扩散系数识别PINN模型在Fick定律中的问题
Dongchen Li1, Bin Yan1, Tianya Gao1
1School of Civil Engineering, Central South University, Changsha 410075, People's Republic of China.
ACS omega
|January 29, 2024
概括
本研究介绍了一种高效的物理信息神经网络 (PINN) 模型,用于估计反向问题的扩散系数. PINN模型准确地确定了在各种场景中具有高计算效率的扩散系数.
科学领域:
- 计算物理学的计算物理.
- 材料科学是一种材料科学.
- 化学工程是化学工程的组成部分.
背景情况:
- 在许多科学领域中,确定扩散系数至关重要.
- 涉及扩散系数的反向问题带来了诸如不稳定性和高计算成本等挑战.
- 在不同的条件下,现有的方法可能缺乏效率和准确性.
研究的目的:
- 开发一个高效和准确的模型来估计反向问题的扩散系数.
- 为了应对不稳定性和计算需求在扩散系数确定中的挑战.
- 创建适用于已知/未知扩散流和度梯度的不同场景的多功能模型.
主要方法:
- 一个物理信息神经网络 (PINN) 框架是通过整合Fick的定律来开发的.
- 该PINN模型的设计是基于可用的扩散流量和度梯度数据来处理三个不同的场景.
- 进行了灵敏度分析以验证模型的性能和稳定性.
主要成果:
- 对于所考虑的三个场景,PINN模型在1000次,2000次和3000次以下的代中实现了扩散系数的高效估计.
- 敏感性分析证实了模型的有效性,并强调了有效数据比例对趋同的积极影响.
- 该模型显示与一般的扩散系数模式保持一致.
结论:
- 开发的PINN模型是准确估计扩散系数的强大而有效的工具.
- 该模型为与扩散有关的反向问题提供了强大的解决方案,克服了以前的局限性.
- 这种方法在扩散系数识别领域取得了重大进展.
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