STUDY OF THE ACCURACY OF PHYSICALLY INFORMED NEURAL NETWORKS USING THE EXAMPLE OF BEAM DEFORMATION

The paper investigates the accuracy of beam deformation prediction using physically informed neural networks (PINN) compared to conventional fully connected neural networks. For the experiment, an analytical solution to the deflection problem of a beam hinged at one end, fixed at the other, and loaded with a point force was used. A dataset was created in which the position of load application was varied to obtain different deflection values. The architecture of the neural network was based on a fully connected structure trained for deflection prediction. During the study, two loss functions were compared: a standard one that minimizes the mean square error (MSE) and a complex one that includes a physical component. The latter took into account the laws of mechanics, in particular the differential equations of beam deflection, which were integrated into the learning process through the gradients of the network's output data. The results showed that incorporating physical laws into the training process significantly improves the accuracy of predictions, especially with limited data. The comparison demonstrated that the physically informed neural network provides better results than the conventional model and more accurately reflects the behavior of the beam under load. The obtained findings emphasize the effectiveness of the PINN approach for solving engineering problems where physical models and laws play an important role.