基于物理学的神经网络用于解决复杂光束系统中的前向和反向问题.
IEEE transactions on neural networks and learning systems
|September 19, 2023
概括
基于物理学的神经网络 (PINNs) 提供了一种新的方法来模拟复杂的结构系统,准确地解决光束理论的前向和反向问题. 这种方法对涉及梁结构的工程应用有希望.
科学领域:
- 结构力学 结构力学
- 计算工程 计算工程
- 在工程领域的人工智能.
背景情况:
- 复杂的结构系统往往涉及由欧勒-伯努利和蒂莫申科理论支配的复杂的束行为.
- 模拟这些系统,特别是基础上的相互连接的双梁,会带来重大的计算挑战.
- 传统的数值方法可能会在前进和反向问题所需的准确性和稳定性方面扎.
研究的目的:
- 引入一个使用物理信息神经网络 (PINNs) 模拟单波和双波系统的新框架.
- 为解决与欧勒-伯努利和蒂莫申科束理论相关的前向和反向问题.
- 为了证明PINNs在解决结构分析的复杂部分微分方程 (PDEs) 中的有效性.
主要方法:
- 实现一个PINN框架来解决非维的欧勒-伯努利和蒂莫申科束方程.
- 利用物理知情损失函数来强制执行神经网络中的物理规律.
- 解决前进问题以计算横移和横截面旋转.
- 解决反向问题以识别未知的模型参数和应用力,即使有噪音数据.
主要成果:
- 在解决复杂光束PDEs的前向问题时,PINNs实现了高精度 (误差<1e-3%).
- 反向问题得到了强有力的解决,成功地确定了未知的无维参数和应用力.
- 该框架在整个时空领域表现出有效性,处理杂的输入数据.
结论:
- PINNs提供了一种强大而准确的策略,用于模拟涉及单梁和双梁的复杂结构系统.
- 拟议的框架为梁力学中的前向和反向问题提供了强大的解决方案.
- 这种方法在推进工程结构和机器的分析和设计方面具有重大潜力.
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