Several mathematical approaches have been developed for solving the pressure-diffusivity equation governing unsteady-state flow in petroleum reservoirs. However, conventional similarity formulations may exhibit significant deviations at early dimensionless times because of the line-source approximation. In this study, an improved semi-analytical similarity framework is developed by introducing two time-dependent correction factors to enhance the accuracy of the finite-wellbore pressure response in an infinite-acting reservoir. The correction functions are formulated as data-informed functions of dimensionless time and calibrated against Chatas’ numerical reference solution. Their robustness was assessed using five-fold cross-validation and an independent hold-out test. Model 1 provided the best predictive performance, with a test MAPE of 0.938%, RMSE of 1.554%, maximum absolute error of 4.660%, and R^2=0.999. A controlled synthetic reservoir-parameter recovery analysis further demonstrated the practical significance of the improved pressure representation: permeability and skin-factor errors were reduced to 0.008% and 0.014%, respectively, for Model 1. The proposed formulation therefore for transient simple and accurate semi-analytical alternative for transient pressure calculation and can improve the interpretation of pressure-transient responses, particularly in the formation-dominated early-time regime.