<p>Accurate and stable long-term simulation of mechanical systems, particularly those exhibiting Hamiltonian chaos or operating under kinematic constraints, remains a critical challenge. Traditional numerical methods often struggle with energy drift or constraint violations, while standard neural network approaches may lack physical consistency. This study introduces EnhancedSympNet, an innovative framework that seamlessly integrates symplectic integration with physics-informed neural networks (PINNs) to simulate mechanical systems with high accuracy and stability. By combining the structure-preserving properties of symplectic methods with the adaptability of neural networks, EnhancedSympNet excels in modeling both unconstrained Hamiltonian systems and constrained differential–algebraic equations (DAEs). Its versatility is demonstrated across four benchmark systems: the Hénon–Heiles system, simple pendulum, double pendulum, and slider-crank mechanism. EnhancedSympNet employs a tailored physics-informed loss function to enforce physical laws, including energy conservation and kinematic constraints, while adaptive time-stepping and time-weighted training ensure robust handling of complex dynamics. Compared to traditional numerical methods and existing simple neural network approaches, EnhancedSympNet achieves superior long-term accuracy and empirically demonstrates superior energy conservation, as well as robust constraint satisfaction for DAEs. This framework may offer a powerful tool for computational mechanics, with potential applications in engineering design, control, and beyond.</p>