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

• 批准号: 2345048
• 负责人: Omer San
• 金额: $ 15万
• 依托单位: University of Tennessee Knoxville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-10-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2345048&HistoricalAwards=false
• 关键词: Collaborative; Research; Data; Driven; Variational

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 many times models with millions or even billions of unknowns. 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 (such as a laptop). Reduced order models (ROMs) are extremely 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 finally 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.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, i.e., 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 (ML) 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 project will support one graduate student each year at each of the three institutions.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知识的基本工具。他们在实践中的使用取决于它们的可靠性和效率。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。效率在优化问题中尤其重要，其中计算过程确定了复杂系统的最佳工作条件。这些要求导致以数百万甚至数十亿个未知数的方式解决多次模型。此过程可能需要数天或数周的高性能计算设施计算。为了减轻这些成本，我们需要新的建模策略，这些策略允许在本地计算设施（例如笔记本电脑）中以几分钟到几个小时的数小时进行模型运行。减少的订单模型（ROM）是极低的近似值，可以通过数量级来降低当前计算模型的计算成本。考虑到生物医学和风力工程应用，该项目提出了模型还原的新方法。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，以获取在前所未有的水平上达到效率和准确性的ROM。新的数据驱动的ROM框架最终将使主动脉解剖，小儿手术或在几分钟内对笔记本电脑上的风电场优化进行数字模拟，并旨在成为决策过程中的关键和可信赖的工具。DATA同化（DA）（DA），不确定的定量（UQ）和形式的开发（如此之多）的开发（so and Speactiation（uq）和形式的开发功能（如此之多的开发）。由于这些应用需要大量的模型模拟，因此通常禁止运行昂贵的全订单模型（FOM）。对于显示主要结构的系统，减少订单模型（ROM）可以通过数量级降低FOM计算成本。对于上述临床和工程应用程序，ROM似乎是在高性能计算设施上运行的违禁昂贵的FOM的自然而实用的替代方案。不幸的是，要捕获主动脉解剖的血液动力学中的所有几何量表，或者要应对风电场优化中的较大雷诺数，需要数百万种ROM模式。这些相对较高的维度仍然不适用于有效执行DA，UQ，左右。需要的是ROM不仅是低维和高效的，而且还准确。要开发在现实，解决不足的政权上准确的ROM，需要解决ROM关闭问题，即，需要对废弃的ROM模式对ROM动态的影响进行建模。拟议的研究提出了一个新的数据驱动的ROM范式，该范式围绕变异多尺度（VMS）方法的层次结构，并利用现代机器学习（ML）和数值和观察数据来开发结构性rom闭合，这些封闭式可以以适度的计算成本以适度的计算成本急剧提高ROM准确性。新型数据驱动的VMS-ROM范式保持了当前ROM的计算成本较低，但大大提高了ROM的准确性。在胸腔和小儿手术中的生物医学应用（主动脉夹层和方tan手术 - 患者的命运显着取决于血管形状）以及风力工程应用。数据驱动的VMS-ROM框架最终将使有效的DA，UQ，因此在这些框架中，并且可能依赖数学和计算建模的其他字段。该项目将每年在三个机构中的每个机构中为一名研究生提供支持。该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准来评估，被认为是珍贵的支持。