A novel mesoscopic multi-head PI-DeepONet framework for generalized phase change prediction of porous composite PCMs in multi-dimensional parameter spaces

Porous composite phase change materials (PCMs) are frequently used in latent heat thermal energy storage systems. The phase change process of these materials is influenced by multiple parameters. In practical applications, optimal parameter combinations are usually determined within a multi-dimensional space. To enable rapid prediction of these processes across various parameter combinations in multi-dimensional parameter space, a mesoscopic multi-head PI-DeepONet model is constructed. Two validation scenarios and three performance types are evaluated. The results indicate the model exhibits strong generalized prediction performance within the defined space and reliable extrapolation capabilities at representative external points. Furthermore, through a systematic evaluation of out-of-distribution test sets, reliable extrapolation directions are quantitatively determined. This establishes a unified physical criterion based on combined convection intensity to recommend safe multi-dimensional generalization boundaries. Under Validation Scenario 2, involving altered boundary conditions, the model maintained high predictive accuracy after retraining without requiring network framework modifications. Further testing in this scenario reveals an anomalous trend in which the complete melting time initially increases and then decreases with a rising Rayleigh (Ra) number. The model's rapid prediction capability is utilized to verify this trend's universality across a broader domain. Complete melting times for 10,000 parameter combinations on the Rayleigh-Stefan plane are obtained in just 145 s. The critical transition ridge on this parameter plane is revealed accordingly. This study not only demonstrates the model's strong predictive and computational acceleration capabilities but also verifies its significant potential in global optimization and practical applications.