Study α decay and proton emission based on data-driven symbolic regression

α decay and proton emission were combined using symbolic regression to improve the accuracy of predicting their respective half-lives using two theoretical formulations: (1) adjustable parameters for the universal decay law and universal decay law for proton emission are obtained by regressions with fully-constrained symbolic regressions. (2) New theoretical formulas for calculating the half-life of proton emission and α decay are obtained using unconstrained symbolic regressions combined with nuclear data. Our computational analysis indicates that fully-constrained symbolic regressions and unconstrained symbolic regressions are reliable for specific and general nuclei, respectively, in terms of replicating experimental results, and are sufficiently robust to produce accurate half-life predictions. Unlike other machine learning methods that generate complex and opaque results, our approach integrates physics and machine learning to create interpretable formulas that provide intuitive parametric outcomes and transparent and dependable inferences of half-lives, even in areas with limited experimental data. The test results show that the equation yields accurate results, and can be easily applied to future α decay and proton emission studies.