Nowadays in highly competitive precision industries, the micromachining of advanced engineering materials is extremely demand as it has extensive application in the fields of automobile, electronic, biomedical and aerospace engineering. The present work addresses the modeling and optimization study on dimensional deviations of square-shaped microgroove in laser micromachining of aluminum oxide (Al 2 O 3) ceramic material with pulsed Nd:YAG laser by considering the air pressure, lamp current, pulse frequency, pulse width and cutting speed as process parameters. Thirty-two sets of laser microgrooving trials based on central composite design (CCD) design of experiments (DOEs) are performed, and response surface method (RSM), artificial neural network (ANN) and genetic algorithm (GA) are subsequently applied for mathematical modeling and multi-response optimization. The performance of the predictive ANN model based on 5-8-8-3 architecture gave the minimum error (MSE = 0.000099) and presented highly promising to confidence with percentage error less than 3% in comparison with experimental result data set. The ANN model combined with GA leads to minimum deviation of upper width, lower width and depth value of − 0.0278 mm, 0.0102 mm and − 0.0308 mm, respectively, corresponding to optimum laser microgrooving process parameters such as 1.2 kgf/cm 2 of air pressure, 19.5 Amp of lamp current, 4 kHz of pulse frequency, 6% of pulse width and 24 mm/s of cutting speed. Finally, the results have been verified by performing a confirmatory test.