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<p>This paper introduces a novel method to find first integrals for two-dimensional transcendental function systems. We propose a self-fission similarity learning method, which enables a symbolic mapping model to capture underlying mathematical relationships and thereby find first integrals. Experiments demonstrate that the model successfully discovers new and different first integrals for some transcendental function systems, with high accuracy and wonderful predictive generalization capabilities. In addition, famous mathematical software Maple’s DEtools fails for the above examples. It makes a new way for finding first integrals of transcendental function systems.</p>

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Self-Fission Similarity Learning: a New Method for Finding First Integrals, With Symbolic Transformers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月30日

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  • Chongrui Luo,
  • Yuqian Zhou,
  • Qian Liu,
  • Jun Guo

摘要

This paper introduces a novel method to find first integrals for two-dimensional transcendental function systems. We propose a self-fission similarity learning method, which enables a symbolic mapping model to capture underlying mathematical relationships and thereby find first integrals. Experiments demonstrate that the model successfully discovers new and different first integrals for some transcendental function systems, with high accuracy and wonderful predictive generalization capabilities. In addition, famous mathematical software Maple’s DEtools fails for the above examples. It makes a new way for finding first integrals of transcendental function systems.