Regime identification and control of extremes in the non-autonomous Lorenz model with chaos and intransitivity

TL;DR

This paper introduces novel finite-time adaptive chaos control strategies for a non-autonomous, seasonally forced Lorenz84 model with noise, using Lyapunov exponents and Hidden Markov Models to identify and mitigate extreme events.

Contribution

It presents the first finite-time adaptive chaos control methods for a non-autonomous Lorenz model, integrating LLE and NHMM-based triggers for real-world weather applications.

Findings

NHMM triggers align with positive LLE regimes, indicating dynamical relevance.

Control strategies successfully mitigate extreme behaviors in the Lorenz84 model.

Results bridge chaos control with deep learning approaches for weather prediction.

Abstract

Adaptive chaos control has been studied extensively for autonomous systems. For real world, non-autonomous systems, such as the planetary weather, observations of the system state in response to seasonally and diurnally varying forcing are available only at discrete times and locations, over which system trajectories are likely to have diverged given uncertainties in initial conditions. We consider a stochastic representation of such systems, as a building block for adaptive control, and develop and test control strategies in an idealized setting. We present the first example of finite time adaptive chaos control for a seasonally forced and noise-perturbed Lorenz84 model. We demonstrate two strategies for triggering control: (1) local Lyapunov exponents (LLE), and (2) transition probabilities for the latent states of a non-homogeneous Hidden Markov Model (NHMM). The second approach is motivated by thinking of future applications to a latent embedding space of planetary atmospheric circulation that would get us closer to real world analyses. The NHMM triggers are found to coincide with strongly positive LLE regimes, confirming their dynamical interpretability. These results provide a conceptual bridge towards the use of deep learning based weather and climate foundation models, whose hidden states could be leveraged for adaptive control to mitigate extreme weather events.