This paper presents an efficient numerical method for solving the Cahn–Hilliard equation, incorporating a data assimilation term to improve the accuracy and stability of the solution. The method uses a feedback control strategy guided by observed data, ensuring that the computational solution aligns with real-world observations. The Crank–Nicolson formula is employed for discretization, and a scalar auxiliary variable approach is adopted to preserve energy dissipation. The proposed scheme achieves second-order accuracy in both time and space dimensions and is theoretically proven to be unconditionally energy stable. Numerical experiments are conducted to validate the effectiveness of the method. The paper also reviews existing methods for solving the Cahn–Hilliard equation and discusses the advantages and challenges of data assimilation techniques, particularly the nudging method, which adds a feedback control term to the governing equation to drive the system state variables towards observed values.This paper presents an efficient numerical method for solving the Cahn–Hilliard equation, incorporating a data assimilation term to improve the accuracy and stability of the solution. The method uses a feedback control strategy guided by observed data, ensuring that the computational solution aligns with real-world observations. The Crank–Nicolson formula is employed for discretization, and a scalar auxiliary variable approach is adopted to preserve energy dissipation. The proposed scheme achieves second-order accuracy in both time and space dimensions and is theoretically proven to be unconditionally energy stable. Numerical experiments are conducted to validate the effectiveness of the method. The paper also reviews existing methods for solving the Cahn–Hilliard equation and discusses the advantages and challenges of data assimilation techniques, particularly the nudging method, which adds a feedback control term to the governing equation to drive the system state variables towards observed values.