Physics-informed neural networks offer a modern deep learning approach to solving partial differential equations, embedding physics into their loss functions. However, excessive reliance on automatic differentiation often limits their accuracy and optimization capabilities, particularly in parameter identification problems - a critical challenge for understanding physical systems. To address these issues, we propose a hybrid framework combining PINNs with discrete schemes, such as forward Euler method or Backward Differentiation Formula (BDF). By discretizing both spatial and temporal domains, the problem is reformulated as an optimizer framework with soft constraints, integrating observational data to estimate parameters and predict future solutions. Unlike traditional methods, this approach handles arbitrary functions and extends beyond parameter estimation to solve high-dimensional, complex problems. Focusing on the Navier-Stokes equations, our method uses grid-like observational data over time to accurately identify parameters and predict unsteady solutions in future time steps. This hybrid approach enhances PINNs’ robustness and accuracy, offering a powerful alternative for solving real-world problems.