A Kolmogorov-Arnold Neural Model for Cascading Extremes

2025-05-19

AI Summary

Assessing risks of cascading extreme events—such as earthquakes triggering tsunamis or heatwaves inducing droughts—remains challenging due to complex, nonlinear dependencies among extremes. Method: We propose a novel framework integrating extreme-value theory with interpretable neural networks, centered on the KANE model: a Kolmogorov–Arnold Network (KAN) augmented with a unit-interval natural constraint layer, enabling bounded, physically grounded, and interpretable neural modeling of extremal dependence parameters; conditional extreme probabilities are explicitly modeled to quantify the likelihood that a precursor extreme event triggers a subsequent one given covariates. Results: Experiments demonstrate substantial improvements in cascading probability estimation accuracy. The model exhibits strong generalizability and physical consistency in joint risk analysis of earthquake sequences and climate extremes, offering a theoretically rigorous and interpretable paradigm for assessing compound hazard chains.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

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's architecture to enforce the definition of the parameter of interest 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.

Problem

• Assessing cascading extreme events like earthquake-tsunami sequences
• Modeling conditional probability of one extreme triggering another
• Enforcing parameter constraints in neural networks for risk estimation

Innovation

• Kolmogorov-Arnold network for cascading extremes
• Extra layer enforces unit interval parameter
• Exhaustive numerical studies validate KANE model