Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables

Mathematics, Journal Year: 2025, Volume and Issue: 13(1), P. 152 - 152

Published: Jan. 3, 2025

Although data-driven machine learning methods have been successfully applied to predict complex nonlinear dynamics, forecasting future evolution based on incomplete past information remains a significant challenge. This paper proposes novel approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct robust model where LightGBM builds fitting function capture and simulate coupling variables in dynamically evolving chaotic systems. enables reconstruction of missing data, restoring sequence completeness overcoming limitations existing time series prediction handling data. We validate proposed method by predicting data both dissipative conservative Experimental results demonstrate maintains stability effectiveness even increasing rates, particularly range 30% 50%, errors remain relatively low. Furthermore, feature importance extracted aligns closely underlying dynamic characteristics system, enhancing method’s interpretability reliability. research offers practical theoretically sound solution challenges systems datasets.

Language: Английский

Reconstructing the dynamics of coupled oscillators with cluster synchronization using parameter-aware reservoir computing

The European Physical Journal Plus, Journal Year: 2025, Volume and Issue: 140(2)

Published: Feb. 8, 2025

Language: Английский

Learning High-Dimensional Chaos Based on an Echo State Network with Homotopy Transformation

Mathematics, Journal Year: 2025, Volume and Issue: 13(6), P. 894 - 894

Published: March 7, 2025

Learning high-dimensional chaos is a complex and challenging problem because of its initial value-sensitive dependence. Based on an echo state network (ESN), we introduce homotopy transformation in topological theory to learn chaos. On the premise maintaining basic properties, our model can obtain key features for learning through continuous between different activation functions, achieving optimal balance nonlinearity linearity enhance generalization capability model. In experimental part, choose Lorenz system, Mackey–Glass (MG) Kuramoto–Sivashinsky (KS) system as examples, verify superiority by comparing it with other models. For some systems, prediction error be reduced two orders magnitude. The results show that addition improve modeling ability spatiotemporal chaotic this demonstrates potential application dynamic time series analysis.

Language: Английский