论文标题
模拟昂贵的计算机代码的顺序自适应设计
Sequential adaptive design for emulating costly computer codes
论文作者
论文摘要
高斯工艺（GPS）通常被视为模拟基于计算机基于计算机的模拟器的黄金标准替代模型。但是，使用最少数量的模型评估培训GP的问题仍然具有挑战性。我们通过提出一个称为VIGF的新型自适应采样标准（全球拟合的改进方差）来解决这个问题。在任何时候，改进函数是GP模拟器与最近观察到的模型输出的偏差的度量。在建议的算法的每次迭代中，在VIGF是最大的情况下进行了新的运行。然后，将新样本添加到设计中，并相应地更新模拟器。还提出了批处理版本的VIGF版本，该版本可以节省并行计算时的用户时间。此外，VIGF扩展到多保真案例，在较低的保真度模拟器的协助下预测了昂贵的高保真模型。这是通过分层kriging执行的。我们的方法的适用性是在一堆测试功能上评估的，并将其性能与几种顺序采样策略进行了比较。结果表明，在大多数情况下，我们的方法在预测基准功能方面具有较高的性能。 DGPSI r软件包中可提供VIGF的实现，可以在Cran上找到。
Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of model evaluations remains challenging. We address this problem by suggesting a novel adaptive sampling criterion called VIGF (variance of improvement for global fit). The improvement function at any point is a measure of the deviation of the GP emulator from the nearest observed model output. At each iteration of the proposed algorithm, a new run is performed where VIGF is the largest. Then, the new sample is added to the design and the emulator is updated accordingly. A batch version of VIGF is also proposed which can save the user time when parallel computing is available. Additionally, VIGF is extended to the multi-fidelity case where the expensive high-fidelity model is predicted with the assistance of a lower fidelity simulator. This is performed via hierarchical kriging. The applicability of our method is assessed on a bunch of test functions and its performance is compared with several sequential sampling strategies. The results suggest that our method has a superior performance in predicting the benchmark functions in most cases. An implementation of VIGF is available in the dgpsi R package, which can be found on CRAN.
