Fault detection in dynamic systems is essential for ensuring safety, reliability, and optimal performance across various engineering domains. However, it faces significant challenges in complex systems exhibiting nonlinearity, high-order dynamics, and time-variant characteristics. Traditional fault detection methods prove inadequate for addressing the complexity of modern systems. This study introduces a novel framework termed the Laplace Neural Operator-Based Physically Informed Neural Network (LNO-PINN). By integrating physical laws with machine learning, the algorithm employs the Laplace neural operator to effectively handle complex spatio-temporal dependencies. This innovative approach enhances its capability to tackle nonlinear characteristics, high-order dynamics, and time-varying behaviors. Extensive numerical simulations validate its effectiveness in fault detection for complex dynamic systems, particularly in systems exhibiting high-order nonlinear dynamics, thereby providing a groundbreaking methodology for this research field.