Multi-station multi-variable weather prediction delivers crucial meteorological forecasts for distributed geographical locations, with significant implications for human activities. Existing methods often overlook the underlying physical dynamics governing atmospheric processes and fail to capture complex interdependencies between weather variables, limiting their predictive accuracy. To address these limitations, we propose the Dynamical Interaction Network (DIN), which integrates physical processes with data-driven learning through two synergistic modules. The spatiotemporal dynamical modeling module captures multiscale atmospheric processes by integrating local dynamics, cross-regional patterns, and temporal evolution. The higher-order cross-variable interaction module learns the complex dependencies among meteorological variables by using convolutions to simulate differential operators. Extensive experiments on the Global Wind/Temp dataset demonstrate that DIN achieves state-of-the-art performance.