Comparison of Sampling Strategies for Gaussian Process Models, with Application to Nanoparticle Dynamics

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• 作者：Andres F. Hernandez ; Martha A. Grover
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2011
• 出版时间：February 2, 2011
• 年：2011
• 卷：50
• 期：3
• 页码：1379-1388
• 全文大小：330K
• 年卷期：v.50,no.3(February 2, 2011)
• ISSN：1520-5045

文摘

Gaussian process modeling (GPM) is widely used in engineering design as a surrogate model for more complex and computationally demanding simulations. However, few fundamental studies focus on GPM as a surrogate for stochastic or high-dimensional dynamic systems. This paper provides a critical evaluation of selection strategies for sample collection in GPM from a stochastic dynamic multivariable simulation. Since the simulation may have high computational demands, it is important that the finite number of sample locations be carefully designed to be highly informative for building the GPM. Because the simulations are stochastic, one must determine whether repetitions at each point are necessary to accurately capture the noise behavior, or rather if the points should be spread out over the sampling space. A case study based on nanoparticle synthesis is used here to motivate and illustrate the GPM approach and several options and challenges for sample selection in the context of dynamic systems modeling. Our results show that the use of more repetitions does not provide a clear benefit when the total number of simulation samples is fixed. Our work also shows that including trend functions in GPM improves the prediction accuracy over a single discrete time step. However, when GPM is used recursively to predict dynamic trajectories, the trend functions may instead lead to extrapolation of the dynamic trajectory creating larger errors.