A Kolmogorov-Arnold Neural Model for Cascading Extremes

TL;DR

This paper introduces KANE, a neural network model based on Kolmogorov-Arnold networks, to assess the probability of cascading extreme events like earthquakes and tsunamis, with applications in seismology and climatology.

Contribution

It develops a novel neural network framework integrating extreme value theory to model domino effects in cascading extreme events, with a natural parameter enforcement layer.

Findings

Demonstrates effectiveness through numerical studies

Successfully applied to real-world seismology data

Provides a new tool for risk assessment of cascading extremes

Abstract

This paper addresses the growing concern of cascading extreme events, such as an extreme earthquake followed by a tsunami, by presenting a novel method for risk assessment focused on these domino effects. The proposed approach develops an extreme value theory framework within a Kolmogorov-Arnold network (KAN) to estimate the probability of one extreme event triggering another, conditionally on a feature vector. An extra layer is added to the KAN architecture to ensure that the parameter of interest lies within the unit interval, and we refer to the resulting neural model as KANE (KAN with Natural Enforcement). The proposed method is backed by exhaustive numerical studies and further illustrated with real-world applications to seismology and climatology.