A physics-informed relaxation-decomposed neural collision model for discrete Boltzmann dynamics

Accurate modeling of collision operators is essential for reliable mesoscopic simulation of complex multiphase flows, where interfacial dynamics and long-time evolution are highly sensitive to the relaxation process. In this work, we propose a relaxation-decomposed network (RDN) for learning collision operators in discrete Boltzmann equations. The proposed model takes the discrete distribution function as the modeling variable and represents the collision term through two coupled components: an equilibrium-target correction and a relaxation-time model. These two components are parameterized by the E-net and the τ-net, respectively, leading to a structured equilibrium–relaxation formulation of the neural collision operator. Physical consistency is treated at different levels: the positivity of the constructed target equilibrium and relaxation time is enforced by the relaxation-decomposed parameterization, conservation is promoted through a soft moment-regularization term, and entropy-related behavior is assessed through theoretical estimates and numerical diagnostics. The proposed framework is instantiated within a pseudopotential lattice Boltzmann framework for multiphase flows and evaluated on representative benchmark problems, including phase separation, a static bubble, and droplet impact on a solid wall. Compared with standard neural networks and residual neural networks, numerical results show that the RDN achieves better interface preservation, smaller deviations in macroscopic quantities, and improved long-time stability during multiphase-flow evolution. The entropy-related analysis further indicates that the relaxation-decomposed structure helps maintain more stable thermodynamic behavior during long-time prediction. These results demonstrate that incorporating an explicit equilibrium–relaxation decomposition into neural collision learning provides a promising route toward robust and physically consistent mesoscopic modeling of complex multiphase flows.