Physics-informed neural networks for analyzing size effect and identifying parameters in piezoelectric semiconductor nanowires

Piezoelectric semiconductors (PSCs) are crucial in micro-electromechanical systems, but analyzing their size effects and accurately determining flexoelectric parameters is challenging due to the complexity of multi-scale and multi-field coupling. Physics-informed neural networks (PINNs), which merge physical laws with machine learning, provide a promising approach for solving partial differential equations and parameter inversion. In this paper, we develop a PINN model to solve a system of fourth-order partial differential equations for PSC nanowires, accounting for strain gradient and flexoelectric effects. Predictions by the model closely match results from traditional numerical methods. Additionally, with minimal labeled data, the PINN model can predict both physical solutions and material parameters, such as the flexoelectric coefficient. It is expected that PINNs offer an effective method for analyzing PSC nanowires and inverting key material properties.