Efficient calibration for high-dimensional computer model output using basis methods
Efficient calibration for high-dimensional computer model output using basis methods
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DOI：
10.1615/int.j.uncertaintyquantification.2022039747
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发表时间：
2019-06
影响因子：
1.7
通讯作者：
James M. Salter;D. Williamson
中科院分区：
文献类型：
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作者：
James M. Salter;D. Williamson
具有高维输出场的昂贵计算机模型的校准可以通过历史匹配来实现。如果整个输出字段都匹配，并且位置或时间点之间的模式或相关性被表示，则计算单个输入设置的观测数据和模型输出之间的距离度量需要对高维矩阵进行时间密集型求逆。通过使用一个低维的基础表示，而不是单独模拟每个输出，我们定义了一个度量在减少的空间，允许该字段的不可信性被有效地计算，只需要小的矩阵求逆，使用投影，这是一致的方差规格的不可信性。我们表明，投影使用的L_2 $范数可能会导致不同的结论，与点的顺序不保持的基础上，历史匹配和概率方法的影响。我们证明了我们的方法的可扩展性，通过历史匹配的加拿大大气模型，CanAM 4，比较基础的方法，每个输出单独的仿真，基础的方法可以更准确，同时也更有效。
Calibration of expensive computer models with high-dimensional output fields can be approached via history matching. If the entire output field is matched, with patterns or correlations between locations or time points represented, calculating the distance metric between observational data and model output for a single input setting requires a time intensive inversion of a high-dimensional matrix. By using a low-dimensional basis representation rather than emulating each output individually, we define a metric in the reduced space that allows the implausibility for the field to be calculated efficiently, with only small matrix inversions required, using projection that is consistent with the variance specifications in the implausibility. We show that projection using the $L_2$ norm can result in different conclusions, with the ordering of points not maintained on the basis, with implications for both history matching and probabilistic methods. We demonstrate the scalability of our method through history matching of the Canadian atmosphere model, CanAM4, comparing basis methods to emulation of each output individually, showing that the basis approach can be more accurate, whilst also being more efficient.