In recent years, modern information technologies have been actively used in various industries. The oil industry is no exception, since high-performance computing technologies, artificial intelligence algorithms, methods of collecting, processing and storing information are actively used to solve the problems of increasing oil recovery. Deep learning has made remarkable strides in a variety of applications, but its use for solving partial differential equations has only recently emerged. In particular, you can replace traditional numerical methods with a neural network that approximates the solution to a partial differential equation. Physically Informed Neural Networks (PINNs) embed partial differential equations into the neural network loss function using automatic differentiation. A numerical algorithm and PINN have been developed for solving the one-dimensional pressure equation from the Buckley-Leverett mathematical model. The results of numerical solution and prediction of the PINN neural network for solving the pressure equation are obtained.