Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables
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 a novel data-driven approach that leverages the dynamical relatio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/152 |
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| author | Jingchan Lv Hongcun Mao Yu Wang Zhihai Yao |
| author_facet | Jingchan Lv Hongcun Mao Yu Wang Zhihai Yao |
| author_sort | Jingchan Lv |
| collection | DOAJ |
| description | 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 a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct a robust model where LightGBM builds a fitting function to capture and simulate the complex coupling relationships among variables in dynamically evolving chaotic systems. This approach enables the reconstruction of missing data, restoring sequence completeness and overcoming the limitations of existing chaotic time series prediction methods in handling missing data. We validate the proposed method by predicting the future evolution of variables with missing data in both dissipative and conservative chaotic systems. Experimental results demonstrate that the model maintains stability and effectiveness even with increasing missing rates, particularly in the range of 30% to 50%, where prediction errors remain relatively low. Furthermore, the feature importance extracted by the model aligns closely with the underlying dynamic characteristics of the chaotic system, enhancing the method’s interpretability and reliability. This research offers a practical and theoretically sound solution to the challenges of predicting chaotic systems with incomplete datasets. |
| format | Article |
| id | doaj-art-2524af3d5a27484f8608351d5a108f3e |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-2524af3d5a27484f8608351d5a108f3e2025-01-10T13:18:26ZengMDPI AGMathematics2227-73902025-01-0113115210.3390/math13010152Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between VariablesJingchan Lv0Hongcun Mao1Yu Wang2Zhihai Yao3Department of Physics, Changchun University of Science and Technology, Changchun 130022, ChinaDepartment of Physics, Changchun University of Science and Technology, Changchun 130022, ChinaDepartment of Physics, Changchun University of Science and Technology, Changchun 130022, ChinaDepartment of Physics, Changchun University of Science and Technology, Changchun 130022, ChinaAlthough 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 a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct a robust model where LightGBM builds a fitting function to capture and simulate the complex coupling relationships among variables in dynamically evolving chaotic systems. This approach enables the reconstruction of missing data, restoring sequence completeness and overcoming the limitations of existing chaotic time series prediction methods in handling missing data. We validate the proposed method by predicting the future evolution of variables with missing data in both dissipative and conservative chaotic systems. Experimental results demonstrate that the model maintains stability and effectiveness even with increasing missing rates, particularly in the range of 30% to 50%, where prediction errors remain relatively low. Furthermore, the feature importance extracted by the model aligns closely with the underlying dynamic characteristics of the chaotic system, enhancing the method’s interpretability and reliability. This research offers a practical and theoretically sound solution to the challenges of predicting chaotic systems with incomplete datasets.https://www.mdpi.com/2227-7390/13/1/152chaotic time series predictionmissing data reconstructionmultivariate time seriesdynamical correlationmachine learning |
| spellingShingle | Jingchan Lv Hongcun Mao Yu Wang Zhihai Yao Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables Mathematics chaotic time series prediction missing data reconstruction multivariate time series dynamical correlation machine learning |
| title | Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables |
| title_full | Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables |
| title_fullStr | Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables |
| title_full_unstemmed | Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables |
| title_short | Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables |
| title_sort | reconstruction and prediction of chaotic time series with missing data leveraging dynamical correlations between variables |
| topic | chaotic time series prediction missing data reconstruction multivariate time series dynamical correlation machine learning |
| url | https://www.mdpi.com/2227-7390/13/1/152 |
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