Project start: 1.10.2025.

Physics-informed neural networks (PINN), as a special form of machine learning, have recently attracted a lot of attention due to their exceptional flexibility in solving a wide range of problems and faster training. PINN models integrate the physical equations of the system – including ordinary and partial differential equations – into the loss function, thereby adding knowledge based on physical principles to the model.

It was shown that the accuracy of the PINN method when solving vibrational equations, especially for free vibrations, decreases with increasing simulation time, which is the main motivation for this project proposal. Several approaches have been proposed in the literature to solve this problem. So far, the best published results are based on the analysis of the spectral properties of the Neural Tangent Kernel (NTK). NTK converges to a defined limiting value of the kernel and remains constant till the end of the learning process at the moment when the width of the neural network becomes infinite. However, if the described PINN method is trained on beam impulse responses and associated frequency response functions (FRF), the method will accurately calculate FRF up to about 20 Hz according to recent literature. Given that in practice FRF should cover the frequency range up to 1000 Hz and more, there is considerable room for further improvements and contributions.

The goals of this project are creatina an database for training and testing and to reduce the accumulated error and improve the learning efficiency of the PINN model for beam vibration analysis with all boundary conditions. Furthermore, from such measurements it is possible to perform a modal analysis of the beam, so this procedure, using an inverse approach, can serve as a basis for identifying natural frequencies and vibration modes and damping in the material, covering the frequency band needed in practice.