With the advent of integrated computational materials engineering, there is a drive to exchange statistical confidence in a design obtained from repeated experimentation with one developed through modeling and simulation. Since these models are often missing physics or include incomplete knowledge or simplifying assumptions into their mathematical construct, they may not capture the physical system or process adequately over the entire domain. This can lead to a systematic discrepancy, otherwise known as model misfit, between the model output and the system it represents over at least part of the domain. However, by accounting for this discrepancy in uncertainty analyses, reliable inference, and prediction on the model parameters and material behavior can be made despite the missing physics. The previous statement is contingent on two conditions: (1) the discrepancy is systematic, and (2) the structure of the discrepancy is well understood, which is required to minimize issues with non-identifiability among unknown model components. We illustrate these insights via a case study of inference and prediction in a phenomenological meso-scale VPSC crystal plasticity model, which does not contain physics describing the elastic regime of deformation. Inference is performed via a Bayesian approach enabled by posterior simulation. Posterior uncertainty about unknown model parameters takes into account observation error, uncertainty stemming from aleatoric sample-to-sample variability, and model form error. Posterior uncertainty in the unknown Voce hardening parameters is propagated to generate a distribution of the stress–strain response in both the elastic and plastic regimes. Additionally, posterior predictive distributions are simulated to establish uncertainty bounds for future unobserved data.

中文翻译：

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贝叶斯框架内的模型差异的不确定性量化会计

随着集成计算材料工程学的出现，人们对通过反复实验获得的设计与通过建模和仿真开发的设计交换统计置信度的驱动力。由于这些模型通常缺少物理学，或者在其数学构造中包含不完整的知识或简化了假设，因此它们可能无法在整个域中充分捕获物理系统或过程。这可能会导致模型输出和它代表至少部分域的系统之间的系统差异，也称为模型失配。但是，通过考虑不确定性分析中的这种差异，尽管缺少物理原理，但仍可以进行可靠的推断以及对模型参数和材料行为的预测。上一个语句取决于两个条件：（1）差异是系统性的，并且（2）差异的结构得到了很好的理解，这是将未知模型组件之间的不可识别性问题最小化所必需的。我们通过在现象学的中尺度VPSC晶体可塑性模型中进行推理和预测的案例研究来说明这些见解，该模型不包含描述变形弹性态的物理学。通过后验仿真启用的贝叶斯方法进行推理。关于未知模型参数的后验不确定性考虑了观察误差，源于样本间差异的不确定性以及模型形式误差。未知Voce硬化参数的后验不确定性会传播，从而在弹性和塑性状态下产生应力-应变响应的分布。另外，