CAREER: Forward and Inverse Uncertainty Quantification of Cardiovascular Fluid-Structure Dynamics via Multi-fidelity Physics-Informed Bayesian Geometric Deep Learning

基于图像的心血管系统计算模型在推进心血管生理学的基础认识和支持临床诊断和治疗计划方面发挥着越来越重要的作用。然而，传统的模型主要是基于数值求解的适定物理，由于建模条件的未知或不确定，其可靠性受到限制。另一方面，由于医学成像技术（如流磁共振图像）的快速发展，稀疏和噪声数据变得越来越多，可以用于模型推理和减少不确定性。因此，心血管模拟中的正向不确定性量化和反向数据同化对于增强预测信心和促进临床翻译工作至关重要。该项目将利用科学机器学习的最新进展，为数据支持的正向和逆随机心血管建模开发计算网络基础设施。该项目旨在建立一种数据增强心血管流体结构模拟的新范式，这可能有助于改变个性化的心血管诊断/治疗方法，从而提高生活质量。此外，该研究项目还将尝试通过促进互动和包容的学习策略，解决长期以来在K-12、本科和研究生教育中有效吸引学生参与STEM教育的挑战。特别是，PI将(1)设计教学软件，使用物理知识迁移学习，基于手绘草图进行快速交互式流体模拟；(2)为美国教育部三重奏项目开发人工智能和力学的新模块，吸引来自低收入家庭的K-12学生参与新兴的跨学科STEM领域。该CAREER计划的总体目标是开创一种可扩展和变革性的计算网络基础设施，用于基于物理Bayesian几何深度学习的心血管建模的正向和反向不确定性量化（UQ），利用物理/生理知识实现稀疏和噪声数据的高效概率学习。该项目解决了心血管流体-结构相互作用（FSI）动力学建模的传统范式所面临的基本挑战。在提出的框架中，几何深度学习模型将以贝叶斯方式基于（部分）已知的物理和稀疏测量数据构建，从而实现具有量化不确定性的高效正向和反向FSI模拟。具体来说，PI将(1)使用图卷积网络制定一个基于变分pde的离散化学习框架，并使用降基来约束解空间的维度，从而促进网络训练；(2)实现基于可扩展变分贝叶斯推理的学习框架的高维UQ能力；(3)建立多保真元学习策略，在物理参数空间参数化解，实现快速代理建模，实现实时心血管仿真。将利用深度学习模型的快速推理速度、强可表达性和GPU并行化来实现具有特定患者几何形状的大规模随机FSI模拟。该项目将为开发下一代心血管FSI建模的计算网络基础设施奠定坚实的基础。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。

Image-based computational models of the cardiovascular system play an increasingly important role in advancing the fundamental understanding of cardiovascular physiology and supporting clinical diagnosis and treatment planning. However, traditional models are primarily based on well-posed physics that are solved numerically, and their reliability is limited because of unknown or uncertain modeling conditions. On the other hand, sparse and noisy data have become increasingly available thanks to the rapid development of medical imaging techniques (e.g., flow MR images), which can be utilized for model inference and uncertainty reduction. Hence, forward uncertainty quantification and inverse data assimilation in cardiovascular simulations are of paramount importance to enhancing predictive confidence and prompting clinical translation efforts. This project will develop computational cyberinfrastructure for data-enabled forward and inverse stochastic cardiovascular modeling by leveraging recent advances in scientific machine learning. The project aims to establish a novel paradigm of data-augmented cardiovascular fluid-structure simulations, which could help transform personalized cardiovascular diagnostics/therapeutics, leading to higher quality of life. Moreover, this research program will also try to address long-standing challenges in effectively engaging students in STEM education across K-12, undergraduate, and graduate education by promoting an interactive and inclusive learning strategy. In particular, the PI will (1) design pedagogical software using physics-informed transfer learning for rapid interactive fluid simulation based on hand-drawn sketches; (2) develop new modules on Artificial Intelligence & Mechanics for U.S. Department of Education TRiO programs to engage K-12 students from low-income families in emerging interdisciplinary STEM fields. The overarching goal of this CAREER program is to pioneer a scalable and transformative computational cyberinfrastructure for forward and inverse uncertainty quantification (UQ) of cardiovascular modeling based on physics-informed Bayesian geometric deep learning, leveraging physics/physiological knowledge to enable efficient probabilistic learning with sparse and noisy data. This project tackles the fundamental challenges faced by the traditional paradigm of modeling cardiovascular fluid-structure interaction (FSI) dynamics. In the proposed framework, geometric deep learning models will be constructed based on both (partially) known physics and sparse measurement data in a Bayesian manner, enabling efficient forward and inverse FSI simulations with quantified uncertainties. Specifically, the PI will (1) formulate a variational PDE-informed, discretization-based learning framework using graph convolutional networks and use a reduced basis to constrain the dimension of the solution space, facilitating network training; (2) enable high-dimensional UQ capability of the proposed learning framework based on scalable variational Bayesian inference; (3) establish a multi-fidelity meta-learning strategy to parameterize solutions in the physical parameter space for rapid surrogate modeling, on the path to real-time cardiovascular simulations. The fast inference speed, strong expressibility, and GPU parallelization of deep learning models will be exploited to enable large-scale stochastic FSI simulations with patient-specific geometries. This project will build a solid foundation for developing the next-generation computational cyberinfrastructure of cardiovascular FSI modeling.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.