Computer simulators are often used as a substitute of complex real-life phenomena which are either expensive or infeasible to experiment with. This paper focuses on how to efficiently solve the inverse problem for an expensive to evaluate time series valued computer simulator. The research is motivated by a hydrological simulator which has to be tuned for generating realistic rainfall-runoff measurements in Athens, Georgia, USA. Assuming that the simulator returns g(x,t) over L time points for a given input x, the proposed methodology begins with a careful construction of a discretization (time-) point set (DPS) of size $k << L$, achieved by adopting a regression spline approximation of the target response series at k optimal knots locations $\{t^*_1, t^*_2, ..., t^*_k\}$. Subsequently, we solve k scalar valued inverse problems for simulator $g(x,t^*_j)$ via the contour estimation method. The proposed approach, named MSCE, also facilitates the uncertainty quantification of the inverse solution. Extensive simulation study is used to demonstrate the performance comparison of the proposed method with the popular competitors for several test-function based computer simulators and a real-life rainfall-runoff measurement model.
翻译:计算机模拟器经常被用来替代复杂的真实生活现象,这些现象要么昂贵,要么难以试验。本文侧重于如何有效解决对一个昂贵的、用于评价时间序列价值计算机模拟器的反问题。研究的动机是水文模拟器,该模拟器必须加以调整,以便在雅典、乔治亚、美国进行切合实际的降雨径流测量。假设模拟器在L时间点上返回一个特定输入x(x,t),提议的方法首先谨慎地构建一个规模为$ ⁇ ⁇ L$ 的离散点(时间点)集(DPS),通过在最理想的节点对目标响应序列进行回归螺旋近似值 $ ⁇ 1, t ⁇ 2,..., t ⁇ k $。随后,我们通过等量估计方法解决对模拟器 $g(x,t ⁇ j) 的反问题。拟议的方法名为MSCE,也便于对反向解决方案进行不确定性的量化。广泛的模拟模拟研究采用了以计算机模拟模型为主的模拟测试模型,并用计算机测试模拟机床测试模拟器演示了各种模拟模型的模拟模型的模拟模拟模拟模拟测试性能的模拟比较。