Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often the largest contributor to the overall predictive uncertainty. This work builds on a recently developed framework of embedded, internal model correction, in order to represent and quantify structural errors, together with model parameters, within a Bayesian inference context. We focus specifically on a Polynomial Chaos representation with additive modification of existing model parameters, enabling a non-intrusive procedure for efficient approximate likelihood construction, model error estimation, and disambiguation of model and data errors' contributions to predictive uncertainty. The framework is demonstrated on several synthetic examples, as well as on a chemical ignition problem.

中文翻译：

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贝叶斯模型校准的嵌入式模型误差表示

模型误差估计仍然是不确定性量化和预测科学的主要挑战之一。对于复杂物理系统的计算模型，模型误差，也称为结构误差或模型不足，通常是整体预测不确定性的最大贡献者。这项工作建立在最近开发的嵌入式内部模型校正框架的基础上，以便在贝叶斯推理上下文中表示和量化结构误差以及模型参数。我们特别关注对现有模型参数进行加性修改的多项式混沌表示，从而启用非侵入式程序，以实现有效的近似似然构建、模型误差估计以及模型和数据误差对预测不确定性的贡献的消歧。