Predicting Multiple Numerical Solutions to the Duffing Equation Using Machine Learning

doi:10.3390/app131810359

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題名:	Predicting Multiple Numerical Solutions to the Duffing Equation Using Machine Learning
作者:	Wang, Yi-ren
關鍵詞:	Duffing equation;deep learning;neural networks;recurrent neural networks;long short-term memory
日期:	2023-09-15
上傳時間:	2023-10-25 12:05:23 (UTC+8)
出版者:	MDPI
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.
關聯:	Applied Sciences 2023 13(18),　10359
DOI:	10.3390/app131810359
顯示於類別:	[航空太空工程學系暨研究所] 期刊論文

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