Prediction of Large Events in Directed Sandpiles

TL;DR

This paper investigates the predictability of large avalanche events in directed sandpile models, demonstrating that certain strategies can predict large events in finite systems but not in the thermodynamic limit.

Contribution

It introduces and analytically evaluates two prediction strategies for large avalanches, highlighting their effectiveness and limitations in different system sizes.

Findings

Large events are predictable in finite systems using local anticorrelation strategies.

Predictability diminishes and disappears in the thermodynamic limit.

Exact conditional probabilities and ROC curves are derived for the excess density strategy.

Abstract

The degree of predictability of large avalanche events in the directed sandpile model is studied. A waiting time based prediction strategy which exploits the local anticorrelation of large events is discussed. With this strategy we show analytically and numerically that large events are predictable to some extent, and that this predictability persists in the thermodynamic limit. We introduce another strategy which predicts large avalanches in the future based on the present excess density in the sandpile. We obtain the exact conditional probabilities for large events given an excess density, and use this to determine the exact form of the ROC predictability curves. We show that for this strategy, the model is predictable only for finite lattice sizes, and unpredictable in the thermodynamic limit. This behaviour is to be contrasted with previously established numerical studies carried out for Manna sandpiles.