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

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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.