Laplacian deep ensembles: Methodology and application in predicting dUT1 considering geophysical fluids

Abstract

Increasing the accuracy and reliability of deep learning models is a crucial yet challenging task. The Bayesian approach is typically inefficient in achieving this goal, because of its daunting computational complexity. A promising alternative approach is based on ensembling of models with disparate initial parameters, which result in different model predictions. However, this approach is mainly based on the assumption of Gaussian distribution for data, which might suffer from the presence of outliers, out-of-distribution data, and the lack of diversity among ensemble members. Here we propose to consider Laplacian distribution for data, and introduce Laplacian Deep Ensembles (LDE). We present the formulation of LDE and show that it is akin to the familiar L1 norm minimization, thus being more resilient to outliers and out-of-distribution data. We also introduce the repulsive form of the LDE that enhances the diversity among ensemble members and is aysmptotically convergent to the Bayesian approach. We present an application in the field of geodesy, for the short-term prediction of dUT1, which represents the deviation of universal time (tied to Earth’s rotation) from the coordinated universal time (based on atomic clocks) due to the effect of geophysical fluids (namely atmosphere, ocean, land hydrology, and sea-level variations). We show that dUT1 is predictable with high accuracy up to 10 days ahead. We demonstrate that not only is LDE more accurate than its Gaussian counterpart, but also the repulsive LDE represents on average $\sim$12% improvement compared to alternative, state-of-the-art predictions. This improvement has considerable importance for various applications that rely on precise timekeeping, such as satellite navigation.