The velocity of laser-induced shock waves affects the efficiency and efficacy of laser-based processes. The ability to accurately estimate shock wave velocity is critical for optimizing experimental combinations, creating laser-based systems, and assuring desired results. Traditional approaches to predict shock wave velocity involve empirical equations and analytical models based on simplified assumptions. However, these methods often lack accuracy and fail to capture the complex dynamics of laser-matter interactions. To overcome these limitations, we used a combination of an artificial neural network and a genetic algorithm to predict shock wave velocity. In this method, the neural network structure is dynamically designed. The optimization method does this by modifying the neural network's weights and figuring out the network's structure on our behalf. Based on the findings, our suggested technique worked very well; it surpassed other comparison methods by achieving the lowest average errors in terms of RMSE and MAE, which are 4.38 and 3.74, respectively. Moreover, the analysis has shown that our proposed method has a high level of reliability in predicting impulsive wave velocity using a neural network.