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研究生物问题中的流固界面。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。液体如何在体内的血管中流动是一个具有挑战性的问题。这种情况在很多情况下都会发生，比如在主动脉抽血、肺部毛细血管反复空气流动、周期性哺乳时乳汁通过哺乳乳房运输等。由于这些软材料的计算复杂性和几何复杂性，这些问题的研究尤其具有挑战性。该项目以一种新颖的方式将机器学习技术应用于该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。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，流体在可变形管道中的流动以及流体力学和弹性力之间的相互作用产生了各种具有生物学意义的现象，包括非线性压降和流量关系、波的传播、不稳定性的产生以及分叉节理处的流动振荡。这些物理现象是由相应的高度非线性和高度耦合的偏微分方程控制的。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，这些现象在多尺度上的理解一直受到计算问题的阻碍。前者是基于在神经网络训练中将控制方程纳入损失函数。后者旨在解决多尺度分岔问题，其基础是在不同尺度上训练表示单个分岔的子网络，并将它们组合成一个整体网络架构，其连接受到多尺度分岔几何的启发。除了取得具体成果外，该项目还有助于就机器学习在科学计算中的应用进行更广泛的对话。该奖项反映了美国国家科学基金会的法定使命，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.