标题： 基于随机先验的深度算子网络的可扩展不确定性量化 显示英文标题

标题： Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors

摘要： 我们提出了一种简单而有效的方法，用于深度算子网络（DeepONets）的后验不确定性量化；这是一种在函数空间中监督学习的新兴范式。 我们采用基于随机先验集合的频率学方法，并提出了一种高效的向量化实现，以便在加速硬件上进行快速并行推理。 通过计算力学和气候建模中的代表性示例，我们表明所提出的方法有四个优点。 (1) 与确定性 DeepONets 相比，它能够提供更稳健和准确的预测。 (2) 它在稀缺数据集上具有多尺度函数对时，能提供可靠的不确定性估计。 (3) 它可以有效地检测分布外和对抗性示例。 (4) 它可以无缝地量化由于模型偏差以及数据中的噪声干扰引起的不确定性。 最后，我们提供了一个优化的 JAX 库称为{\em UQDeepONet}，它可以容纳大型模型架构、大型集成规模以及在加速硬件上具有出色并行性能的大数据集，从而使得在现实中的大规模应用中对 DeepONets 进行不确定性量化成为可能。 显示英文摘要

摘要： 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 {\em 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.