A method for identifying causality in the response of nonlinear dynamical systems

TL;DR

This paper introduces a novel frequency-domain method to identify causality in nonlinear dynamical systems using noisy measurements, without requiring a high-fidelity model, aiding in better data-driven modeling.

Contribution

It presents a new approach to determine causality from input-output data in nonlinear systems with output noise, filling a gap where no existing solutions are available.

Findings

Effective causality identification in noisy nonlinear systems

Applicable across various scientific disciplines

No need for a complete benchmark model

Abstract

Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires experimental measurements of the system input and output, but it can be difficult to determine whether inaccuracies in the model stem from modelling errors or noise. This paper presents a novel method to identify the causal component of the input-output data from measurements of a system in the presence of output noise, as a function of frequency, without needing a high fidelity model. An output prediction, calculated using an available model, is optimally combined with noisy measurements of the output to predict the input to the system. The parameters of the algorithm balance the two output signals and are utilised to calculate a nonlinear coherence metric as a measure of causality. This method is applicable to a broad class of nonlinear dynamical systems. There are currently no solutions to this problem in the absence of a complete benchmark model.