Uncovering Extreme Event Mechanisms for Prediction and Control with Sensitivity-Balanced Projections

2026-06-03

AI Summary

Extreme events—such as earthquakes and coronal mass ejections—frequently arise in chaotic systems, yet their underlying mechanisms remain elusive and challenging to predict or control. This work proposes an interpretable, data-driven framework that innovatively integrates Covariance-Based Reduced-Order Subspace identification (CoBRAS), automatic differentiation, and neural network surrogate models. By employing a locally sensitive balanced projection, the approach uncovers causal precursors of extreme events while circumventing the computational complexity of traditional adjoint methods. The methodology achieves high-fidelity prediction and effective suppression of extreme events in diverse systems, including two-dimensional Kolmogorov flow, networks of FitzHugh–Nagumo oscillators, and a modified nonlinear Schrödinger equation. Furthermore, it successfully extends to experimental settings, significantly enhancing our understanding and controllability of spatially localized extreme events.

Abstract

Extreme events -- such as earthquakes and coronal mass ejections -- are common in many chaotic dynamical systems, yet are difficult to characterize and predict due to the subtle instability mechanisms that drive them. In this work, we develop an interpretable technique that reveals the underlying mechanisms behind extreme events and uses them to build data-driven forecasts and intuitive event suppression controllers. In particular, we utilize the covariance balancing reduction using adjoint snapshots (CoBRAS) method to identify linear oblique projections that best capture the sensitivity of a quantity of interest and reconstruct the original state. Importantly, we bypass the need for cumbersome adjoint calculations, instead using backpropagation via modern automatically differentiable numerical frameworks. To accommodate spatially localized events, we also introduce a new variant of CoBRAS to obtain local sensitivity-balanced projections. We demonstrate the utility of this approach to characterize extreme events across a diverse set of challenging systems, including turbulent bursts of energy dissipation in the 2D Kolmogorov Flow, spontaneous synchronization in networks of coupled FitzHugh-Nagumo oscillators, and the localized formation of ocean rogue waves from a modified nonlinear Schrödinger equation. For each example, we show that our simple forecast models accurately predict extreme events and that the underlying mechanisms may be used to design control laws to prevent these events. Finally, we demonstrate that by learning a neural network surrogate model of the dynamics directly from data, we may extend this approach to experimental systems and systems that are not natively written in an automatically differentiable programming language.

Problem

• extreme events
• chaotic dynamical systems
• prediction
• instability mechanisms
• sensitivity

Innovation

• CoBRAS
• sensitivity-balanced projections
• extreme event prediction
• automatic differentiation
• data-driven control