在化工製程中能夠透過量測直接得到之變量為觀察變量(observable variable)，而無法直接透過量測得到之變量為狀態變量(state variable)，然而透過狀態觀察(state observation)獲得狀態變量能夠使我們獲取製程上更多資訊。
研究目標為透過導入物理資訊的物理信息神經網路(physics-Informed Neural Networks)與將神經網路訓練成為運算子的深度運算子神經網路(Deep Operator Networks)對乙烷裂解非線性系統進行建模，並對於該系統進行動態預測、參數回歸以及將透過以知的物理訊息導入模型中進行狀態觀察。
物理信息神經網路與深度運算子神經網路對於動態預測與參數回歸均有很好的預測效果，然而對於狀態觀察，有別於物理信息神經網路multiple to multiple微分數值預測不佳，深度運算子神經網路不僅準確觀測出狀態變數，並且運用觀測出之狀態變數，準確預測積分後數值，預測之R2皆達0.9以上，我們成功使用該模型同時進行狀態觀察與動態預測。

In the chemical process, variables that can be directly obtained through measurement are observable variables, and variables that cannot be directly obtained through measurement are state variables. However, obtaining state variables through state observation can help ous get more information on the process.
The research goal is to build a nonlinear system of ethane cracking through physics-Informed Neural Networks that import physical information into model and Deep Operator Networks that train neural networks as operators, then using them to perform dynamic prediction, parameter regression, and state observation of the system by importing known physical information into the model.
The physical information neural networks and the deep operator neural networks have good prediction effects for dynamic prediction and parameter regression. However, for state observation, different from the physical information neural networks multiple to multiple differential numerical prediction is not good. The deep operator neural networks not only accurately observes the state variables, but also use the observed state variables to accurately predict the value after integration. The predicted R2 is above 0.9. We successfully use this model to perform state observation and dynamic prediction at the same time.

摘要 i
Abstract ii
致謝 iii
目錄 Table of Contents iv
圖目錄List of Figures vi
表目錄List of Tables viii
第一章 緒論 1
一.1 神經網路模型和深度學習模型 1
一.1.1人工神經網路模型 1
一.1.2深度學習模型 2
一.2 物理信息神經網路(physics-Informed Neural Networks) 4
一.3深度運算子神經網路(Deep Operator Networks) 6
一.4 狀態觀察(states observation) 9
一.5 研究動機與目標 10
第二章 案例介紹 11
二.1 乙烷裂解 11
二.2 數據生成與資料分析 13
數據生成方式 13
資料分析 15
第三章 物理信息神經網路 17
三.1 動態預測 19
模型結構 19
訓練數據 19
模型訓練結果 19
三.2 參數回歸 21
模型結構 21
訓練數據 21
模型訓練結果 22
三.3 狀態觀察 23
模型結構 23
訓練數據 24
模型訓練結果 24
三.4 章節總結 29
第四章 深度運算子神經網路 30
四.1動態預測 30
模型結構 30
訓練數據 31
模型訓練結果 32
四.2參數回歸 34
模型結構 34
訓練數據 34
模型訓練結果 35
四.3狀態觀察 36
模型結構 36
訓練數據 37
模型訓練結果 38
四.4章節總結 43
第五章 結論 44
參考文獻 45

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