Uncertainty Quantification for Signal-to-Signal Regression-Based Neural Operator Frameworks

Recently, operator learning frameworks have gained significant attention in the field of scientific machine learning because of their ability to approximate mathematical operators from data. However, despite their ability to model complex physical phenomena, they cannot be directly employed in safety-critical applications without ascertaining the reliability of their predictions. Therefore, in this work, different strategies for modeling uncertainty associated with predictions of signal-to-signal regression-based neural operator frameworks are developed and evaluated on a variety of differential equations from the field of mechanics. Specifically, the probabilistic Fourier neural operator is developed and coupled with the deep ensemble method in order to separately quantify aleatoric and epistemic uncertainty. In addition, a randomized prior Fourier neural operator is developed for the quantification of uncertainty in the predictive setting of spatiotemporal trajectory rollout. Furthermore, a bi-fidelity Fourier neural operator-based ensemble model is also proposed. Moreover, the performance assessment of the propounded models is conducted using multiple case studies.