Simulations are often used for the design of complex systems as they allow one to explore the design space without the need to build several prototypes. Over the years, the simulation accuracy, as well as the associated computational cost, has increased significantly, limiting the overall number of simulations during the design process. Therefore, metamodeling aims to approximate the simulation response with a cheap to evaluate mathematical approximation, learned from a limited set of simulator evaluations. Kernel-based methods using stationary kernels are nowadays widely used. In many problems, the smoothness of the function varies in space, which we call nonstationary behavior [20]. However, using stationary kernels for nonstationary responses can be inappropriate and result in poor models when combined with sequential design. We present the application of two recent techniques: Deep Gaussian Processes and Gaussian Processes with nonstationary kernel, which are better able to cope with these difficulties. We evaluate the method for nonstationary regression on a series of real-world problems, showing that these recent approaches outperform the standard Gaussian Processes with stationary kernels. Results show that these techniques are suitable for the simulation community, and we outline the variational inference method for the Gaussian Process with nonstationary kernel.

中文翻译：

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用于改进元建模的分层高斯过程模型

模拟通常用于复杂系统的设计，因为它们允许人们探索设计空间而无需构建多个原型。多年来，仿真精度以及相关的计算成本显着增加，限制了设计过程中的仿真总数。因此，元建模旨在通过从一组有限的模拟器评估中学习到的廉价数学近似来近似模拟响应。现在广泛使用使用固定内核的基于内核的方法。在很多问题中，函数的平滑度在空间上是不同的，我们称之为非平稳的行为[20]。但是，将平稳核用于非平稳响应可能是不合适的，并且在与顺序设计相结合时会导致模型不佳。我们介绍了两种最新技术的应用：深度高斯过程和具有非平稳核的高斯过程，它们能够更好地应对这些困难。我们评估了一系列实际问题的非平稳回归方法，表明这些最近的方法优于具有平稳内核的标准高斯过程。结果表明，这些技术适用于仿真界，我们概述了具有非平稳核的高斯过程的变分推理方法。