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A Non-Intrusive Reduced-Order Model (NIROM) based on Proper Orthogonal Decomposition (POD) has been proposed for predicting the flow fields of transonic airfoils with geometry parameters. To provide a better reduced-order subspace to approximate the real flow field, a domain decomposition method has been used to separate the hard-to-predict regions from the full field and POD has been adopted in the regions individually. An Artificial Neural Network (ANN) has replaced the Radial Basis Function (RBF) to interpolate the coefficients of the POD modes, aiming at improving the approximation accuracy of the NIROM for non-samples. When predicting the flow fields of transonic airfoils, the proposed NIROM has demonstrated a high performance.