使用物理知情神经网络对空间变化的扩散系数进行反向解析
Sukirt Thakur1, Ehsan Esmaili1, Sarah Libring2
1School of Mechanical Engineering,Purdue University, West Lafayette, 47907, Indiana, USA.
ArXiv
|March 18, 2024
概括
这项研究引入了一种使用物理信息神经网络 (PINNs) 的新方法,以准确地从图像数据中确定空间变化的扩散系数. 该方法对数值和实验数据集都显示出高准确性,有助于诸如药物递送系统等应用.
科学领域:
- 多学科科学 多学科科学
- 计算建模计算建模
- 生物物理学的生物物理.
背景情况:
- 精确确定扩散系数对于生物和工程系统至关重要.
- 空间变化的扩散系数在离散数据的反向问题中提出了挑战.
- 现有的方法在扩散系数确定时,与杂且位置不佳的数据集作斗争.
研究的目的:
- 开发一个强大的反向解决器,用于计算空间变化的扩散系数.
- 为了解决这个反向问题,利用基于物理学的神经网络 (PINNs).
- 用数字和实验数据验证方法.
主要方法:
- 开发了一个使用物理信息神经网络 (PINNs) 的反向解决器.
- 将短暂扩散方程的余数最小化以确定扩散系数.
- 使用数值和实验图像数据集测试了解决器的稳定性.
主要成果:
- 与所有数值基准相比,错误率低于6.31%.
- 从实验数据计算的扩散系数与报告的文献值保持一致.
- 在预测和数字和实验基准之间表现出良好的一致性.
结论:
- 基于物理学的神经网络 (PINNs) 为解决空间变化的扩散系数提供了一个强大的工具.
- 开发的方法对于各种生物和工程应用来说是强大而准确的.
- 潜在的应用包括改善药物释放植入物的设计,用于再生医学和瘤学.
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