According to the 2024 drilling safety report of Tarim Oilfield, 31% of well control accidents are attributed to calculation deviations of downhole kick velocity. To address the challenge of time-varying nonlinear modeling in the monitoring of downhole fluid migration during oil and gas drilling, a hybrid intelligent model integrating feature engineering, physical constraints, and deep learning was proposed, and an optimized calculation framework for kick velocity driven by both physics and data was established. Deep purification of data was achieved by constructing a three-tier feature screening system: the noise filtering layer employed an improved Savitzky-Golay filter to suppress time-frequency domain noise; the physical correlation layer constructed a feature relevance tensor based on Darcy's Law to screen effective feature pairs; the difference amplification layer enhanced the distinguishability of key features using manifold learning, which increased the proportion of effective features to 79%. On this basis, a hybrid SENet-LSTM-Arps architecture was designed: the SENet channel attention mechanism was introduced to dynamically modulate channel weights; a bidirectional LSTM(long short-term memory) network was utilized to capture temporal dependencies; the Arps production decline model was embedded to construct a physical constraint layer, and the fusion of data-driven and knowledge-driven approaches was achieved via the Lagrange multiplier method. Experimental results based on the measured data from Well Duwa 103 in the Tarim Basin (with hyperparameter combinations determined by Bayesian optimization) show that: in the calculation of lag time, the coefficient of determination (R²) of this architecture reaches 0.992 5, the mean squared error (MSE) is as low as 0.837 1, and its performance is improved by two orders of magnitude compared with traditional methods; the synergistic effectiveness of the SENet module and the Arps constraint layer is verified by ablation experiments. The research results provide a full-link optimization paradigm of “feature engineering-physical constraints-temporal modeling” for the accurate calculation of kick velocity in complex reservoir environments. In engineering applications, the early warning time can be advanced to 15 minutes (a 65% reduction compared with traditional methods), and the well control early warning accuracy reaches 97.3%.