物理引导的多阶段神经网络: 一个物理引导的网络,用于阶段初始值和分散冲击波现象
1Taiyuan University of Technology, School of Mathematics, Taiyuan 030024, China.
Physical review. E
|February 7, 2025
概括
这项研究引入了物理引导的多阶段神经网络 (PgMSNN),以准确模拟复杂的分散性冲击波 (DSW). 增强的物理信息神经网络 (PINN) 模型提高了非线性动态的模拟精度和稳定性.
科学领域:
- 非线性动力学是一种非线性动力学.
- 计算物理 计算物理
- 机器学习 机器学习
背景情况:
- 分散式冲击波 (DSW) 在非线性动态中至关重要,但模拟很难.
- 现有的物理信息神经网络 (PINNs) 需要对复杂的分散现象进行增强.
研究的目的:
- 改进PINN对DSWs的模拟能力.
- 为非线性动态系统开发一种高效灵活的工具.
- 用步骤初始条件来解决通用加德纳方程的演变.
主要方法:
- 集成的残留学习和分散因子分成PINNs.
- 开发了用于时间域代的Deep Runge-Kutta方法.
- 制定了一个以物理为导向的多阶段神经网络 (PgMSNN),并进行多阶段训练.
主要成果:
- 在模拟DSW时,PgMSNN模型表现出更高的准确性和稳定性.
- 成功解决了前问题,模型稳定性和参数反转.
- 超越了最先进的神经网络模拟方法的性能.
结论:
- 该PgMSNN模型显著提高了PINN对DSW现象的准确性和稳定性.
- 为模拟复杂的非线性系统提供了一种高效灵活的工具.
- 物理指导的深度学习策略显示出复杂物理问题的巨大潜力.
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