本研究旨在預測電離層的動態變化，根據電離層物理理論，科學家利用已知參數建立電離層模式以模擬電離層電漿濃度的變化。然而使用數值模式來進行電離層預測會因為物理理論模式與經驗模式的限制，往往無法精準的預測電離層，而資料同化模式則因為系集運算的關係，需要使用到大量的運算資源，會有運算時間過長以及對於硬體需求較高的問題，所以運行環境並不是那麼容易建置。伴隨著近年利用AI人工智慧預測電離層電漿濃度的技術逐漸成熟，科學家開始嘗試使用AI進行電離層預測。人工智慧可以在不需要耗費龐大的運算資源下，就能達到相當不錯的預測精準度，但其卻不能以物理原理或理論依據去理解，使得對於預測結果難以從電離層物理角度加以解釋和驗證。本研究利用非線性動態稀疏識別法(The sparse identification of nonlinear dynamics method，簡稱為 SINDy 法)與具控制之非線性動態稀疏識別法(Sparse Identification of Nonlinear Dynamics With Control，簡稱SINDYc法)，透過分析電離層全電子含量(Total electron content, TEC)參數以及電離層中不同的參數變化(例如電漿速度、離子溫度、太陽天頂角等)，其不僅可以保留人工智慧的優勢，也可以透過電離層物理來解釋，並輸出電離層動態系統的非線性運動方程式。本研究進一步與現有的電離層物理公式(電漿連續方程式與動量方程式)進行比較，評估和修正SINDy法與SINDYc法所反推的公式中各個函數的種類、各個參數的權重，並判斷探討其與現有的公式的差異。結果發現，在不同預測條件下，如SINDy與SINDYc的使用、地點上不同方位的資料、閾值、太陽活動性與季節的不同，皆會使預測準確度不同。經由多種不同方位資料與閾值組合測試下，本研究建構出最佳的電離層預測方程式組，其中TEC預測均方根偏差(Root-mean-square error, RMSE)在背景電漿濃度較小時期為0.58-1.9 TECU，而在背景電漿濃度較大時期則為2.09-3.87 TECU。

This study uses the Sparse Identification of Nonlinear Dynamics (SINDy) and the Sparse Identification of Nonlinear Dynamics with Control (SINDYc) to develop a set of ionospheric forecasting equations. By analyzing the Total Electron Content (TEC) and various ionospheric parameters (such as plasma velocity, ion temperature, solar zenith angle, etc.), this approach not only retains the advantages of AI but also can be explained by ionospheric physics. It can output the nonlinear dynamics equations of the ionospheric system. This study further compares the results with existing ionospheric physical formulas (plasma continuity equation and momentum equation). It evaluates and corrects the types of functions and the weights of parameters in the equations inferred by the SINDy and SINDYc methods, determining whether they are reasonable equations and exploring the differences from existing formulas.
The results indicate that Root-Mean-Square Error (RMSE) values of prediction would be affected by solar activity and the ionospheric plasma densities. For instance, the TEC prediction results show RMSE values ranging from 0.58 to 1.9 during lower ionospheric plasma density periods and from 2.09 to 3.87 during higher ionospheric plasma density periods.

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