Data-Driven Soliton Modeling in Conformable Coupled Dispersionless Systems Using Jacobi Elliptic Functions and Bayesian-Regularized Neural Networks

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Abstract
The primary objective of this study was to investigate the complex dynamics of coupled dispersionless equations formulated using conformable derivatives. Exact soliton solutions are first derived using the Jacobi elliptic function expansion method. These solutions were then used to train a datadriven model based on a Bayesian regularization-backpropagation neural network. The trained network is evaluated against the exact solutions through visual comparison using surface plots, contour plots, and corresponding error graphs. Furthermore, statistical metrics are computed for varying values of the conformable derivative parameter to assess the prediction accuracy and robustness. The close agreement between the predicted and exact solutions confirms the effectiveness of the proposed data-driven approach. This study highlights the potential of integrating analytical soliton solutions with neural network models to model nonlinear systems involving conformable derivatives.

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