Abstract
ABSTRACT This paper examines the application of PINN models to solving a two‐dimensional cylinder flow problem with limited data. Using data obtained by direct numerical simulation, a surrogate PINN model was developed and trained. The model utilizes the governing equations of fluid dynamics and heat transfer, enabling it to accurately predict flow parameters such as velocity components, pressure, and temperature. The direct computational flow model was numerically solved using the SIMPLE algorithm, which couples pressures and velocities. The results showed that the PINN model, which does not contain initial and boundary conditions from direct numerical simulation, is capable of reproducing complex dynamic processes such as the formation of a Kármán vortex street behind a cylinder. However, limitations were identified due to the lack of initial and boundary conditions, which led to increased errors at the boundaries of the computational domain. For example, from the data obtained using the PINN model, a very small absolute difference in error for the velocity and temperature components between the reference data and the predicted values can be noted. Thus, for the horizontal velocity component, the maximum relative error was no more than 2.5%. For the temperature component, the relative error was no more than 0.02%. However, the relative error for pressure was 60%–75%. The main reason for this large error is the lack of a reference pressure value or initial pressure conditions in the loss function. The results show that the PINN surrogate model with eight hidden layers of 200 neurons successfully copes with the task of modeling complex unsteady flow. The integration of physical laws made it possible to achieve relatively satisfactory accuracy using only 10,000 data points.