Abstract 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.
Luo et al. (Tue,) studied this question.