In this work, a novel approach to Bayesian model calibration routines is developed which reinterprets the traditional definition of model discrepancy as defined by Kennedy and O'Hagan (KOH). The novelty lies in the integration of $δ_θ(x_i)$ GPs within the simulator, which is approximated as a GP surrogate model to ensure computational tractability. This approach assumes that the utilized simulator sufficiently predicts observed trends when calibrated with respect to the application domain, and that all model-form errors can be attributed to uncertainty in the input parameters. In contrast, the KOH method assumes discrepancy to be inherently decoupled from the simulator, acting as a 'catch-all' for various sources of model error. The new method is applied to Molecular Dynamics observations of the critical stress to drive dislocation dipoles, and equivalent predictions using a Discrete Dislocation Dynamics simulator whose coarse-grained physical interpretation of the underlying physical mechanisms requires calibration against MD observations. We present an overview of similar state-aware calibration routines; differentiate the provided approach through redefining the commonly used discrepancy Gaussian process and benchmark against KOH. A philosophical argument as to when application of the proposed method is appropriate is provided, and future directions for expanding upon this methodology are proposed.

翻译：本研究提出了一种贝叶斯模型校准方法的新范式，该方法重新诠释了Kennedy与O'Hagan（KOH）提出的传统模型差异定义。其创新性在于将$δ_θ(x_i)$高斯过程集成至模拟器内部，并通过高斯过程代理模型进行近似以保证计算可行性。该方法假设所使用的模拟器在针对应用领域进行校准时能充分预测观测趋势，且所有模型形式误差均可归因于输入参数的不确定性。相比之下，KOH方法默认差异与模拟器本质解耦，其作用是对各类模型误差源的"统括式"处理。新方法应用于分子动力学观测中驱动位错偶极子的临界应力预测，并采用离散位错动力学模拟器进行等效预测——该模拟器对底层物理机制的粗粒度物理解释需基于分子动力学观测进行校准。本文综述了具有状态感知能力的同类校准方法；通过重新定义常用差异高斯过程来区分所提出的方法，并与KOH基准进行对比。文中阐述了该方法适用场景的学理论证，并提出了拓展该方法体系的未来研究方向。