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<p>Deterministic learning theory has been successful in accurately identifying the nonlinear dynamics of unknown system, and the most direct application of this dynamics information is to forecast the future behavior of the system. This study applies deterministic learning to the field of chaotic time series forecasting for the first time, proposing a novel approach for prediction based on dynamics knowledge, which includes: (1) modeling time series dynamics through deterministic learning; (2) constructing a multi-step recursive predictor using the forward Euler model with the acquired dynamics knowledge; (3) incorporating a prediction error corrector to rectify predicted values in real-time. The significance of this paper lies in introducing a novel idea for forecasting the evolution of chaotic time series through inherent nonlinear dynamics and designing an effective prediction-correction mechanism to mitigate the common issue of cumulative errors in multi-step recursive prediction. Numerical experiments on the Lorenz and Chen benchmark chaotic systems demonstrate that the proposed method outperforms other advanced algorithms in short-term prediction accuracy and exhibits high potential for mid to long-term prediction.</p>

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Chaotic time series forecasting of dynamical systems based on deterministic learning

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Chen Sun,
  • Weiming Wu,
  • Junnan Guo,
  • Zirui Zhang,
  • Cong Wang

摘要

Deterministic learning theory has been successful in accurately identifying the nonlinear dynamics of unknown system, and the most direct application of this dynamics information is to forecast the future behavior of the system. This study applies deterministic learning to the field of chaotic time series forecasting for the first time, proposing a novel approach for prediction based on dynamics knowledge, which includes: (1) modeling time series dynamics through deterministic learning; (2) constructing a multi-step recursive predictor using the forward Euler model with the acquired dynamics knowledge; (3) incorporating a prediction error corrector to rectify predicted values in real-time. The significance of this paper lies in introducing a novel idea for forecasting the evolution of chaotic time series through inherent nonlinear dynamics and designing an effective prediction-correction mechanism to mitigate the common issue of cumulative errors in multi-step recursive prediction. Numerical experiments on the Lorenz and Chen benchmark chaotic systems demonstrate that the proposed method outperforms other advanced algorithms in short-term prediction accuracy and exhibits high potential for mid to long-term prediction.