After long-term operation of the suspension system, the factors such as uncertainty disturbance under complex working conditions may result in inaccurate system model parameters, which can cause the degradation of control performance or even lead to train operation failures in severe cases. Thus, it is necessary to identify the key parameters of the system. The present paper proposed two data-driven methods for the inverse problem for the suspension system excited by jump and diffusion stochastic track excitation. Due to the existence of the stochastic jump process, the Kolmogorov equation becomes an integro-differential equation. A physics-informed neural networks (PINNs) method with Monte Carlo simulation is introduced to solve this integro-differential equation, which successfully avoid using the mesh grid. To alleviate the numerical difficulty caused by the system parameters, a residual-based adaptive sampling method is introduced. Based on this neural network structure, two data-driven methods for the inverse problem are proposed. The first method consider the case where the data available is directly on the PDF. These known data is treated similar as the boundary condition to supervise neural network. The second method addresses a more realistic scenario, where only sparse data are given on the trajectories of the stochastic suspension system, which are not sufficient to accurately construct the PDF. A new loss using the Kullback–Leibler divergence is introduced to learn the known knowledge in the data from the stochastic trajectories. All the two methods can infer the unknown parameters and subsequently obtain the solution of the forward Kolmogorov equation. Numerical results show that both of the methods are effective on solving the inverse problems. In addition, some random noises are added to the known data to test the robustness of the proposed methods. The results show that two methods can accurately identify the unknown parameters under certain level of noise intensity, which shows good robustness of the two methods.