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调查物理知情神经网络用于大断层场景的使用情况
Kinza Mumtaz1, Muhammad Waasif Nadeem2, Adnan Khan1
1Department of Mathematics, LUMS University, Lahore, Pakistan.
PloS one
|September 19, 2025
概括
物理信息神经网络 (PINNs) 为实时洪水预测提供了一个有前途的方法. 这些模型有效地解决浅水方程 (SWEs),与传统方法相比,提供更平滑和可接受的波传播估计.
科学领域:
- 计算流体动力学的流体动力学.
- 机器学习应用 机器学习应用
- 环境工程 环境工程
背景情况:
- 由于浅水方程 (SWE) 数值解决方案的高计算成本,实时洪水预测面临挑战.
- 传统方法需要精细的分辨,并与复杂的边界条件和固有的非线性作斗争.
研究的目的:
- 调查物理信息神经网络 (PINNs) 的应用,以解决1D和2DSWEs在水破坏场景中的应用.
- 为了比较PINN解决方案与经典的数值方案,如Lax-Wendroff.
主要方法:
- 开发PINNs是为了将管理的部分微分方程和初始/边界条件直接纳入培训过程.
- 对1D和2D水破裂问题的PINN估计和Lax-Wendroff数值解决方案进行了系统的比较.
- 混合PINNs,将数值解决方案纳入训练中,被探索以提高准确性.
主要成果:
- 与标准的数值结果相比,1D SWEs的PINNs产生了更平滑,更可接受的波传播估计.
- 对于2D SWEs,PINNs以更高的精度重现了数值基线,并避免了虚假的振荡.
- 混合PINN通过进一步调整显示出更高的准确性.
结论:
- PINNs提供了一个无网格,可扩展和可通用的框架,用于近似解决非线性超标系统的解决方案.
- 预先训练有素的,以物理学为基础的模型显示出其作为复杂领域的实时洪水预测的可行替代方案的潜力.
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