  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.
