CDS&E: Collaborative Research: Surrogates and Reduced Order Modeling for High Dimensional Coupled Systems

CDS

• 批准号: 2053858
• 负责人: Susan Minkoff
• 金额: $ 10万
• 依托单位: University of Texas at Dallas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-08-01 至 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2053858&HistoricalAwards=false
• 关键词: CDS&E; Collaborative; Research; Surrogates; Reduced

Increasingly, mathematical modeling of complex scientific systems plays a crucial role both in understanding and in making predictions about these systems. To understand the effects of different model assumptions and parameter values, one might need millions of computational simulations to fully probe a system's behavior. This computational burden is compounded by the fact that many complex systems are modeled not by just one computational model or algorithm, but rather by sets of sub-models and codes that need to interact with each other. This project aims to develop efficient and flexible approximations to such coupled computational models, to take the computational bottleneck out of the mathematical modeling-based scientific discovery process. The research will focus on a prototype coupled model of fluid flow and mechanical deformation that can be adapted to model both hydraulic fracturing and cartilage biomechanics. Students will be involved and trained in interdisciplinary aspects of the project. Computational simulation of systems of scientific and practical interest often requires coupling two or more mathematical models of physical phenomena. Such simulations typically depend on many input parameters, while validation of the models is constrained by limited available data. Numerical simulators of coupled mathematical models use approaches of full or loose coupling. Full coupling involves solving a single set of equations simultaneously, but due to computational complexity, feasible run times often necessitate simplified physics models. Conversely, loose coupling connects independent codes simulating distinct physical processes; it is often infeasible to run even loosely coupled simulations the large number of times required to perform uncertainty quantification. This project aims to develop methodology for Gaussian process emulation of high-dimensional coupled simulators and thus enable uncertainty quantification for challenging yet ubiquitous multi-physics models; the approaches will involve surrogate or reduced-order models of the governing model equations to allow quick approximation of the full physical simulator at different inputs. The efforts will entail developing (i) new ideas for dimension reduction, (ii) a novel method to emulate space-time fields, and (iii) an analysis of errors owing to both dimension reduction and emulation.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.

越来越多的复杂科学系统的数学建模在理解和预测这些系统方面起着至关重要的作用。为了理解不同模型假设和参数值的影响，可能需要数百万次计算模拟来充分探测系统的行为。这种计算负担由于以下事实而变得更加复杂：许多复杂系统不是由一个计算模型或算法来建模，而是由需要彼此交互的子模型和代码集来建模。该项目旨在开发有效和灵活的近似这种耦合的计算模型，以消除基于数学建模的科学发现过程中的计算瓶颈。该研究将集中在流体流动和机械变形的原型耦合模型上，该模型可用于水力压裂和软骨生物力学建模。学生将参与并接受该项目跨学科方面的培训。科学和实际感兴趣的系统的计算模拟通常需要耦合两个或更多个物理现象的数学模型。这种模拟通常取决于许多输入参数，而模型的验证受到有限的可用数据的限制。耦合数学模型的数值模拟器采用全耦合或松耦合的方法。完全耦合涉及同时求解一组方程，但由于计算复杂性，可行的运行时间通常需要简化的物理模型。相反，松散耦合连接独立的代码模拟不同的物理过程;它往往是不可行的，即使是松散耦合的模拟所需的大量时间来执行不确定性量化。该项目旨在为高维耦合模拟器的高斯过程仿真开发方法，从而为具有挑战性但普遍存在的多物理模型提供不确定性量化;该方法将涉及控制模型方程的代理或降阶模型，以允许在不同输入下快速近似完整的物理模拟器。这些努力将需要开发（i）新的降维思想，（ii）新的模拟时空场的方法，（iii）分析由于降维和模拟而产生的误差。该奖项反映了NSF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。