Dynamic spatiotemporal modeling of fluids and fluidized beds is vital for enhancing process control and product quality in industrial applications. However, the complexity and nonlinear dynamics of spatiotemporal evolving features in these systems present major challenges for developing unified predictive models. In this work, a local interaction and relative position augmented transformer (LIRT), which combines the local interaction module (LIM) and relative positional encoding (RPE), is proposed to address this issue. LIRT consistently outperforms transformer in capturing nonlinear dynamics across datasets covering laminar, turbulent, and gas–solid two-phase flows. The learning dynamics of models are investigated and compared using signal-to-noise ratio and geometric complexity measures. Furthermore, the contributions of LIM and RPE in improving predictive accuracy are quantitatively analyzed via Shapley game theory, respectively. These findings suggest that LIRT is a generalizable and interpretable solution for spatiotemporal modeling in fluid-related systems, with potential applications in a wide range of scientific and industrial domains.
Liu et al. (Sun,) studied this question.