<p>Numerical simulation of the solidification field is computationally intensive and time-consuming, limiting its application in real-time optimization of process parameters. To overcome this limitation, a rapid prediction and inverse design framework for the solidification field is developed by integrating proper orthogonal decomposition (POD), backpropagation neural network (BPNN), and Gappy POD. First, an active learning strategy based on a Kriging surrogate model is adopted to enrich the training samples, enabling the construction of a high-quality solidification dataset with limited additional simulation cost. Subsequently, POD is employed to perform dimensionality reduction and reconstruction of the solidification field, while a BPNN model captures the nonlinear mapping between process parameters and modal coefficients, achieving efficient prediction under untrained operating conditions. Finally, an iterative Gappy POD algorithm is introduced for inverse identification of process parameters corresponding to target solidification fields. Results demonstrate that, compared with the initial dataset, the prediction error of key geometric features was reduced by approximately 33% with only 17% additional simulation samples. The average global relative error of the predicted solidification field under unseen conditions remains below 0.02. The global relative error between the inversely identified and target fields is less than 0.015, demonstrating strong consistency in critical geometric features. The proposed framework significantly improves computational efficiency and provides an effective approach for precise control and rapid parameter optimization in copper alloy horizontal continuous casting.</p>