用物理信息的神经网络在非热带材料中的热量和湿度转移的分数顺序建模
Yaroslav Sokolovskyy1, Kazimierz Drozd2, Tetiana Samotii3
1Department of Computer-Aided Design, Lviv Polytechnic National University, 12 S. Bandery Street, 79013 Lviv, Ukraine.
Materials (Basel, Switzerland)
|October 16, 2024
概括
本研究引入了使用分数计算在异性质材料中传递热量和湿度的新型分数模型. 分形物理信息的神经网络方法为模拟这些复杂的物理过程提供了一种高效的方法.
科学领域:
- 多物理学的多重物理.
- 材料科学 材料科学 材料科学
- 计算数学 计算数学 计算数学
背景情况:
- 异性质材料中的热量和湿度转移是复杂的现象.
- 现有的模型往往缺乏捕捉碎形特征的能力.
- 分数计算为模拟非局部和复杂的运输过程提供了一个强大的框架.
研究的目的:
- 提出新的双因素碎形数学模型,用于异性质材料中的热量和水分传递.
- 使用碎形物理信息神经网络 (PINNs) 开发一个数值实现.
- 为弥补有关合热和湿度转移的分形建模的文献上的差距.
主要方法:
- 使用整微分的微积分计算来制定模型.
- 调整基于物理原理的碎形神经网络方法.
- 开发了一种脱的碎形PINN架构,具有基于物理的损失函数.
- 对分数运算符和损失函数组件实施有限差异方案.
主要成果:
- 开发了一种新的分形物理信息的神经网络算法,用于传输热量和水分.
- 拟议的方法在数值模拟中证明了效率.
- 通过与有限差方法和实验数据进行比较来验证.
结论:
- 开发的分形PINN方法为模拟异型材料中的热量和湿度转移提供了有效的工具.
- 分数计算和分数方法为先进的材料运输模拟提供了有前途的途径.
- 拟议的方法推进了复杂材料中合物理过程的计算建模.
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