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，这些要求导致求解具有数百万甚至数十亿个未知数的多次模型，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。为了降低这些成本，我们需要新的建模策略，允许模型在本地计算设备（例如笔记本电脑）上运行几分钟到几小时。降阶模型（ROM）是极低维的近似，可以降低当前的计算成本。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 ROM 的新方法。兼顾效率和准确性新的数据驱动 ROM 框架最终将使在笔记本电脑上在几分钟内进行主动脉夹层、儿科手术或风电场优化的数值模拟成为可能，并旨在成为决策过程中关键且值得信赖的工具。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的计算模型开发的核心，因为这些应用需要大量的模型模拟，运行昂贵的全订单。模型对于显示主导结构的系统，降阶模型 (FOM) 通常非常昂贵，因此，对于上述临床和工程应用，降阶模型 (ROM) 可以降低 FOM 计算成本，这是一种自然且实用的替代方案。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，需要成百上千的 ROM 模式。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，我们需要的 ROM 不仅是低维的、高效的，而且是准确的。 ，未解决的机制，需要解决 ROM 闭包问题，即需要对被丢弃的 ROM 模式对 ROM 动态的影响进行建模。该研究提出了一种新的以数据驱动的 ROM 范式。围绕变分多尺度 (VMS) 方法的分层结构，并利用现代机器学习 (ML) 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。该范例保持了当前 ROM 的低计算成本，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 - 患者的命运很大程度上取决于血管形状）中的生物医学应用的准确性。数据驱动的 VMS-ROM 框架最终将使这些领域以及其他可能依赖数学和计算建模的领域的高效 DA、UQ 和 SO 成为可能。这三个机构每年都会招收研究生。该奖项反映了 NSF 的法定使命，并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，被认为值得支持。