Quantification of uncertainty of a technical system is often based on a surrogate model of a corresponding simulation model. In any application, the simulation model will not describe the reality perfectly, and consequently the surrogate model will be imperfect. In this article, we combine observed data from the technical system with simulated data from the imperfect simulation model in order to estimate an improved surrogate model consisting of multilayer feedforward neural networks, and we show that under suitable assumptions, this estimate is able to circumvent the curse of dimensionality. Based on this improved surrogate model, we show a rate of the convergence result for density estimates. The finite sample size performance of the estimates is illustrated by applying them to simulated data. The practical usefulness of the newly proposed estimates is demonstrated by using them to predict the uncertainty of a lateral vibration attenuation system with piezo-elastic supports.

中文翻译：

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神经网络不确定性量化中改进代理模型的估计

技术系统不确定性的量化通常基于相应模拟模型的替代模型。在任何应用中，仿真模型都不会完美地描述现实，因此替代模型将是不完美的。在本文中，我们将来自技术系统的观测数据与来自不完美模拟模型的模拟数据相结合，以估计由多层前馈神经网络组成的改进替代模型，并且我们表明，在适当的假设下，该估计能够规避维度诅咒。基于这个改进的代理模型，我们展示了密度估计的收敛结果的速率。通过将它们应用于模拟数据来说明估计的有限样本量性能。