Unsupervised learning-based model for predicting interfaces in variable specific heat ratio gas flows

Compressible multi-material and multi-species flows involving shock waves and chemical reactions are central to explosion mechanics and shock dynamics. Machine learning approaches for solving multi-material Riemann problems and capturing interface coupling effects have emerged as an active research area. However, existing neural network-based approaches generally assume calorically perfect gases with constant specific heat ratios, and are therefore incapable of handling variations in the specific heat ratio arising from compositional changes or from the excitation of molecular vibrational energy modes under high-temperature conditions. Such variations are frequently encountered in realistic detonation and reactive flow problems. To address this limitation, an unsupervised physics-constrained neural network model, termed PCNN-RS-γ, was proposed, which extended the previously developed Physics-Constrained Neural Network framework for multi-material Riemann Solvers (PCNN-RS) from calorically perfect gases to thermally perfect gases with variable specific heat ratios. Parameters characterizing the specific heat ratios on both sides of the material interface were incorporated into the input layer, enabling the model to effectively account for variations induced by chemical reactions or by high-temperature vibrational excitation. The Rankine-Hugoniot jump conditions and the thermally perfect gas equation of state were embedded in the loss function, thereby establishing an unsupervised learning framework requiring no labeled training data. The trained model was further integrated into the modified ghost fluid method (MGFM), enabling effective coupling with computational fluid dynamics solvers for multi-species reactive flow simulations. Comprehensive numerical experiments demonstrate that the proposed model exhibits strong generalization capability, high fidelity, and high computational efficiency. In terms of generalization, the model establishes a unified framework applicable to various gaseous material with specific heat ratios ranging from 1.2 to 1.7, accurately capturing variable specific heat ratio effects while remaining fully applicable to conventional two-gas flows with constant specific heat ratios. In terms of fidelity, the predictions of the model agree closely with those of standard implicit iterative methods, and the model faithfully resolves complex flow structures such as detonation waves and shock-bubble interactions involving chemical reactions. In terms of efficiency, the model eliminates the need for iterative interface prediction, and its computational cost is significantly lower than that of traditional implicit iterative approaches. These results indicate that the proposed model provides a reliable and efficient numerical tool for multi-species reactive flow simulations with variable specific heat ratio effects in explosion mechanics and shock dynamics.