A method for identifying causality in the response of nonlinear dynamical systems
Keywords: Nonlinear dynamical systems, causality, application to physical sciences, deep learning, noise estimation
TL;DR: This paper presents a method for identifying the causal relationship between the input and output of a nonlinear dynamical system, in the presence of output noise.
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. Therefore there is a need to determine the maximum component of the output that could theoretically be predicted using the input, if an improved model was to be developed through the investment of resources. This paper presents a novel method to identify the component of the output that could potentially be modelled, and quantify the level of noise in the output, as a function of frequency. The method uses input-output measurements and an available, but approximate, model of the system. A trainable, frequency dependent parameter balances an output prediction generated by the model with noisy measurements of the output to predict the input to the system. This parameter is utilised to estimate the noise level and then calculate a nonlinear coherence metric as a measure of causality or predictability from the input. There are currently no solutions to this problem in the absence of an accurate benchmark model.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 6934
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