Seo Yun Am, Park Jeong-Soo
AI Weather Forecast Research Team, National Institute of Meteorological Sciences, Seogwipo 697-010, Korea.
Department of Statistics, Chonnam National University, Gwangju 61186, Korea.
Entropy (Basel). 2020 Dec 31;23(1):53. doi: 10.3390/e23010053.
The approximated non-linear least squares (ALS) tunes or calibrates the computer model by minimizing the squared error between the computer output and real observations by using an emulator such as a Gaussian process (GP) model. A potential defect of the ALS method is that the emulator is constructed once and it is no longer re-built. An iterative method is proposed in this study to address this difficulty. In the proposed method, the tuning parameters of the simulation model are calculated by the conditional expectation (E-step), whereas the GP parameters are updated by the maximum likelihood estimation (M-step). These EM-steps are alternately repeated until convergence by using both computer and experimental data. For comparative purposes, another iterative method (the max-min algorithm) and a likelihood-based method are considered. Five toy models are tested for a comparative analysis of these methods. According to the toy model study, both the variance and bias of the estimates obtained from the proposed EM algorithm are smaller than those from the existing calibration methods. Finally, the application to a nuclear fusion simulator is demonstrated.
近似非线性最小二乘法（ALS）通过使用诸如高斯过程（GP）模型这样的模拟器，使计算机输出与实际观测值之间的平方误差最小化，从而对计算机模型进行调整或校准。ALS方法的一个潜在缺陷是模拟器只构建一次，不再重新构建。本研究提出了一种迭代方法来解决这一难题。在所提出的方法中，模拟模型的调谐参数通过条件期望（E步）计算，而GP参数通过最大似然估计（M步）更新。通过交替重复这些EM步骤，直到使用计算机数据和实验数据收敛。为了进行比较，还考虑了另一种迭代方法（最大-最小算法）和一种基于似然的方法。对五个玩具模型进行测试，以对这些方法进行比较分析。根据玩具模型研究，从所提出的EM算法获得的估计值的方差和偏差均小于现有校准方法的方差和偏差。最后，展示了该方法在核聚变模拟器中的应用。
