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Neural network-based symbolic calculation approach for solving the Korteweg–de Vries equation

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  • Xie, Xiao-Ran
  • Zhang, Run-Fa

Abstract

In this study, we propose an innovative method that combines neural network models and symbolic computing to quickly solve exact solutions to nonlinear partial differential equations (NLPDEs). By combining the high accuracy of symbolic computing with the strong adaptability of neural networks, this method significantly improves the efficiency and accuracy of decomputation. As an application, this paper uses the neural network symbol calculation method to successfully obtain multiple sets of new analytical solutions of the Korteweg–de Vries equation, and constructs a variety of new neural network models and their heuristic functions. This study provides a new computational paradigm for solving the exact solution of NLPDEs, and has the potential for a wide range of scientific and engineering applications.

Suggested Citation

  • Xie, Xiao-Ran & Zhang, Run-Fa, 2025. "Neural network-based symbolic calculation approach for solving the Korteweg–de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002450
    DOI: 10.1016/j.chaos.2025.116232
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