Physics-Constrained Deep Learning for Surrogate Modeling of Dynamics of Fluids and Fluid-Structure Interaction

该项目将开发一个基于深度学习的流体-结构耦合动力学的创新建模框架，这将为动态系统的快速建模贡献新的知识。复杂的流体及其与周围结构的相互作用在自然和工业过程中普遍存在，例如，顺应性血管中的血液流动，微型扑翼飞行器，海上工业中的柔性立管。流固耦合问题的预测建模在众多工程应用中具有重要意义。然而，现有的模型主要基于第一原理方法和数值离散化技术，这些方法计算昂贵，需要大量的领域专业知识。这一缺陷对实时预测(例如血管疾病的临床诊断)和多查询应用(例如飞机的优化设计和高后果系统中的不确定性量化)提出了巨大的挑战。这笔赠款将支持通过利用机器学习的最新进展和物理原理的先验知识来开发新的建模框架的基础研究。这一新方法将使流体-结构系统动力学的快速建模和快速预测成为可能，这将对包括心血管诊断、空气动力学设计和主动流动控制在内的广泛的现实世界问题产生强大的实际影响。因此，这项研究的结果可以帮助提高美国的医疗保健/健康、国家安全和经济竞争力。此外，跨物理建模和人工智能的多学科研究课题可以激发年轻人对STEM学科的兴趣，从而对科学和工程教育产生积极影响。基于数据的代理建模是解决需要快速预测或重复模型评估的流固耦合问题的一种计算可行的方法。深度学习因其处理强非线性和高维的能力而成为一种流行的代理建模方法。然而，目前计算机科学界深度学习的成功在很大程度上依赖于大规模的标记数据，而这些数据在物理建模社区中通常是不可用的。为了应对这一挑战，本研究旨在开创一个物理约束的深度学习框架，用于流体-结构相互作用动力学的代理建模，从而实现在稀疏训练数据下的高效学习。具体地说，将设计一个结构化的深度神经网络来编码初始条件和边界条件，并在训练期间通过重新设计损失(或似然)函数来施加控制方程以符合物理。计划对一组动态流固耦合问题进行数值实验，以回答在深度学习中添加物理约束的效果及其在参数设置下模拟复杂物理系统的潜力。该项目解决了长期存在的非线性、高维、数据稀缺的复杂动态系统的代理建模问题，为一般的动态系统建模做出了贡献。学习框架将对数据驱动的代理建模带来革命性的影响，将范式从黑箱、数据密集型学习转变为物理约束、数据稀缺的学习。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop an innovative modeling framework for coupled dynamics of fluid-structure systems based on deep learning, which will contribute new knowledge on rapid modeling of dynamic systems in general. Complex fluids and their interactions with surrounding structures are ubiquitous in natural and industrial processes, e.g., blood flows in compliant vessels, flapping-wing miniature air vehicles, flexible risers in the offshore industry. Predictive modeling of fluid-structure interaction problems is of great significance in numerous engineering applications. However, existing models are primarily based on first-principles methods and numerical discretization techniques, which are computationally expensive and require significant domain expertise. This drawback poses great challenges to real-time predictions (e.g., clinical diagnosis of vascular diseases) and many-query applications (e.g., optimization design of aircraft and uncertainty quantification in high-consequence systems). This grant will support fundamental research on the development of a novel modeling framework by leveraging recent advances in machine learning and prior knowledge of physical principles. This new approach will enable rapid modeling and fast prediction for dynamics of fluid-structure systems, which will have strong practical impacts on a broad spectrum of real-world problems, including cardiovascular diagnosis, aerodynamic design, and active flow control. Therefore, the results of this research can help enhance U.S. healthcare/wellness, national security, and economic competitiveness. Moreover, the multi-disciplinary research topics across physical modeling and artificial intelligence can stimulate interest in the STEM disciplines among young people and thus will have a positive impact on science and engineering education.Data-based surrogate modeling is a computationally feasible way to tackle fluid-structure interaction problems that require rapid predictions or repeated model evaluations. Deep learning is becoming a popular surrogate modeling approach due to its capability of handling strong nonlinearity and high dimensionality. However, current success of deep learning in the computer science community heavily relies on large-scale labeled data, which are usually not available in the physical modeling community. To address this challenge, this research aims to pioneer a physics-constrained deep learning framework for surrogate modeling of fluid-structure interaction dynamics, which will enable efficient learning with sparse training data. Specifically, a structured deep neural network will be devised to encode the initial and boundary conditions, and the governing equations will be imposed during the training by redesigning the loss (or likelihood) functions to conform to the physics. Numerical experiments of a suite of dynamic fluid-structure interaction problems are planned to answer questions regarding the effect of adding physical constraints in deep learning and their potential in modeling complex physical systems in a parametric setting. This project tackles long-standing difficulties in surrogate modeling of complex dynamical systems with nonlinearity, high-dimensionality, and data scarcity, and contributes to the modeling of dynamical systems in general. The learning framework will bring revolutionary impacts on data-driven surrogate modeling by shifting the paradigm from black-box, data-intensive learning to physics-constrained, data-scarce learning.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.