一个以物理为基础的神经网络架构,用于科学和工程中的移动边界问题
Sanchita Malla1, Dietmar Oelz2, Sitikantha Roy3
1UQ-IITD Academy of Research (UQIDAR), Indian Institute of Technology, Delhi New Delhi, 110016, India; School of Mathematics and Physics, University of Queensland, 4072, QLD, Australia; Department of Applied Mechanics, Indian Institute of Technology, Delhi New Delhi, 110016, India.
概括
本研究介绍了一种新的物理信息神经网络 (PINN) 架构,用于解决复杂的移动边界问题. 新的PINN方法有效地处理不断变化的空间领域,为科学和工程提供强大的模拟平台.
科学领域:
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
- 机器学习 机器学习
背景情况:
- 移动边界问题在科学和工程方面至关重要,但由于未知的接口,这也带来了挑战.
- 传统的数值方法在移动接口和系统变量之间的动态合方面存在困难.
- 深度学习提供了新的方法,物理信息神经网络 (PINNs) 显示出解决部分微分方程 (PDEs) 的希望.
研究的目的:
- 开发一种新且通用的物理信息神经网络 (PINN) 架构,专门设计用于移动边界问题.
- 解决现有方法在处理空间领域随着时间的推移而演变的问题方面的局限性.
- 为复杂的移动边界动态提供一个更可行的和有效的计算工具.
主要方法:
- 建议采用两个独立的神经网络的新型PINN架构.
- 一个网络预测自由边界,而另一个预测依赖系统变量.
- 这种无网格方法将PDE问题转换为基于管理方程的余值的优化任务.
主要成果:
- 拟议的PINN架构成功地解决了各种移动边界问题.
- 它在具有随时间变化的空间域的场景中表现出有效性.
- 通过PINNs获得的解决方案显示出强度和复杂模拟的潜力.
结论:
- 新的PINN架构为解决移动边界问题提供了显著的进步.
- 它为复杂的动态提供了比传统方法更容易获得和可行的替代方案.
- 这种方法使PINNs成为科学和工程应用的强大的模拟平台.
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