Laser micro-machining has gained significant attraction from industries and researchers due to the wide range of processability and material flexibility with micro-scale accuracy. However, only a few process variables and soft computing approaches are taken into consideration in micro-scale sectors. This provides the opportunity to explore a new and relatively unexplored area of physics-informed advanced soft computing techniques for laser beam machining. This study aims to develop a framework to investigate the micro-milling capabilities of 10 mm thick poly-methyl-methacrylate (PMMA) using various input parameters such as laser power (8–16 W), scanning speed (25–50 mm/s), number of passes (2–6), and incident energy (0.107–0.64 J/mm). A soft computing technique to build depth, width and surface roughness prediction models on a CO2 laser machine, is presented. Advanced soft computing approaches such as random forest, gradient boost, ridge regression, linear regression, support vector regression and gaussian process regression are evaluated to predict the microchannel's depth, surface roughness, and kerf width. The proposed work is validated experimentally and compared with the different prediction/regression models available in the literature. The values of hyper tuning parameters are optimized using by grid search method. Based on the 5-fold cross-validation analysis, the most accurate predictions of the depth, surface roughness and kerf width could be achieved through the gaussian process regression (GPR) model with highest accuracy of 98.34 %, 97.68 % and 96.38 % for depth, surface roughness and kerf width respectively.