Sound generated by turbulent flows is considered as a major source of environmental noise, which comes as the second threat to health directly after air pollution according to WHO. A typical example is the turbulent jet from aero-engine exhaust, which is the dominant source when an aircraft takes off. The noise generation by turbulence is highly related to the coherent structures[1]. Linear model can produce the on-average dynamical behaviour of the coherent structures, but significantly underpredict the noise radiation. This indicates that nonlinearity plays a key role in generating noise. In this research, we aim to identify the nonlinear interactions of coherent structures that underpins the noise generation by learning a reduced-order model (ROM) from high-fidelity simulation data with the SINDy method. To enhance the accuracy and interpretability of data-driven ROM, the physical constraint has been applied to preserve the energy transfer in the turbulence cascade with a closure model used to account for the interactions with unresolved parts. In addition to modelling the deterministic interactions between coherent structures, an additional forcing is formulated to account for the stochastic effects of fine-scale turbulence. Figure 1a shows that the derived ROM can well represent the nonlinear dynamics for a turbulent mixing layer, compared to a linear model. The acoustic field, shown in Figure 1b, is obtained by solving the Acoustics Perturbation Equation with reduced-order modelled sources, offering insights into the relationship between the nonlinear dynamics of coherent structures and noise generation.