Collaborative Research: Data-Driven Variational Multiscale Reduced Order Models for Biomedical and Engineering Applications

协作研究：用于生物医学和工程应用的数据驱动的变分多尺度降阶模型

基本信息

批准号：
2012253
负责人：
Traian Iliescu
金额：
$ 15万
依托单位：
Virginia Polytechnic Institute and State University
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：
2020-06-01 至 2025-05-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012253&HistoricalAwards=false
关键词：
Collaborative Research Data Driven Variational

项目摘要

Mathematical models are a fundamental tool for improving our knowledge of natural and industrial processes. Their use in practice depends on their reliability and efficiency. Reliability requires a fine-tuning of the model parameters and an accurate assessment of the sensitivity to noisy inputs. Efficiency is particularly critical in optimization problems, where the computational procedure identifies the best working conditions of a complex system. These requirements lead to solving models with millions or even billions of unknowns many times. This process may require days or weeks of computations on high-performance computing facilities. To mitigate these costs, we need new modeling strategies that allow model-runs in minutes to hours on local computing facilities. Reduced order models (ROMs) are low-dimensional approximations that can decrease the computational cost of current computational models by orders of magnitude. Having in mind biomedical and wind-engineering applications, this project proposes novel methods of model reduction. Data and numerical results from the expensive (or high-fidelity) models are combined with machine learning approaches, to obtain ROMs that attain both efficiency and accuracy at an unprecedented level. The new data-driven ROM framework will make possible the numerical simulation of aortic dissections, pediatric surgery, or wind farm optimization on a laptop in minutes, and aims at becoming a critical and trustworthy tool in decision-making processes. This project will support one graduate student each year at each of the three institutions.Data assimilation (DA), uncertainty quantification (UQ), and shape optimization (SO) are central to the development of computational models for significant biomedical and engineering applications. Since these applications require a large number of model simulations, running an expensive full order model (FOM) is generally prohibitively expensive. For systems that display dominant structures, reduced order models (ROMs) can decrease the FOM computational cost by orders of magnitude. Thus, for the clinical and engineering applications above, ROMs appear as a natural and practical alternative to the prohibitively expensive FOMs running on high-performance computing facilities. Unfortunately, to capture all the geometric scales in the hemodynamics of aortic dissections or to cope with the large Reynolds number in the wind farm optimization, hundreds and thousands of ROM modes are necessary. These relatively high-dimensional ROMs are still not viable to effectively perform DA, UQ, or SO for these applications. What is needed is ROMs that are not only low-dimensional and efficient, but also accurate. To develop ROMs that are accurate in realistic, under-resolved regimes, the ROM closure problem needs to be solved, that is, the effect of the discarded ROM modes on the ROM dynamics needs to be modeled. The proposed research puts forth a new data-driven ROM paradigm that centers around the hierarchical structure of variational multiscale (VMS) methodology and utilizes modern machine learning and numerical and observational data to develop structural ROM closures that can dramatically increase the ROM accuracy at a modest computational cost. The novel data-driven VMS-ROM paradigm maintains the low computational cost of current ROMs but dramatically increases the ROM accuracy. Biomedical applications in thoracic and pediatric surgery (aortic dissections and Fontan procedure – where the fate of the patient depends significantly on the shape of the vessels) as well as wind-engineering applications are specifically targeted. The data-driven VMS-ROM framework will finally make possible the efficient DA, UQ, and SO in these and, possibly, other fields relying on mathematical and computational 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.

数学模型是提高我们对自然和工业过程的了解的基本工具，其在实践中的使用取决于其可靠性和效率。可靠性需要对模型参数进行微调，并准确评估对噪声输入的敏感性。在优化问题中尤其重要，其中计算过程确定复杂系统的最佳工作条件，这些要求导致多次求解具有数百万甚至数十亿个未知数的模型，此过程可能需要在高性能计算上进行数天或数周的计算。设施。为了减轻这些成本，我们需要新的建模策略，允许模型在本地计算设施上运行几分钟到几小时。降阶模型（ROM）是低维近似，可以将当前计算模型的计算成本降低几个数量级。考虑到生物医学和风力工程应用，该项目提出了模型简化的新方法，将昂贵（或高保真）模型的数据和数值结果与机器学习方法相结合，以获得同时达到效率和准确性的 ROM。达到前所未有的水平。数据驱动的 ROM 框架将使主动脉夹层、儿科手术或风电场优化在几分钟内在笔记本电脑上进行数值模拟成为可能，并旨在成为决策过程中关键且值得信赖的工具。该项目将为一名研究生提供支持。数据同化 (DA)、不确定性量化 (UQ) 和形状优化 (SO) 是重要生物医学和工程应用计算模型开发的核心，因为这些应用需要大量数据。模型模拟、运行昂贵的全阶模型 (FOM) 通常非常昂贵，对于显示主导结构的系统来说，降阶模型 (ROM) 可以将 FOM 计算成本降低几个数量级，因此，对于上述临床和工程应用，ROM 表现为：不幸的是，为了捕获主动脉夹层血流动力学的所有几何尺度或应对风电场优化中的大雷诺数，它是运行在高性能计算设施上的昂贵的 FOM 的自然而实用的替代方案。 ROM 模式是必要的。这些相对高维的 ROM 仍然无法有效地执行这些应用的 DA、UQ 或 SO，因此开发 ROM 时需要的不仅是低维且高效的 ROM。在现实的、未解决的情况下是准确的，需要解决 ROM 闭合问题，即需要对被丢弃的 ROM 模式对 ROM 动态的影响进行建模。所提出的研究提出了一种新的数据驱动。 ROM 范式以变分多尺度 (VMS) 方法的分层结构为中心，并利用现代机器学习以及数值和观测数据来开发结构 ROM 闭包，该闭包可以以适度的计算成本显着提高 ROM 精度，从而保持较低的计算成本。现有 ROM 的改进，但显着提高了 ROM 在胸外科和小儿外科（主动脉夹层和 Fontan 手术）中的生物医学应用 - 患者的命运很大程度上取决于 ROM 的形状。数据驱动的 VMS-ROM 框架将最终使这些领域以及其他可能依赖于高效数学和计算建模的领域的 DA、UQ 和 SO 成为可能。通过使用基金会的智力价值和更广泛的影响审查标准进行评估，NSF 的法定使命被认为值得支持。

项目成果

期刊论文数量（13）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Verifiability of the Data-Driven Variational Multiscale Reduced Order Model

数据驱动的变分多尺度降阶模型的可验证性

DOI：
10.1007/s10915-022-02019-y
发表时间：
2022
期刊：
Journal of Scientific Computing
影响因子：
2.5
作者：
Koc, Birgul;Mou, Changhong;Liu, Honghu;Wang, Zhu;Rozza, Gianluigi;Iliescu, Traian
通讯作者：
Iliescu, Traian

On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition

DOI：
10.1137/20m1371798
发表时间：
2020-10
期刊：
ArXiv
影响因子：
0
作者：
Birgul Koc;S. Rubino;M. Schneier;J. Singler;T. Iliescu
通讯作者：
Birgul Koc;S. Rubino;M. Schneier;J. Singler;T. Iliescu

Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents

使用有限时间 Lyapunov 指数的拉格朗日降阶建模

DOI：
10.3390/fluids5040189
发表时间：
2020
期刊：
Fluids
影响因子：
1.9
作者：
Xie, Xuping;Nolan, Peter J.;Ross , Shane D.;Mou , Changhong;Iliescu, Traian
通讯作者：
Iliescu, Traian

Hybrid data-driven closure strategies for reduced order modeling

用于降阶建模的混合数据驱动闭合策略

DOI：
10.1016/j.amc.2023.127920
发表时间：
2023
期刊：
Applied Mathematics and Computation
影响因子：
4
作者：
Ivagnes, Anna;Stabile, Giovanni;Mola, Andrea;Iliescu, Traian;Rozza, Gianluigi
通讯作者：
Rozza, Gianluigi

Data-driven variational multiscale reduced order models