Multiple energy flow calculation (MEFC) serves as a fundamental technology within Integrated Energy Systems (IESs). Nevertheless

MEFC has faced increasing challenges due to the complex coupling among heterogeneous energy sources

information constraints

and extreme scenarios. This study proposes a data-driven approach for the MEFC task based on an edge-enhanced heterogeneous graph attention mechanism (EEHGAT). A heterogeneous graph structure is first employed to model the electricity-gas-heat coupled IES with three types of nodes and four types of edges. Then

a dual-model architecture comprising a node model and an edge model is constructed. This architecture aims to fully map MEFC information while simultaneously preventing error accumulation. Subsequently

a multitask learning framework incorporating a variable-weight loss function is integrated to enhance the flexibility of the training process. Moreover

visualized interpretability is developed to de-mystify the “black-box” nature of the neural network. Numerical results demonstrate that the Mean Absolute Percentage Error (MAPE) for the proposed node and edge models is 0.1012% and 0.2060%

respectively. Meanwhile

under conditions such as measurement errors

information limitations

and extreme scenarios

the proposed method exhibits greater adaptability and robustness than the Newton-Raphson method and traditional data-driven methods.