One neuron is more informative than a deep neural network for aftershock pattern forecasting

TL;DR

This paper shows that a single neuron or simple logistic regression models can predict earthquake aftershocks as effectively as complex deep neural networks, questioning the added value of deep learning in this domain.

Contribution

The study demonstrates that deep neural networks do not outperform simpler models like logistic regression in aftershock prediction, highlighting the limited benefit of complex models for this task.

Findings

A single neuron achieves similar AUC as deep neural networks.

Simple models with fewer parameters perform as well as complex deep learning models.

Distance and slip measurements improve prediction accuracy over stress metrics.

Abstract

29 August 2018: "Artificial intelligence nails predictions of earthquake aftershocks". This Nature News headline is based on the results of DeVries et al. (2018) who forecasted the spatial distribution of aftershocks using Deep Learning (DL) and static stress feature engineering. Using receiver operating characteristic (ROC) curves and the area under the curve (AUC) metric, the authors found that a deep neural network (DNN) yields AUC = 0.85 compared to AUC = 0.58 for classical Coulomb stress. They further showed that this result was physically interpretable, with various stress metrics (e.g. sum of absolute stress components, maximum shear stress, von Mises yield criterion) explaining most of the DNN result. We here clarify that AUC c. 0.85 had already been obtained using ROC curves for the same scalar metrics and by the same authors in 2017. This suggests that DL - in fact - does not improve prediction compared to simpler baseline models. We reformulate the 2017 results in probabilistic terms using logistic regression (i.e., one neural network node) and obtain AUC = 0.85 using 2 free parameters versus the 13,451 parameters used by DeVries et al. (2018). We further show that measured distance and mainshock average slip can be used instead of stress, yielding an improved AUC = 0.86, again with a simple logistic regression. This demonstrates that the proposed DNN so far does not provide any new insight (predictive or inferential) in this domain.