We present a simple and effective approach for posterior uncertainty quantification in deep operator networks (DeepONets); an emerging paradigm for supervised learning in function spaces. We adopt a frequentist approach based on randomized prior ensembles, and put forth an efficient vectorized implementation for fast parallel inference on accelerated hardware. Through a collection of representative examples in computational mechanics and climate modeling, we show that the merits of the proposed approach are fourfold. (1) It can provide more robust and accurate predictions when compared against deterministic DeepONets. (2) It shows great capability in providing reliable uncertainty estimates on scarce data sets with multi-scale function pairs. (3) It can effectively detect out-of-distribution and adversarial examples. (4) It can seamlessly quantify uncertainty due to model bias, as well as noise corruption in the data. Finally, we provide an optimized JAX library called UQDeepONet that can accommodate large model architectures, large ensemble sizes, as well as large data sets with excellent parallel performance on accelerated hardware, thereby enabling uncertainty quantification for DeepONets in realistic large-scale applications. All code and data accompanying this manuscript will be made available at https://github.com/PredictiveIntelligenceLab/UQDeepONet.

我们提出了一种简单有效的方法来量化深度运营商网络（DeepONets）中的后验不确定性；功能空间中监督学习的新兴范式。我们采用一个基于随机先验集成的频率论方法，并提出了一种有效的矢量化实现，用于在加速硬件上进行快速并行推理。通过收集计算力学和气候建模中的代表性示例，我们表明所提出方法的优点是四方面的。(1) 与确定性 DeepONets 相比，它可以提供更稳健和准确的预测。(2) 它显示出强大的能力，可以为具有多尺度函数对的稀缺数据集提供可靠的不确定性估计。（3）它可以有效地检测出分布外和对抗性的例子。(4) 它可以无缝量化由于模型偏差以及数据中的噪声损坏造成的不确定性。最后，我们提供了一个优化的 JAX 库，称为UQDeepONet它可以适应大型模型架构、大型集成规模以及在加速硬件上具有出色并行性能的大型数据集，从而在现实的大规模应用中实现 DeepONets 的不确定性量化。本手稿随附的所有代码和数据将在 https://github.com/PredictiveIntelligenceLab/UQDeepONet 上提供。