This study presents a probabilistic deep learning framework that analyzes the uncertainty in nonlinear differential systems using a physics-informed neural network. The framework utilizes a latent variable model(i.e. noise/random variable model), to create a probability-based model of the system state. Physical laws that are described using partial differential equations are incorporated into the training process to establish constraint relationships, which provides an effective way to train using small samples. The proposed probabilistic physics information neural network (PPINN) algorithm provides a flexible framework, representing the uncertainty of the physical system output caused by the randomness in the input or the noise in the observation, which helps avoid the high costs associated with repeated sampling or expensive experiments. Finally, the effectiveness of the proposed algorithm is demonstrated through some nonlinear system examples containing random variables.