Computational strategies for constructing emulators of complex high-dimensional engineering systems

构建复杂高维工程系统模拟器的计算策略

• 批准号: 402090-2011
• 负责人: Nair, PrasanthBalagopal
• 金额: $ 1.97万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=487933
• 关键词: Computational; strategies; constructing; emulators; complex

When engineers build computer models of real-world engineering systems, they wish to do more than just predict the nominal performance of a single design: they also wish to predict what happens when the design parameters are changed, study the impact of uncertainty on system performance and safety, and ultimately carry out design improvement studies to optimize performance. However, a major obstacle to the successful adoption of computational modeling tools in engineering design practice is computational cost. It is not always practically feasible to run a high-fidelity computational model thousands of times to study various design alternatives or to examine performance variability. This obstacle is becoming more challenging since the fidelity with which engineers desire to model engineering systems has kept pace with advances in computer hardware. A very promising approach for tackling the computational cost issue is through the use of an emulator. An emulator is an approximation model of the original computational model that can be evaluated very cheaply (ideally in real-time). In practically important applications such as uncertainty analysis, design optimization and inverse parameter estimation, where the computer model needs to be run at several points in the parameter space, emulators can thus mitigate the problem of computational expense. The proposed research program will address the key fundamental, theoretical issues and computational challenges in this area in order to develop novel computational strategies for constructing emulators of a broad class of complex, high-dimensional engineering systems. The key elements of the proposed research program will include: (i) Bayesian methods for constructing emulators of the spatio-temporal response of black-box systems; (ii) Galerkin projection schemes for nonlinear, time-dependent parameterized systems; (iii) numerical methods for operator equations defined over parameterized domains; (iv) adaptive function decomposition strategies for circumventing the curse of dimensionality; and (v) parallel implementation of the algorithms developed and application to a range of real-world engineering problems.

当工程师建立真实世界工程系统的计算机模型时，他们希望做的不仅仅是预测单个设计的标称性能：他们还希望预测当设计参数改变时会发生什么，研究不确定性对系统性能和安全性的影响，并最终进行设计改进研究以优化性能。然而，在工程设计实践中成功采用计算建模工具的一个主要障碍是计算成本。实际上，运行高保真计算模型数千次来研究各种设计方案或检查性能变化并不总是可行的。这一障碍正变得越来越具有挑战性，因为工程师希望对工程系统建模的保真度已经与计算机硬件的进步保持同步。解决计算成本问题的一种非常有前途的方法是使用仿真器。仿真器是原始计算模型的近似模型，可以非常便宜地进行评估（理想情况下是实时的）。在实际重要的应用，如不确定性分析，设计优化和逆参数估计，其中的计算机模型需要在参数空间中的几个点上运行，仿真器，从而可以减轻计算费用的问题。拟议的研究计划将解决这一领域的关键基础，理论问题和计算挑战，以开发新的计算策略，用于构建广泛的复杂，高维工程系统的仿真器。拟议的研究计划的主要内容将包括：（一）贝叶斯方法构建仿真器的时空响应的黑箱系统;（二）Galerkin投影计划的非线性，时间依赖的参数化系统;（三）数值方法的算子方程定义的参数化域;（四）自适应功能分解策略，以规避灾难的维数;以及（v）所开发的算法的并行实现和对一系列现实世界工程问题的应用。