本研究評估三種類型的預測模型：Forward Euler 方法，代表傳統數值模型；儲備池計算網路（Reservoir Computing， RC），為一種輕量級機器學習模型，訓練成本低但精度有限；以及長短期記憶網路（Long Short-Term Memory， LSTM），一種具有高複雜度但具備強大預測能力的深度學習模型。本研究在不同條件下進行系統性測試，包括不同擾動強度、預測長度，以及有效性指標（如有效預測時間與有效比例）。結果顯示，資料同化方法能穩定提升所有預測模型的表現。其中，LSTM--EKF 混合模型表現最佳，在強擾動條件下仍能維持可靠的預測能力，顯示結合先進機器學習模型與資料同化技術在複雜混沌系統中的潛力。;With the widespread adoption of artificial intelligence， forecasting has become increasingly important in diverse applications. As datasets grow larger， more complex predictive models are developed to improve accuracy， but this comes at the cost of increased computational and memory requirements. To address this challenge， this paper introduces a hybrid approach that integrates predictive models with data assimilation techniques， specifically the Extended Kalman Filter (EKF). Rather than increasing model complexity or performing extensive fine-tuning， we derive analytical tangent linear models of the predictors， enabling their seamless integration with EKF to achieve improved accuracy while maintaining similar computational costs.
This study evaluates three types of predictors: the Forward Euler method， representing traditional numerical models; the reservoir computing (RC) model， a lightweight machine learning predictor with low training cost but limited accuracy; and the Long Short-Term Memory (LSTM) network， a deep learning model with high complexity and strong predictive power. We systematically test these models under varying conditions， including different perturbation scales， forecast lengths， and validity metrics such as valid time and valid percentage. The results demonstrate that data assimilation consistently enhances the performance of all predictors. Notably， the LSTM--EKF hybrid achieves the highest accuracy and robustness， maintaining reliable forecasts even under strong perturbations， highlighting the potential of combining advanced machine learning models with data assimilation for complex chaotic systems.
