Multi-fidelity Gaussian process regression for computer experiments
Multi-fidelity Gaussian process regression for computer experiments
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发表时间：
2013-10
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通讯作者：
Loic Le Gratiet
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作者：
Loic Le Gratiet
这项工作是关于基于高斯过程的代码的近似，它可以在不同的精度水平上运行。其目标是使用复杂计算机代码的快速近似来改进对该代码的代理模型的预测。提出了一种新的基于协同克立格法的方法。具体地说，该公式允许快速实施，并允许在多保真框架中的通用协克里格法的预测均值和方差的闭合形式表达式，这是一个突破，因为它确实允许这种方法在实际情况中的实际应用。此外，快速交叉验证、序贯实验设计和灵敏度分析方法已扩展到多保真协克里格法框架。本文还讨论了关于学习曲线(即均方误差的衰减率)相对于基础函数的光滑性的一个猜想。在相当一般的情况下(包括具有平稳协方差函数的基于高斯过程的元模型的经典模型)，得到了一个证明，而以前的证明只适用于退化核(即当过程实际上是有限维的时候)。这一结果有助于解决严格的实际问题，例如在多保真框架内不同级别的代码之间最佳分配预算。
This work is on Gaussian-process based approximation of a code which can be run at different levels of accuracy. The goal is to improve the predictions of a surrogate model of a complex computer code using fast approximations of it. A new formulation of a co-kriging based method has been proposed. In particular this formulation allows for fast implementation and for closed-form expressions for the predictive mean and variance for universal co-kriging in the multi-fidelity framework, which is a breakthrough as it really allows for the practical application of such a method in real cases. Furthermore, fast cross validation, sequential experimental design and sensitivity analysis methods have been extended to the multi-fidelity co-kriging framework. This thesis also deals with a conjecture about the dependence of the learning curve (ie the decay rate of the mean square error) with respect to the smoothness of the underlying function. A proof in a fairly general situation (which includes the classical models of Gaussian-process based metamodels with stationary covariance functions) has been obtained while the previous proofs hold only for degenerate kernels (ie when the process is in fact finite-dimensional). This result allows for addressing rigorously practical questions such as the optimal allocation of the budget between different levels of codes in the multi-fidelity framework.