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In the non-intrusive measurement of swirling air flow, helium-filled soap bubbles (HFSBs) are ideal neutrally buoyant tracer particles However, there are some researchers that do not use HFSBs in the non-intrusive measurement of swirling air flow, leading to some kind of measurement inaccuracy. Since the flow velocity data has been implicitly included in the physical equations of any kind of tracer particles, it is possible to extract such hidden flow velocity from particle trajectory. In this study we propose a physics-informed procedure of adopting SINDy algorithm to identify the hidden physical equations of non-neutrally buoyant particle dynamics, so that the implicit flow velocity can be discovered. First of all, the numerical experiment is conducted to generate particle trajectory in a 2D swirling air flow in small cyclone separator. Based on the numerical experiment trajectory data, the input variables for SINDy algorithm are properly constructed. The output of SINDy algorithm, which are the identified physical equations, are evaluated and validated on two different-density particle trajectory data. Our results show that the physical equations of tracer particle dynamics can be identified and the discovered flow velocity data has a maximum deviation of 1.4% from the truth (R2≥0.999). The proposed method may remove the requirement of NB tracer particle in non-intrusive measurement of swirling air flow, and may be applied to recognize the physical equations of complex particle laden flow.