在高频波模拟中扎. 一个新的Gabor-PINN使用可训练的Gabor函数来实现更快,更准确的波场模拟,从而提高合性和稳定性.
科学领域:
- 计算物理
- 应用数学
- 波传播模型
背景情况:
- 物理信息神经网络 (PINNs) 提供了一种灵活的,无网格的方法来解决部分微分方程.
- 传统的PINN表现出低频偏差,阻碍高频波场模拟的性能,并限制融合速度和准确性.
研究的目的:
- 开发一种新的简化PINN框架,以增强高频波场模拟.
- 提高PINN的融合速度,准确性和稳定性,以解决分散的赫尔姆霍尔茨方程.
主要方法:
- 包含明确的可训练的Gabor基础函数以捕捉波场振荡.
- 重新定义网络的任务,学习非线性映射到自定义的Gabor坐标系统,将Gabor参数吸收到已学习的映射中.
- 完美匹配层 (PML) 集成与实值损失组件和分析背景波场表达的有效制定.
主要成果:
- 与传统的PINN和之前基于Gabor的方法相比,拟议的Gabor-PINN显示了更快的趋同.
- 在数值实验中实现更高的准确性和更强大的结构设计和初始化.
- 有效地捕捉波场的局部和振荡性,克服低频偏差.
结论:
- 通过将复杂性整合到已知的坐标转换中,Gabor-PINN框架提供了一个更简单但更有效的方法.
- 这种方法提高了PINN用于高频波场模拟的能力,解决了现有技术的局限性.
- 公开的实施促进了波浪现象的物理信息机器学习的可重现性和进一步研究.
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