The highest prediction accuracy of RBF neural network was obtained, and its average relative error was 0.11.

The optimal application rate of the sprinkler irrigation prediction model of radial basis function (RBF) neural network was constructed with total irrigation water, soil bulk density, initial water content and soil texture as inputs and compared with BP neural network and generalized regression neural network. To make the neural network convenient for predicting the optimal application rate of sprinkler irrigation (the maximum application rate of sprinkler irrigation without runoff) in practice, the time of waterlogging, was multiplied by the optimal application rate of sprinkler irrigation to obtain the total irrigation volume. Soil water accumulation time for different soil’s initial water content, bulk density, sprinkler application rate and soil texture were derived by the finite element method, and these data were used as a training database for the neural network. In this study, a mathematical model of soil infiltration for sprinkler irrigation with water and fertilizer integration machines was developed. Therefore, it is necessary to provide a feasible scientific and theoretical basis for developing a reasonable application rate. If the value is too large, the equipment will produce runoff if it is too small, the equipment will run too long and waste energy. The application rate for sprinkler irrigation of water–fertilizer integration machines is an important technical parameter for efficient operation.

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