Despite the known influence of chemical composition on the mechanical properties of basalt fibers, a clear understanding of this relationship is lacking. Chemical composition analysis and mechanical property tests are performed on basalt fiber samples. Test data is collected from various countries and regions to expand the dataset. An improved Physics-Informed Neural Network (PINN) approach is specifically designed to address the complexities of this relationship. By incorporating physical models like the Makishima-Mackenzie model, Rocherulle model and a symbolic regression formula, the PINN leverages established physical principles to enhance its ability to understand the underlying mechanisms governing the influence of chemical composition on mechanical properties. This focus on physical mechanisms not only improves the interpretability of the model but also empowers it to make accurate predictions, as evidenced by the high squared correlation coefficients of 0.8767 and 0.8145 between predicted and experimental values of modulus and strength, respectively.