Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error representations, along with other model parameters, would be ideally done while separating the contributions of each of the two sets of parameters, in order to ensure meaningful stand-alone model predictions. This work builds an embedded model error framework using a weight-space representation of Gaussian processes (GPs) to flexibly capture model-error spatiotemporal correlations and enable inference with GP-embedding in non-linear models. To disambiguate model and model-error/bias parameters, we extend an existing orthogonal GP method to the embedded model-error setting and derive appropriate orthogonality constraints. To address the increased dimensionality introduced by the GP representation, we employ the likelihood-informed subspace method. The construction is demonstrated on linear and non-linear examples, where it effectively corrects model predictions to match data trends. Extrapolation beyond the training data recovers the prior predictive distribution, and the orthogonality constraints lead to meaningful stand-alone model predictions and nearly uncorrelated posteriors between model and model-error parameters.

翻译：复杂物理系统的计算模型通常依赖于简化假设，这些假设不可避免地引入模型误差，从而导致预测误差。给定模型可观测量数据，参数化模型误差表示与其他模型参数的估计，理想情况下应在分离两组参数各自贡献的同时进行，以确保有意义的独立模型预测。本研究构建了一个嵌入式模型误差框架，利用高斯过程（GPs）的权重空间表示来灵活捕捉模型误差的时空相关性，并实现在非线性模型中进行GP嵌入推断。为区分模型参数与模型误差/偏差参数，我们将现有正交GP方法扩展至嵌入式模型误差场景，并推导出适当的正交性约束。针对GP表示引入的维度增加问题，我们采用似然信息子空间方法。该构建在线性和非线性示例中得到验证，能有效修正模型预测以匹配数据趋势。在训练数据之外的区域进行外推可恢复先验预测分布，且正交性约束使得独立模型预测具有实际意义，同时模型参数与模型误差参数的后验分布几乎不相关。