Deep ensemble is a simple and straightforward approach for approximating Bayesian inference and has been successfully applied to many classification tasks. This study aims to comprehensively investigate this approach in the multi-output regression task to predict the aerodynamic performance of a missile configuration. By scrutinizing the effect of the number of neural networks used in the ensemble, an obvious trend toward underconfidence in estimated uncertainty is observed. In this context, we propose the deep ensemble framework that applies the post-hoc calibration method, and its improved uncertainty quantification performance is demonstrated. It is compared with Gaussian process regression, the most prevalent model for uncertainty quantification in engineering, and is proven to have superior performance in terms of regression accuracy, reliability of estimated uncertainty, and training efficiency. Finally, the impact of the suggested framework on the results of Bayesian optimization is examined, showing that whether or not the deep ensemble is calibrated can result in completely different exploration characteristics. This 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:深度集成是一种简单直观的方法,用于逼近贝叶斯推理,在许多分类任务中都取得了成功。本研究旨在全面调查这种方法在多输出回归任务中的应用,以预测导弹构型的空气动力性能。通过研究使用的神经网络数量的影响,观察到估计不确定性的低置信度趋势。我们提出了深度集成框架,应用事后校准方法,证明了其改进的不确定性量化性能。与高斯过程回归进行了比较,后者是工程中用于不确定性量化的最普遍的模型,并证明了其在回归精度、估计不确定性的可靠性和训练效率方面具有卓越的性能。最后,研究了所提出的框架对贝叶斯优化结果的影响,表明深度集成是否被校准会导致完全不同的探索特征。该框架可以无缝地应用和扩展到任何回归任务中,因为没有为本研究中使用的特定问题做任何特殊的假设。