This study aims to comprehensively investigate the deep ensemble approach, an approximate Bayesian inference, in the multi-output regression task for predicting the aerodynamic performance of a missile configuration. To this end, the effect of the number of neural networks used in the ensemble, which has been blindly adopted in previous studies, is scrutinized. As a result, an obvious trend towards underestimation of uncertainty as it increases is observed for the first time, and in this context, we propose the deep ensemble framework that applies the post-hoc calibration method to improve its uncertainty quantification performance. It is compared with Gaussian process regression and is shown to have superior performance in terms of regression accuracy ($\uparrow55\sim56\%$), reliability of estimated uncertainty ($\uparrow38\sim77\%$), and training efficiency ($\uparrow78\%$). Finally, the potential impact of the suggested framework on the Bayesian optimization is briefly examined, indicating that deep ensemble without calibration may lead to unintended exploratory behavior. This UQ framework can be seamlessly applied and extended to any regression task, as no special assumptions have been made for the specific problem used in this study.

翻译：本研究旨在全面探究深度集成方法（一种近似贝叶斯推断）在多输出回归任务中预测导弹构型气动性能的应用。为此，本文深入分析了集成中神经网络数量（先前研究中常被盲目采用）的影响。首次发现随着网络数量增加，存在明显的不确定性低估趋势，并据此提出结合事后校准方法的深度集成框架以提升其不确定性量化性能。将该方法与高斯过程回归进行比较，结果表明其在回归精度（$\uparrow55\sim56\%$）、估计不确定性可靠性（$\uparrow38\sim77\%$）及训练效率（$\uparrow78\%$）方面均表现优越。最后，简要探讨了所提框架对贝叶斯优化的潜在影响，指出未校准的深度集成可能导致非预期的探索行为。由于本研究未对特定问题设置特殊假设，该不确定性量化框架可无缝应用于任何回归任务并进行扩展。