<p>Time-dependent partial differential equations (PDEs) are important mathematical tools for studying nonlinear dynamics. The recently emerged machine learning methodologies, such as Physics-Informed Neural Networks (PINN), offer an appealing alternative to traditional PDE solvers. These approaches are distinguished by their advanced flexibility and the effortless integration of observed data. However, when solving complex PDEs, especially time-dependent ones, PINN encounters training difficulties, manifesting in convergence to nonphysical solutions. This may be due to the insufficient capability of PINN to maintain the correct time evolution, leading to the difficulty in preserving the accuracy of solutions at later times, even if the initial values are correct. To lessen training difficulties, we aim to enhance PINN’s utilization of temporal information, thereby strengthening its capability to converge in accordance with the underlying physical dynamics of PDEs. Inspired by the temporal marching inherent of traditional numerical methods, we develop the dual-level time-marching neural network. For the outer time-marching level, we employ a neural network to progressively learn the solution in divided temporal sub-domains. For the inner one, as the model learns the solution within the current sub-domain, an implicit pseudo time-stepping loss is used to guide the model to converge along the trajectory of temporal evolution. The outer and inner levels of time-marching mechanisms are both essential in enhancing the model’s ability to handle time evolution. By investigating the spatio-temporal dynamics of a series of time-dependent PDEs, our proposed method is demonstrated to offer accurate predictions and significantly enhance both accuracy and efficiency when compared to PINN and two related improved methods.</p>