Output-recurrent gated state space model for multiphase flows modeling and uncertainty quantification of exhaust vehicles

This paper presents an Output-Recurrent Gated State Space Model (OR-GSSM) for complex multiphase flows modeling and uncertainty quantification of exhaust vehicles during motion. By establishing the state-space formulation of the gas-liquid Navier-Stokes equations applying semigroup theory and Galerkin projection, explicitly characterizing the dynamic coupling evolution between the velocity, pressure, and volume fraction fields. A novel Gated State Space Transition (GSST) unit is designed to learn parameterized transition and input matrices with adaptive timescales, enhancing physical interpretability and computational efficiency. The output recursion mechanism aligns with the numerical solution characteristics of state-space equations, mitigating long-term error accumulation and addressing training-inference pattern mismatch issues inherent in teacher forcing and scheduled sampling. Validations on the underwater cone-head and water-exit hemisphere-head vehicles demonstrate that: OR-GSSM outperforms OR-ConvLSTM and OR-ConvGRU baselines in accuracy and computational efficiency through its physics-informed adaptive state-space unit design and parallel matrix operations; The output recursion mechanism ensures more stable training, better generalization, and higher prediction accuracy than teacher forcing and scheduled sampling; OR-GSSM accurately captures the gas-phase expansion, gas-liquid mixing formation, backflow jet generation, bubble shedding, and entire water-exit process, etc, showcasing outstanding modeling capability; Its uncertainty quantification effectively characterizes flow features and uncertainty distributions, validating prediction reliability. The proposed method resolves the accuracy-real-time trade-off in traditional computational fluid dynamics, advancing machine learning for multiphase flow modeling and uncertainty quantification in exhaust vehicles.