In this study, we focus on developing efficient calibration methods via Bayesian decision-making for the family of compartmental epidemiological models. The existing calibration methods usually assume that the compartmental model is cheap in terms of its output and gradient evaluation, which may not hold in practice when extending them to more general settings. Therefore, we introduce model calibration methods based on a "graybox" Bayesian optimization (BO) scheme, more efficient calibration for general epidemiological models. This approach uses Gaussian processes as a surrogate to the expensive model, and leverages the functional structure of the compartmental model to enhance calibration performance. Additionally, we develop model calibration methods via a decoupled decision-making strategy for BO, which further exploits the decomposable nature of the functional structure. The calibration efficiencies of the multiple proposed schemes are evaluated based on various data generated by a compartmental model mimicking real-world epidemic processes, and real-world COVID-19 datasets. Experimental results demonstrate that our proposed graybox variants of BO schemes can efficiently calibrate computationally expensive models and further improve the calibration performance measured by the logarithm of mean square errors and achieve faster performance convergence in terms of BO iterations. We anticipate that the proposed calibration methods can be extended to enable fast calibration of more complex epidemiological models, such as the agent-based models.

翻译：本研究聚焦于针对仓室流行病学模型族，通过贝叶斯决策开发高效校准方法。现有校准方法通常假设仓室模型的输出与梯度计算成本较低，但在扩展至更一般化场景时，该假设在实践中往往难以成立。为此，我们提出基于"灰盒"贝叶斯优化（BO）框架的模型校准方法，实现对广义流行病学模型的高效校准。该方法采用高斯过程作为高成本模型的代理模型，并利用仓室模型的功能结构特性以提升校准性能。此外，我们通过解耦决策策略开发了贝叶斯优化校准方法，进一步挖掘了功能结构的可分解特性。基于模拟真实疫情过程的仓室模型生成的多样化数据以及真实世界COVID-19数据集，我们对多种提出方案的校准效率进行了评估。实验结果表明，所提出的灰盒贝叶斯优化变体方案能有效校准计算成本高昂的模型，在均方误差对数指标上进一步提升校准性能，并在贝叶斯优化迭代中实现更快的性能收敛。我们预期所提出的校准方法可扩展至更复杂的流行病学模型（如基于智能体的模型）的快速校准。