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

用于流体动力学和流固耦合代理建模的物理约束深度学习

• 批准号: 1934300
• 负责人: Jian-Xun Wang
• 金额: $ 30.03万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1934300&HistoricalAwards=false
• 关键词: Physics; Constrained; Deep; Learning; Surrogate

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.

本项目将开发一种基于深度学习的流固耦合动力学创新建模框架，这将为动态系统的快速建模提供新的知识。复杂流体及其与周围结构的相互作用在自然和工业过程中无处不在，例如，柔性容器中的血液流动，扑翼微型飞行器，海上工业中的柔性立管。流固耦合问题的预测建模在许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性原理方法和数值离散化技术，这是计算昂贵的，需要大量的领域专业知识。这一缺陷给实时预测（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）带来了巨大的挑战。该资助将通过利用机器学习的最新进展和物理原理的先验知识，支持开发新型建模框架的基础研究。这种新方法将使流体结构系统的动力学快速建模和快速预测成为可能，这将对广泛的现实问题产生强大的实际影响，包括心血管诊断、空气动力学设计和主动流动控制。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，跨越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一种计算上可行的方法，可以解决需要快速预测或重复模型评估的流固耦合问题。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，当前计算机科学领域深度学习的成功在很大程度上依赖于大规模标记数据，这在物理建模领域通常是不可用的。为了应对这一挑战，本研究旨在开拓一种物理约束的深度学习框架，用于流固耦合动力学的代理建模，这将使稀疏训练数据的高效学习成为可能。具体来说，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，并在训练过程中通过重新设计损失（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，以回答有关在深度学习中添加物理约束的影响及其在参数设置中模拟复杂物理系统的潜力的问题。本课题解决了非线性、高维、数据稀缺等复杂动力系统替代建模长期存在的困难，为动力系统的整体建模做出了贡献。通过将范式从黑箱、数据密集型学习转变为物理约束、数据稀缺学习，学习框架将对数据驱动的代理建模带来革命性的影响。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。

项目成果

PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs

• DOI: 10.1016/j.cma.2021.114399
• 发表时间: 2021-06
• 期刊: ArXiv
• 作者: Pu Ren;Chengping Rao;Yang Liu;Jianxun Wang;Hao Sun-

Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty

• DOI: 10.48550/arxiv.2210.08095
• 发表时间: 2022-10
• 期刊: ArXiv
• 作者: Luning Sun;D. Huang;Hao Sun-;Jian-Xun Wang

Physics-informed deep learning for solving phonon Boltzmann transport equation with large temperature non-equilibrium

• DOI: 10.1038/s41524-022-00712-y
• 发表时间: 2022-02-08
• 期刊: NPJ COMPUTATIONAL MATERIALS
• 影响因子: 9.7
• 作者: Li, Ruiyang;Wang, Jian-Xun;Luo, Tengfei
• 通讯作者: Luo, Tengfei

A non‐iterative domain decomposition method for the interaction between a fluid and a thick structure

流体与厚结构相互作用的非迭代域分解方法

• DOI: 10.1002/num.22771
• 发表时间: 2021
• 期刊: Numerical methods for partial differential equations
• 影响因子: 3.9
• 作者: Seboldt, A;Bukač, M
• 通讯作者: Bukač, M

Numerical Modeling of the Fluid-Porohyperelastic Structure Interaction

流体-多孔超弹性结构相互作用的数值模拟

• DOI: 10.1137/20m1386268
• 发表时间: 2021
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Seboldt, Anyastassia;Oyekole, Oyekola;Tambača, Josip;Bukač, Martina
• 通讯作者: Bukač, Martina