Predictability of extreme events in a branching diffusion model

TL;DR

This paper introduces a comprehensive framework for predicting extreme events in complex systems modeled by a branching diffusion process, revealing characteristic premonitory patterns and a universal mechanism behind them.

Contribution

It provides an analytic description of the system's behavior and identifies premonitory deviations that can signal impending extreme events.

Findings

Identification of specific premonitory deviations from self-similarity.

Analytic description of size- and space-dependent distributions.

Universal mechanism for extreme event precursors.

Abstract

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent multi-type branching diffusion process with immigration. A complete analytic description of the size- and space-dependent distributions of particles is derived. We then formulate an extreme event prediction problem and determine characteristic patterns of the system behavior as an extreme event approaches. In particlular, our results imply specific premonitory deviations from self-similarity, which have been heuristically observed in real-world and modeled complex systems. Our results suggest a simple universal mechanism of such premonitory patterns and natural framework for their analytic study.