Parameter Inference in Non-linear Dynamical Systems via Recurrence Plots and Convolutional Neural Networks

Abstract

Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on system-specific models and involve heavily parametrised formulations, which can limit their general applicability. In this study, we present a methodology that employs recurrence plots as structured representations of non-linear trajectories, which are then used to train convolutional neural networks to infer the values of the control parameter associated with the analysed trajectories. We focus on two representative non-linear systems, namely the logistic map and the standard map, and show that our approach enables accurate estimation of the parameters governing their dynamics. When compared to regression models trained directly on raw time-series data, the use of recurrence plots yields significantly more robust results. Although the methodology does not aim to predict future states explicitly, we argue that accurate parameter inference, when combined with predetermined initial conditions, enables the reconstruction of a system's evolution due to its deterministic nature. These findings highlight the potential of recurrence-based learning frameworks for the automated identification and characterisation of non-linear dynamical behaviours.