On the wave dispersion of a multi-scale hybrid nanocomposite microstructure via deep neural network technique

Abstract

The utilization of machine learning advantages in solving engineering problems has proven to be beneficial and accurate. Dealing with partial differential equations (PDEs), on the other hand, PINN could be enhanced using additional information from the physical mathematics of the problems. In this regard, a physics-informed neural network (PINN) is exploited in the current study to extract phase and group velocities of the multi-scale hybrid composite plate structure. In doing so, the exact differential equations of homogenized plate structure are extracted using Hamilton’s principle based on modified couple stress theory and shear deformation displacement field. The boundary conditions along with initial conditions are also considered in the equations. The PINN tries to minimize the loss function which is defined using extracted PDEs, boundary conditions, and initial conditions. Moreover, the results of PINN are further compared with the analytical solution using harmonic expansion of the displacement variables. The results show highly accurate and reliable results obtained using PINN in comparison to analytical results.