The compressive strength of concrete is a crucial parameter in structural design, yet its determination in a laboratory setting is both time-consuming and expensive. The prediction of compressive strength in fly ash-based concrete can be accelerated through the use of machine learning algorithms with artificial intelligence, which can effectively address the problems associated with this process. This paper presents the most innovative model algorithms established based on artificial intelligence technology. These include three single models—a fully connected neural network model (FCNN), a convolutional neural network model (CNN), and a transformer model (TF)—and three hybrid models—FCNN + CNN, TF + FCNN, and TF + CNN. A total of 471 datasets were employed in the experiments, comprising 7 input features: cement (C), fly ash (FA), water (W), superplasticizer (SP), coarse aggregate (CA), fine aggregate (S), and age (D). Six models were subsequently applied to predict the compressive strength (CS) of fly ash-based concrete. Furthermore, the loss function curves, assessment indexes, linear correlation coefficient, and the related literature indexes of each model were employed for comparison. This analysis revealed that the FCNN + CNN model exhibited the highest prediction accuracy, with the following metrics: R2 = 0.95, MSE = 14.18, MAE = 2.32, SMAPE = 0.1, and R = 0.973. Additionally, SHAP was utilized to elucidate the significance of the model parameter features. The findings revealed that C and D exerted the most substantial influence on the model prediction outcomes, followed by W and FA. Nevertheless, CA, S, and SP demonstrated comparatively minimal influence. Finally, a GUI interface for predicting compressive strength was developed based on six models and nonlinear functional relationships, and a criterion for minimum strength was derived by comparison and used to optimize a reasonable mixing ratio, thus achieving a fast data-driven interaction that was concise and reliable.