Nowadays, numerical models are widely used in most of engineering fields to simulate the behaviour of complex systems, such as for example power plants or wind turbine in the energy sector. Those models are nevertheless affected by uncertainty of different nature (numerical, epistemic) which can affect the reliability of their predictions. We develop here a new method for quantifying conditional parameter uncertainty within a chain of two numerical models in the context of multiphysics simulation. More precisely, we aim to calibrate the parameters $\theta$ of the second model of the chain conditionally on the value of parameters $\lambda$ of the first model, while assuming the probability distribution of $\lambda$ is known. This conditional calibration is carried out from the available experimental data of the second model. In doing so, we aim to quantify as well as possible the impact of the uncertainty of $\lambda$ on the uncertainty of $\theta$. To perform this conditional calibration, we set out a nonparametric Bayesian formalism to estimate the functional dependence between $\theta$ and $\lambda$, denoted $\theta(\lambda)$. First, each component of $\theta(\lambda)$ is assumed to be the realization of a Gaussian process prior. Then, if the second model is written as a linear function of $\theta(\lambda)$, the Bayesian machinery allows us to compute analytically the posterior predictive distribution of $\theta(\lambda)$ for any set of realizations $\lambda$. The effectiveness of the proposed method is illustrated on several analytical examples.

翻译：当今，数值模型广泛应用于大多数工程领域，以模拟复杂系统的行为，例如能源领域的发电厂或风力涡轮机。然而，这些模型受到不同性质的不确定性（数值不确定性、认知不确定性）的影响，从而可能影响其预测的可靠性。本文在多物理场仿真的背景下，提出了一种新方法，用于量化两个数值模型链中条件参数的不确定性。更具体地说，我们旨在根据第一模型参数$\lambda$的值，对链中第二模型的参数$\theta$进行条件校准，同时假设$\lambda$的概率分布是已知的。这种条件校准基于第二模型可用的实验数据完成。通过这种方式，我们旨在尽可能量化$\lambda$的不确定性对$\theta$不确定性的影响。为执行此条件校准，我们提出了一种非参数贝叶斯框架，用于估计$\theta$与$\lambda$之间的函数依赖关系，记为$\theta(\lambda)$。首先，$\theta(\lambda)$的每个分量被假设为高斯过程先验的一个实现。随后，若第二模型被表示为$\theta(\lambda)$的线性函数，贝叶斯机制允许我们解析地计算任意$\lambda$实现集下$\theta(\lambda)$的后验预测分布。所提方法的有效性通过若干解析示例进行了验证。