Calibration or parameter identification is used with computational mechanics models related to observed data of the modeled process to find model parameters such that good similarity between model prediction and observation is achieved. We present a Bayesian calibration approach for surface coupled problems in computational mechanics based on measured deformation of an interface when no displacement data of material points is available. The interpretation of such a calibration problem as a statistical inference problem, in contrast to deterministic model calibration, is computationally more robust and allows the analyst to find a posterior distribution over possible solutions rather than a single point estimate. The proposed framework also enables the consideration of unavoidable uncertainties that are present in every experiment and are expected to play an important role in the model calibration process. To mitigate the computational costs of expensive forward model evaluations, we propose to learn the log-likelihood function from a controllable amount of parallel simulation runs using Gaussian process regression. We introduce and specifically study the effect of three different discrepancy measures for deformed interfaces between reference data and simulation. We show that a statistically based discrepancy measure results in the most expressive posterior distribution. We further apply the approach to numerical examples in higher model parameter dimensions and interpret the resulting posterior under uncertainty. In the examples, we investigate coupled multi-physics models of fluid–structure interaction effects in biofilms and find that the model parameters affect the results in a coupled manner.

中文翻译：

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基于界面变形的不确定性耦合计算力学模型贝叶斯标定

校准或参数识别与与建模过程的观测数据相关的计算力学模型一起使用，以找到模型参数，从而实现模型预测和观测之间的良好相似性。当没有材料点的位移数据可用时，我们基于界面的测量变形提出了计算力学中表面耦合问题的贝叶斯校准方法。与确定性模型校准相比，将此类校准问题解释为统计推断问题在计算上更加稳健，并允许分析人员找到可能解决方案的后验分布，而不是单点估计。拟议的框架还可以考虑每个实验中存在的不可避免的不确定性，这些不确定性有望在模型校准过程中发挥重要作用。为了减轻昂贵的正向模型评估的计算成本，我们建议使用高斯过程回归从可控数量的并行模拟运行中学习对数似然函数。我们介绍并具体研究了三种不同的差异度量对参考数据和模拟之间的变形界面的影响。我们表明，基于统计的差异度量会导致最具表现力的后验分布。我们进一步将该方法应用于更高模型参数维度的数值示例，并解释在不确定性下产生的后验结果。在示例中，