Understanding thermal energy transfer and fracture evolution in submarine hydrothermal systems is essential for sustainable resource utilization, but simulating these complex multiphase, multi-physics processes is challenging. This study integrates the lattice Boltzmann method with a fully connected neural network to investigate hydrothermal phase separation and its effects on chemical dissolution in carbonate fractures at the pore scale. Specifically, the lattice Boltzmann method simulates gas-liquid phase separation induced by seawater boiling, affecting carbonate fracture dissolution at the pore scale. The fully connected neural network predicts the resulting fracture geometry and dissolution quantities under various physical conditions. Analysis of simulation datasets demonstrates that the fully connected neural network achieves high predictive accuracy, with a total loss of 0.01 and reduces computation time by over 20% compared to traditional methods. The coupled lattice Boltzmann method-fully connected neural network model effectively simulates fractures with sizes ranging from millimeters to centimeters, excelling in handling chemical dissolution, multiphase flows, and multicomponent interactions. This approach offers valuable predictive capabilities for applications such as enhanced geothermal systems and oil reservoir exploitation.