High-fidelity computational simulations and physical experiments of hypersonic flows are resource intensive. Training scientific machine learning (SciML) models on limited high-fidelity data offers one approach to rapidly predict behaviors for situations that have not been seen before. However, high-fidelity data is itself in limited quantity to validate all outputs of the SciML model in unexplored input space. As such, an uncertainty-aware SciML model is desired. The SciML model's output uncertainties could then be used to assess the reliability and confidence of the model's predictions. In this study, we extend a DeepONet using three different uncertainty quantification mechanisms: mean-variance estimation, evidential uncertainty, and ensembling. The uncertainty aware DeepONet models are trained and evaluated on the hypersonic flow around a blunt cone object with data generated via computational fluid dynamics over a wide range of Mach numbers and altitudes. We find that ensembling outperforms the other two uncertainty models in terms of minimizing error and calibrating uncertainty in both interpolative and extrapolative regimes.

翻译：高保真计算模拟和高超声速流的物理实验资源消耗巨大。在有限的保真数据上训练科学机器学习模型，为预测未见情况下的行为提供了一种快速方法。然而，高保真数据本身数量有限，无法验证科学机器学习模型在未探索输入空间中的所有输出。因此，需要一种具有不确定性感知能力的科学机器学习模型。该模型输出的不确定性可用于评估模型预测的可靠性和置信度。本研究通过三种不同的不确定性量化机制扩展了DeepONet：均值方差估计、证据不确定性和集成方法。这些具有不确定性感知能力的DeepONet模型在钝锥物体周围的高超声速流数据上进行了训练和评估，数据通过计算流体动力学在广泛马赫数和高度范围内生成。研究发现，在插值和外推条件下，集成方法在最小化误差和校准不确定性方面均优于其他两种不确定性模型。