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Sediment entrainment marks the initiation of particle motion on the bed surface and plays a crucial role in quantifying sediment transport. While the entrainment behavior might vary among different geophysical flows, the underlying mechanisms are often similar. To explore the shared dynamics, we compiled a global database of diverse geophysical flows: stream flow (SF), hyperconcentrated flow (HF), and debris flow (DF), obtained from field observations and laboratory experiments. We first validate existing Shield's number based entrainment frameworks but find them inadequate to account for entrainment fluxes of all flow types, particularly for the HF and DF, across a wide range of excess Shields number (θ/θc) where θc represents the critical value. Utilizing the random forest regression algorithm, we then proposed a new stream power (ω) dependent bursting area formula (AP) for all types of mass flows considered, resulting in a unified ω-based entrainment model. The revised model achieves an R2 of 0.924, which is more than twice that of the θ-based model (R2 = 0.427) when applied to the same compiled database. This work provides valuable insights for improving sediment transport modeling, which are essential for developing effective river management strategies and optimizing the design of related infrastructure systems.