Multiscale modelling of ferroelectrics using a physics-informed neural network driven by molecular dynamics data: parameter identification and field reconstruction

Abstract In multiscale modeling of ferroelectric materials, a fundamental challenge is to transfer discrete atomistic information into a continuum phase-field model (PFM) while retaining an accurate description of mesoscale behavior. In this paper, a physics-informed neural network (PINN) framework is developed, in which the loss function consists of MD-data penalty and partial difference equation (PDE) constraints. By minimizing the loss function, the model not only reconstructs the polarization field along with the full coupled electromechanical response, including strain, stress, electric field, and energy landscape at the continuum scale, but also identifies critical parameters required for the PFM, including the characteristic energy density, characteristic length factor, anisotropy factor, and Landau polynomial coefficients. By using the PINN-predicted parameters to solve the corresponding PDEs within a finite element framework, we perform a cross-verification showing that the two numerical implementations yield consistent results. In addition, the transferability of the learned parameters is further evaluated through extended three-dimensional PF simulations under external tensile and bending loading, in which the domain expansion, shrinkage, annihilation, and fragmentation are in agreement with the corresponding experimental observations. This framework provides an effective methodology for multiscale bridging between atomistic and continuum descriptions for perovskite ferroelectric materials.