MCA: Physics-Informed and Geometry-Informed Machine Learning for Analysis of Multi-scale Distensible Biological Structures

这项工作将支持使用先进的计算技术在生物问题中的流体-结构界面的研究。 机器学习正在成为一种强大的新工具，用于解决计算科学和工程（包括生物力学工程）中的挑战性问题。液体如何流过体内的血管是一个具有挑战性的问题。 这种情况发生在许多情况下，例如通过主动脉泵送血流，通过肺毛细血管重复气流，以及响应于周期性吸吮通过泌乳乳房的乳汁运输。由于这些软材料的计算复杂性和几何复杂性，这些问题的研究特别具有挑战性。 该项目以一种新颖的方式使机器学习技术适应这个问题的独特形状和要求。 这项工作最终将提高我们对人体器官运作的理解。该项目活动的教育成果包括指导本科生、代表性不足的少数民族、残疾人以及K-12外展。更具体地说，各种生物学上重要的现象产生于通过可变形管道驱动的流体流动以及流体-机械和弹性力之间的相互作用，包括非线性压降和流速关系、波传播、不稳定性的产生、以及分叉接头处的流动振荡。这些物理现象是由相应的偏微分方程，是高度非线性和高度耦合。该项目利用物理信息和几何信息神经网络来研究这些复杂的现象，这些现象在多个尺度上的理解受到计算问题的阻碍。前者是基于将控制方程的损失函数的神经网络的训练。后者的目的是解决多尺度分叉，是基于训练子网络表示在不同尺度的单个分叉，并将它们组合成一个整体的网络架构，其连接的灵感来自多尺度分叉几何。 除了具体的成果，该项目还有助于更广泛地讨论机器学习在科学计算中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This work will support research about fluid-structure interfaces in biological problems using advanced computational techniques. Machine learning is emerging as a powerful new tool for challenging problems in computational science and engineering, including biomechanical engineering. How fluid flows through the vessels in the body is a challenging problem. This occurs in many situations, such as in pumping blood flow through aorta, repeated air flow through lung capillaries, and milk transport through lactating breast in response to periodic suckling. These problems are particularly challenging to study because of both computational complexity and the geometric complexity of these soft materials. This project adapts machine learning techniques in a novel manner to the unique shape and requirements of this problem. This work will eventually improve our understanding of the operation of human organs. Educational outcomes of the project activities include mentoring undergraduate students, under-represented minorities, individuals with disabilities, as well as K-12 outreach.More specifically, a variety of biologically significant phenomena arise from fluid flows driven through deformable ducts and the interaction between fluid-mechanical and elastic forces, including nonlinear pressure drop and flow rate relations, wave propagation, generation of instabilities, as well as oscillations of flow at bifurcated joints. These physical phenomena are governed by corresponding partial differential equations that are highly nonlinear and highly coupled. The project utilizes physics-informed and geometry-informed neural networks for studying these complex phenomena, whose understanding at multiple scales has been hampered by computational issues. The former is based on incorporating governing equations into the loss function in the training of neural networks. The latter is designed to address multi-scale bifurcations, and is based on training sub-networks representing single bifurcations at different scales, and combining them into an overall network architecture whose connections are inspired by the multi-scale bifurcation geometry. In addition to the specific outcomes, the project also contributes to the broader dialog on the application of machine learning in scientific computing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.