Recently, there has been a widespread interest in the use of neural network models to solve the forward and inverse problems of system identification. Using a small amount of observation data that is not labelled, physics-informed neural networks (PINNs) can effectively solve the forward and inverse problems of system identification. However, unknown or lost physical information and noise in observation data make PINNs less effective. In comparison, generative adversarial networks (GANs) perform more accurately and flexibly under similar circumstances. Because of adversarial loss, GANs can learn more complex and high-dimensional data distributions better than PINNs, but a large amount of high-quality (or labelled) data is required. The proposed method incorporates the advantages of both GANs and PINNs, enabling the network to learn from a combination of real data and physical constraints. One notable feature of this approach is its ability to handle system identification problems where only a limited amount of real data is available, and certain physical information remains uncertain or unknown. The adversarial training between real data and physics-based constraints minimizes the impact of noise in the available data and reduces the demand for physical information in complex systems. The proposed method has been successfully verified in practical applications, particularly in the domain of structural identification, demonstrating its accuracy and efficiency. The proposed method is also expanded to solve high-dimensional and coupled differential equations.