這篇論文包含了兩種在不同動力學系統的應用：果蠅腦神經極性之分類、有時變外加場之一維易辛模型(Ising Model)。
在論文的第一個部分，我們開發了一種機器學習算法，即基於節點的神經極性分類器（NPIN），以識別神經網絡中資訊流的方向。這是理解腦複雜動態的關鍵之一。我們所提出的模型僅以神經節點的資訊進行訓練，包含細胞體特徵（包含從給定節點到細胞體的空間資訊），和局部特徵（包含給定節點的形態資訊）。透過使用分佈在果蠅大腦不同區域的213個projection neurons的資料集並考慮節點間的空間相關性，NPIN為神經元極性分類提供了高準確度（大於96％），甚至對於擁有兩簇以上的複雜神經也是如此。最後，我們進一步應用NPIN在分類麗蠅的神經極性，該物種的神經數據相較之下少很多。從我們的研究結果顯示，NPIN是分類昆蟲神經極性並繪製出大腦神經網絡資訊流的強大工具。這個部分與此論文相關：Identification of Neuronal Polarity by Node-Based Machine Learning, Chen-Zhi Su, Kuan-Ting Chou, Hsuan-Pei Huang, Chung-Chuan Lo , and Daw-Wei Wang. bioRxiv: https://biorxiv.org/cgi/content/short/2020.06.20.160564v1 (submitted to Neuroninformatics)
在論文的第二部分，我們建構了一個經過調整的遞歸神經網絡（RNN），此網絡可以預測不同參數範圍的物理量。此網絡的結構包含：將系統初始狀態映射至RNN的初始隱藏層變數的編碼器、跟隨RNN一連串隱藏層並透過提取隱藏層變數預測出目標物理量的解碼器。我們將此方法應用於具有時變外加磁場的一維易辛模型。我們藉由在特定的參數範圍內，使用短時間的數據訓練此模型，以預測在其他參數範圍中較長時間尺度的物理量（例如：相關函數、磁化強度和總能量等）。透過調整外加磁場，我們還可以將此方法應用於不同的相。我們的模型顯示了將機器學習應用於多體動力學的可能性。

This thesis contains applications of machine learning in two different dynamical systems: Identification of Neuronal Polarity in Drosophila Brain, and 1D Ising Model with Arbitrary Time-Dependent External Field.
In the first part, we develop a machine learning algorithm, Node-Based Polarity Identifier of Neurons (NPIN), to identify the directions of signal flows in neuronal networks, which is one of the keys for understanding the intricate information dynamics of a living brain. The proposed model is trained by nodal information only and includes both Soma Features (which contain spatial information from a given node to a soma) and Local Features (which contain morphological information of a given node). By using a dataset of 213 projection neurons distributed in different regions of a Drosophila brain and considering the spatial correlations between nodal polarities, NPIN provided high accuracy (>96.0%) for the classification of neuronal polarity, even for complex neurons containing more than two dendrite/axon clusters. Finally, we further apply NPIN to classify the neuronal polarity of the blowfly, which has much less neuronal data available. Our results demonstrate that NPIN is a powerful tool to identify the neuronal polarity of insects and to map out the signal flows in the brain’s neuronal networks. This topic is associated to the project:Identification of Neuronal Polarity by Node-Based Machine Learning, Chen-Zhi Su, Kuan-Ting Chou, Hsuan-Pei Huang, Chung-Chuan Lo , and Daw-Wei Wang. bioRxiv: https://biorxiv.org/cgi/content/short/2020.06.20.160564v1 (submitted to Neuroninformatics)
In the second part, we construct a modified Recurrent Neural Network (RNN) that can predict dynamical observables in different parameter regimes. Our architecture involves an encoder mapping the initial configuration of a given system to the initial hidden variables of RNN, and a decoder following the successive layers extracting the information of hidden variables and giving prediction of targeted quantities. We apply this method to 1D Ising Model with a time-depenent transverse magnetic field. We train the model in a certain parameter regime for a short time, but could simulate physical quantities (such as correlation functions, transverse magnetization, and total energy etc.) in some other parameter regime for a long time behavior. By varying the external magnetic field, we can also apply our approach in the different phases. Our model shows the possibility to apply machine learning in many-body dynamics.

摘要
Abstract
Acknowledgements ------------------------------------------ i
Content ------------------------------------------ ii
I Identification of Neuronal Polarity ------------------------------------------ 1
1 Introduction ------------------------------------------ 2
2 Neuronal Morphology ------------------------------------------ 4
2.1 Dataset ------------------------------------------ 4
2.2 Feature distribution ------------------------------------------ 6
3 Method ------------------------------------------ 9
3.1 Standard Representation ------------------------------------------ 12
3.2 Nodal Polarity ------------------------------------------ 15
3.3 Feature Extraction ------------------------------------------ 17
3.4 Machine Learning Models ------------------------------------------ 17
3.5 Implementation and Spatial Correlation of Nodal Polarity ------------------------------------------ 18
4 Result ------------------------------------------ 19
4.1 Identification Results of Model I: Using Both Soma Features and Local Features ------------------------------------------ 20
4.2 Identification Results of Model II: Using Soma Features Only ------------------------------------------ 22
4.3 Comparison of Models I, II, and III for Complex Neurons ------------------------------------------ 23
4.4 Application: Transfer Learning ------------------------------------------ 26
5 Discussion ------------------------------------------ 29
5.1 Comparison ------------------------------------------ 29
5.2 Neurons with low accuracy ------------------------------------------ 30
5.3 Other types ------------------------------------------ 31
6 Conclusion ------------------------------------------ 32
II Toward Quantum Many-Body Dynamics ------------------------------------------ 33
7 Introduction ------------------------------------------ 34
8 Quantum Ising Model ------------------------------------------ 36
8.1 Transverse Field Ising Chain ------------------------------------------ 36
8.2 Time Dependent External Field ------------------------------------------ 38
8.3 Physical Observables ------------------------------------------ 39
9 Modified Recurrent Neural Network ------------------------------------------ 40
9.1 Overview ------------------------------------------ 40
9.2 Initial Configuration Encoder ------------------------------------------ 41
9.3 Evolution of Hidden Variables ------------------------------------------ 42
9.4 Physical Observable Decoder ------------------------------------------ 43
10 Result ------------------------------------------ 44
10.1 Prediction Result of Task I: Training Data in two different perturbative regimes ------------------------------------------ 44
10.2 Prediction Result of Task II: Training Data in a perturbative regime ------------------------------------------ 47
11 Discussion and Conclusion ------------------------------------------ 50
References ------------------------------------------ 51

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