Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors

TL;DR

This paper introduces a fast, scalable method for uncertainty quantification in deep operator networks using randomized priors, improving robustness, reliability, and out-of-distribution detection in large-scale applications.

Contribution

It proposes a novel frequentist ensemble approach with an efficient implementation, enabling uncertainty quantification in DeepONets for large models and datasets.

Findings

Provides more robust and accurate predictions than deterministic DeepONets.

Effectively detects out-of-distribution and adversarial examples.

Quantifies uncertainty due to model bias and data noise.

Abstract

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.