Multi-energy load forecasting forms the foundation of the operation and scheduling of integrated energy systems. Nevertheless, insufficient data and underutilization of the coupling relationship between the multi-energy load limit the accuracy of load forecasting. This paper presents a predictive model combining neural network Gaussian processes and multi-task learning. The approach is tailored to enhance forecasting accuracy in environments with small-sample datasets. This model capitalizes on the advantageous properties of infinitely wide neural networks for handling small-sample data. Simultaneously, the model effectively extracts the interconnected dynamics of cooling, heating, and electricity loads within the integrated energy system through multi-task learning. In addition, the model applies concrete dropout, enhancing robustness to irregular loads while maintaining the synergistic benefits of the multi-task framework. Furthermore, this paper employs a two-stage gradient descent approach to replace kernel matrix computations of Gaussian processes, reducing the computational cost of parameter optimization and yielding superior forecasting performance in shorter training durations. The simulation results indicate that the proposed model attains a mean accuracy of 97.93% for a 3-day forecasting horizon. Compared with alternative forecasting models, this model exhibits higher accuracy and enhanced generalization capabilities in multi-energy load forecasting for small-sample integrated energy systems.
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