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Current shale gas well production capacity predictions primarily rely on analytical and numerical simulation methods, which necessitate extensive calculations and manual parameter tuning and produce lowly accurate predictions. Although employing neural networks yields highly accurate predictions, they can easily fall into local optima. This paper suggests a new way to use Cuckoo Search (CS)-optimized neural networks to make shale gas well production capacity predictions more accurate and to solve the problem of local optima. It aims to assist engineers in devising more effective development plans and production strategies, optimizing resource allocation, and reducing risk. The method first analyzes the factors influencing the production capacity of shale gas wells in a block located in western China through correlation coefficients. It identifies the main factors affecting the gas test absolute open flow as organic carbon content, small-layer passage rate, fracture pressure, acid volume, pump-in fluid volume, brittle mineral content in the rock, and rock density. Subsequently, we used the CS algorithm to conduct the global training of the neural network, avoiding the problem of local optima, and established a neural network model for predicting shale gas well production capacity optimized by the CS algorithm. A comparative analysis with other relevant methods demonstrates that the CS-optimized neural network model can accurately predict production capacity, enabling a more rational and effective exploitation of shale gas resources, which lower development costs and increase the economic returns of oil and gas fields. Compared to numerical simulation, SVM, and BP neural network algorithms, the CS-optimized BP neural network (CS-BP) exhibits significantly lower prediction error. Its correlation coefficient between predicted and actual values reaches as high as 0.9924. Verification experiments conducted on another shale gas well also demonstrate that, in comparison to the BP neural network algorithm, CS-BP offers superior prediction performance, with model validation showing a prediction error of only 0.05. This study can facilitate more rational and efficient exploitation of shale gas resources, reduce development costs, and enhance the economic benefits of oil and gas fields. [ABSTRACT FROM AUTHOR]