Scalable uncertainty quantification for deep operator networks using randomized priors

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.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study presents a simple and effective method for quantifying posterior uncertainty in deep operator networks (DeepONets). The approach utilizes a frequentist approach with randomized prior ensembles and introduces an efficient vectorized implementation for fast parallel inference. The proposed method exhibits four main advantages: more robust and accurate predictions compared to deterministic DeepONets, reliable uncertainty estimates for sparse data sets with multi-scale function pairs, effective detection of out-of-distribution and adversarial examples, and seamless quantification of uncertainty due to model bias and data noise. Additionally, the study provides an optimized JAX library called UQDeepONet that can handle large model architectures, ensemble sizes, and data sets with excellent parallel performance on accelerated hardware, enabling uncertainty quantification for DeepONets in realistic large-scale applications.