Abstract: Physics-informed neural networks (PINN) are advanced computational methods that integrate deep learning techniques with established physical models, and they have rapidly emerged as a research hotspot in the realm of intelligent scientific computing. However, despite their promising potential, traditional PINN often encounter significant challenges when applied to unsteady partial differential equations. The primary issue is their low training efficiency and insufficient prediction accuracy, which mainly stem from inadequate consideration of the temporal causality inherent in dynamic systems. To overcome those limitations, this paper introduces a novel approach known as the time-weighted physics-informed neural network, abbreviated as TWPINN. By introducing a well-designed time-weighted function that embodies the dynamic features of the system, the loss function is optimized to enhance the temporal causality in the neural network. Recognizing the pivotal role of initial conditions in accurately predicting the system’s long-term behavior, TWPINN assigns higher weights to the data points from earlier time stage. This is achieved through a monotonically decreasing weight value as time progresses, ensuring that the model pays greater attention to the initial state of the system. Additionally, TWPINN features a dynamic weight adjustment strategy during the training phase. As the number of training iterations increases, the model systematically adjusts the weight distribution for subsequent time samples. This dynamic strategy enables the model not only to capture the initial state and short-term variations of the system more effectively but also to significantly enhance its accuracy in predicting long-term evolutionary trends. To validate the performance of TWPINN, we selected the one-dimensional unsteady convection equation and the one-dimensional unsteady reaction-diffusion equation as test cases. The experimental results highlight that TWPINN can produce predictions that are highly consistent with benchmark solutions, while also maintaining a low prediction error for these equations.