Emulating dynamic non-linear simulators using Gaussian processes
Emulating dynamic non-linear simulators using Gaussian processes
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DOI：
10.1016/j.csda.2019.05.006
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发表时间：
2019-11-01
影响因子：
1.8
通讯作者：
Goodfellow, Marc
中科院分区：
文献类型：
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作者：
Mohammadi, Hossein;Challenor, Peter;Goodfellow, Marc
动态仿真的非线性确定性的计算机代码的输出是一个时间序列，可能是多变量，检查。这种计算机模型模拟了一些现实世界现象随时间的演变，例如气候模型或人脑功能。我们感兴趣的模型是高度非线性的，表现出临界点，分叉和混沌行为。但是，每次模拟运行可能太耗时，无法执行需要多次运行的分析，包括量化模型输出相对于输入变化的变化。因此，高斯过程仿真器用于近似代码的输出。要做到这一点，所研究的系统的流程图是在很短的时间内模拟。然后，以迭代的方式使用它来预测整个时间序列。提出了一些方法来考虑到输入的不确定性的仿真器，固定的初始条件后，它们之间的相关性，通过时间序列。该方法说明了两个例子：高度非线性动力系统描述的洛伦兹和货车德尔波尔方程。在这两种情况下，预测性能相对较高，该方法提供的不确定性度量反映了每个系统的可预测性程度。(C)2019年，任作家。由爱思唯尔公司出版
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interested in are highly non-linear and exhibit tipping points, bifurcations and chaotic behaviour. However, each simulation run could be too time-consuming to perform analyses that require many runs, including quantifying the variation in model output with respect to changes in the inputs. Therefore, Gaussian process emulators are used to approximate the output of the code. To do this, the flow map of the system under study is emulated over a short time period. Then, it is used in an iterative way to predict the whole time series. A number of ways are proposed to take into account the uncertainty of inputs to the emulators, after fixed initial conditions, and the correlation between them through the time series. The methodology is illustrated with two examples: the highly non-linear dynamical systems described by the Lorenz and van der Pol equations. In both cases, the predictive performance is relatively high and the measure of uncertainty provided by the method reflects the extent of predictability in each system. (C) 2019 The Authors. Published by Elsevier B.V.