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

CDS

基本信息

批准号：
2053872
负责人：
Elaine Spiller
金额：
$ 10万
依托单位：
Marquette University
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=2053872&HistoricalAwards=false
关键词：
CDS&E Collaborative Research Surrogates Reduced

项目摘要

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.

复杂科学系统的数学建模在理解和预测这些系统方面发挥着越来越重要的作用。为了理解不同模型假设和参数值的影响，人们可能需要数百万次计算模拟来全面探测系统的行为。许多复杂系统不是由一个计算模型或算法建模的，而是由需要相互交互的子模型和代码集建模的，这一事实加重了计算负担。本项目旨在开发这种耦合计算模型的高效和灵活的近似，以解决基于数学建模的科学发现过程中的计算瓶颈。该研究将侧重于流体流动和机械变形的原型耦合模型，该模型可用于模拟水力压裂和软骨生物力学。学生将参与并接受项目跨学科方面的培训。科学和实用系统的计算模拟通常需要耦合物理现象的两个或多个数学模型。这种模拟通常依赖于许多输入参数，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，松散耦合连接了模拟不同物理过程的独立代码；进行不确定性量化所需的大量时间，即使是松散耦合的模拟也常常是不可行的。该项目旨在开发高维耦合模拟器的高斯过程仿真方法，从而实现具有挑战性但普遍存在的多物理模型的不确定性量化；这些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逼近整个物理模拟器。这些努力将需要发展(i)降维的新思想，（ii）模拟时空场的新方法，以及（iii）由于降维和模拟而产生的误差分析。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。