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

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名义性能：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。运行一个高保真计算模型数千次来研究各种设计方案或检查性能的可变性并不总是实际可行的。这一障碍正变得更具挑战性，因为工程师希望对工程系统进行建模的保真度已经跟上了计算机硬件的进步。解决计算成本问题的一个非常有前途的方法是通过使用仿真器。仿真器是原始计算模型的近似模型，其评估成本非常低(理想情况下是实时的)。在诸如不确定性分析、设计优化和逆参数估计等实际重要的应用中，计算机模型需要在参数空间中的多个点运行，因此仿真器可以减轻计算开销的问题。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，以便为构建广泛类别的复杂、高维工程系统的仿真器开发新的计算策略。该研究计划的主要内容将包括：(I)构建黑盒系统时空响应仿真器的贝叶斯方法；(Ii)非线性、依赖于时间的参数化系统的Galerkin投影格式；(Iii)定义在参数区域上的算子方程的数值方法；(Iv)规避维度诅咒的自适应函数分解策略；以及(V)所开发的算法的并行实现并应用于一系列真实世界的工程问题。

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.