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The forward full-wave modeling of ground-penetrating radar (GPR) facilitates the understanding and interpretation of GPR data. Traditional forward solvers require excessive computational resources, especially when their repetitive executions are needed in signal processing and/or machine learning algorithms for GPR data inversion. To alleviate the computational burden, a deep learning-based 2D GPR forward solver is proposed to predict the GPR B-scans of subsurface objects buried in the heterogeneous soil. The proposed solver is constructed as a bimodal encoder-decoder neural network. Two encoders followed by an adaptive feature fusion module are designed to extract informative features from the subsurface permittivity and conductivity maps. The decoder subsequently constructs the B-scans from the fused feature representations. To enhance the network's generalization capability, transfer learning is employed to fine-tune the network for new scenarios vastly different from those in training set. Numerical results show that the proposed solver achieves a mean relative error of 1.28%. For predicting the B-scan of one subsurface object, the proposed solver requires 12 milliseconds, which is 22,500x less than the time required by a classical physics-based solver.