Predicting Multiple Numerical Solutions to the Duffing Equation Using Machine Learning
نویسندگان
چکیده
This study addresses the problem of predicting convergence outcomes in Duffing equation, a nonlinear second-order differential equation. The equation exhibits intriguing behavior both undamped free vibration and forced with damping, making it subject significant interest. In vibration, result oscillates randomly between 1 −1, contingent upon initial conditions. For multiple variables, including conditions external forces, influence patterns, leading to diverse outcomes. To tackle this complex problem, we employ fourth-order Runge–Kutta method gather results for scenarios. Our approach leverages machine learning techniques, specifically Long Short-Term Memory (LSTM) model LSTM-Neural Network (LSTM-NN) hybrid model. LSTM-NN model, featuring additional hidden layers neurons, offers enhanced predictive capabilities, achieving an impressive 98% accuracy on binary datasets. However, when solutions, traditional LSTM excels. research encompasses three critical stages: data preprocessing, training, verification. findings demonstrate that while performs exceptionally well outcomes, surpasses solutions.
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ژورنال
عنوان ژورنال: Applied sciences
سال: 2023
ISSN: ['2076-3417']
DOI: https://doi.org/10.3390/app131810359