Predictors and Predictands of Linear Response in Spatially Extended Systems

TL;DR

This paper introduces a method to evaluate and rank the predictive power of observables in spatially extended systems, using the Lorenz '96 model to understand signal propagation and causal links.

Contribution

It presents a novel approach for quantifying and ranking the predictive ability of observables to infer causal relationships in complex systems.

Findings

Local observables can predict each other's behavior to reveal signal propagation.

Using multiple forcings and observables improves prediction efficiency.

The method provides insights into causal links within spatially extended systems.

Abstract

The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system by using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz '96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.