In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.

中文翻译：

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变分相场断裂问题的贝叶斯估计方法

在这项工作中，我们提出了裂缝扩展问题的参数估计框架。断裂问题用相场法描述。参数估计是用贝叶斯方法实现的。在这里，重点是固体材料参数和临界能量释放率中出现的不确定性。将选择一个参考值（在足够细化的网格上获得）作为测量数据的替换，并获得它们的后验分布。由于问题的时间和网格依赖性，计算成本可能很高。使用贝叶斯反演，我们在相对粗糙的网格上解决问题并拟合参数。在几个数值示例中，我们提出的框架得到证实，并且获得的载荷 - 位移曲线通常是目​​标函数，