Predicting Multiple Numerical Solutions to the Duffing Equation Using Machine Learning
學年 112
學期 1
出版(發表)日期 2023-09-15
作品名稱 Predicting Multiple Numerical Solutions to the Duffing Equation Using Machine Learning
著者 Wang, Yi-ren
著錄名稱、卷期、頁數 Applied Sciences 2023 13(18), 10359
摘要 This study addresses the problem of predicting convergence outcomes in the Duffing equation, a nonlinear second-order differential equation. The Duffing equation exhibits intriguing behavior in both undamped free vibration and forced vibration with damping, making it a subject of significant interest. In undamped free vibration, the convergence result oscillates randomly between 1 and −1, contingent upon initial conditions. For forced vibration with damping, multiple variables, including initial conditions and external forces, influence the vibration patterns, leading to diverse outcomes. To tackle this complex problem, we employ the fourth-order Runge–Kutta method to gather convergence results for both scenarios. Our approach leverages machine learning techniques, specifically the Long Short-Term Memory (LSTM) model and the LSTM-Neural Network (LSTM-NN) hybrid model. The LSTM-NN model, featuring additional hidden layers of neurons, offers enhanced predictive capabilities, achieving an impressive 98% accuracy on binary datasets. However, when predicting multiple solutions, the traditional LSTM method excels. The research encompasses three critical stages: data preprocessing, model training, and verification. Our findings demonstrate that while the LSTM-NN model performs exceptionally well in predicting binary outcomes, the LSTM model surpasses it in predicting multiple solutions.
關鍵字 Duffing equation;deep learning;neural networks;recurrent neural networks;long short-term memory
語言 en_US
ISSN 2076-3417
期刊性質 國外
收錄於 SCI EI
通訊作者 Wang, Yi-ren
國別 CHE
出版型式 ,電子版

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