Recently, physics-informed neural network (PINN) has demonstrated significant potential in solving partial differential equations (PDEs). Nevertheless, PINNs encounter significant challenges, including high computational cost, low accuracy, and limited scalability. To address these issues, physics-encoded recurrent convolutional neural network (PeRCNN) have been proposed as a discrete learning model that incorporates a specified physical framework directly into neural networks. Unlike continuous learning models like PINNs, PeRCNN defines its loss function as the sum of discretized PDE residuals, with initial and boundary conditions (I/BCs) rigorously encoded into the network to ensure strict adherence. Despite these improvements, PeRCNN often struggles with convergence when solving PDEs with large timesteps. In order to address this issue, we introduce a method called TaW-PeRCNN, which employs a time-adaptive weights algorithm. This algorithm assigns trainable weights to each snapshot, offering a novel approach to handling imbalances in multi-part loss functions. Experimental results demonstrate that TaW-PeRCNN improves the accuracy and extrapolability in solving PDEs, surpassing the baseline PeRCNN by up to an order of magnitude.