循環神經網路於混沌系統上的應用

Abstract

本研究主要探討循環神經網路其變形結構長短期記憶網路(LSTM)在混沌系統中的應用與效能評估。物理學中，混沌系統是一種具有非線性特徵且對初始條件高度敏感的動態系統，利用傳統控制方法很難有效預測其行為。我們以五種典型混沌系統做為研究對象，利用LSTM模型訓練進行模擬以及預測，並進一步評估模型的效能。研究結果表示:1. 當兩層隱藏層中的激活函數都使用tanh函數時在多數系統預測中，無論是訓練時間還是預測準確度，都表現出色；而當隱藏層採用不同激活函數組合時，模型在訓練次數較高時，預測效果有所提升，但需要更長的訓練時間。2. 當每層隱藏層的神經元數量增加時，該模型對混沌系統的行為預測的越好，但可能導致訓練時間加長，而對於在大多數系統的預測結果中，當訓練次數設定為100或200時，模型的評估結果已接近最佳；繼續增加訓練次數雖能進一步降低誤差，但訓練所花的時間也越久。3. 當訓練時間控制在30分鐘內，模型仍能達到良好的評估表現。儘管更高的訓練次數能進一步提升預測精度，但對於大部分實驗結果，訓練次數為200的結果已經足夠。由以上結果顯示，本研究證實了LSTM模型在混沌系統預測中的有效性，並指出模型參數設置與激活函數選擇對預測性能有顯著影響。未來可進一步研究更複雜的參數組合或利用GRU模型訓練並與本文結果進行比較，找出更佳的預測方法。This study mainly explores the application and performance evaluation of recurrent neural networks and their variants long short-term memory networks (LSTM) in chaotic systems. In physics, a chaotic system is a dynamic system with nonlinear characteristics and is highly sensitive to initial conditions. It is difficult to effectively predict its behaviors using traditional control methods.We take five typical chaotic systems as the research objects, train the LSTM model using the data of these five system, and further evaluate the performance of the model. The research results indicate:1. Whenboth the two hidden layers use tanh function as the activation functions, most system predictions perform well, both in terms of training time and prediction accuracy; when the hidden layers use different combinations of activation functions, the model makes better predictions when the number ofepoches is large. Although the performance is improved, but longer training time is required.2. When the number of neurons in each hidden layer increases, the model can make better prediction for the behaviors of the chaotic system, but it may lead to longer training time. For most systems, when the number of epoches is set to be 100 or 200, the results of the model are optimal; continuing to increase the number of epoches can further reduce the error, but it takes longer training time.3. When the training time is controlled to be within 30 minutes, the model can still achieve good performance. Although longer training time can further improve prediction accuracy, for most experimental results, a epoch of 200 is sufficient.From the above experimental results, this study confirms the effectiveness of the LSTM model in chaotic system prediction, and points out that model parameter settings and activation functions selection have a significant impact on the prediction performance. In the future, more complex parameter combinations can be considered or GRU model can be used to obtain the best results.