本研究由質量與動量守恆原理進行數學推導，篩選具有物理意義之特徵輸入機器學習模型進行訓練，藉以提高機器學習模型之精度與可解釋性。首先推導出與水位變化有關聯之特徵，以水位、雨量及潮位資料為基礎，結合淺水波方程式，延伸出各種特徵。原始水位模型僅輸入水位、雨量及潮位，並以未來的水位值作為輸出目標，由於原始水位模型直接輸出未來一至六小時的水位值，因此分別訓練六個模型直接預測；原始梯度模型則預測下一個小時水位之梯度，即以水位變化量作為輸出目標，並以此為基礎繼續預測下一個小時水位。以這兩種模型為基礎，本研究增加差分項作為輸入特徵進行比較，延伸出差分水位模型以及差分梯度模型。四種模型均採用梯度提升回歸(gradient boosting regression, GBR)以及長短期記憶(long short-term memory, LSTM)兩種機器學習方法。根據研究結果，運用梯度提升回歸之梯度模型在加入差分特徵後的改善效果最佳。而對於上游的水位站，以梯度模型的表現較佳；針對下游的水位站，則以原始模型的表現效果較好。

Recently, extreme flood events are becoming more frequent due to climate change. In order to reduce economic loss, building a flood warning system is one of the solutions. Based on two machine learning methods called gradient boosting regression (GBR) and long short-term memory (LSTM), additional difference terms were added as input features through the derived results of the shallow water equation in this study. Depending on the output, the models were classified as difference water level model and difference gradient model. For comparison, the study established two models which used only take tide, rainfall, and water level data as input features, namely the original water level models and original gradient models which. The result indicates that the gradient models have better performance in upstream stations, while the water level models have better behavior in downstream stations. After adding difference terms, the GBR gradient models have significant improvements.

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