Nonlinear multi-field coupling analysis of piezoelectric semiconductors via PINNs

We propose a data-driven physics-informed neural networks (PINNs) via task-decomposition (DD-PINNs-TD) for modeling nonlinear thermal-deformation-polarization-carrier (TDPC) coupling mechanical behaviors of piezoelectric semiconductors (PSs). By embedding three-dimensional (3D), plate, and beam equations of PS structures into the constraints of the DD-PINNs-TD framework, respectively, we develop three representative PINNs that exhibit significant advantages in computational efficiency and accuracy compared to traditional PINNs. Using the proposed DD-PINNs-TD models, we investigate the TDPC coupling responses of PS structures under different loadings. Numerical results demonstrate that the proposed models exhibit accuracy and stability of these models in predicting the nonlinear multi-field coupling mechanical behaviors of PSs. Notably, the plate and beam-theory-based DD-PINNs-TD models achieve superior computational efficiency relative to their 3D-equation-based counterparts. This study establishes a theoretical foundation for analyzing nonlinear multi-field coupling responses in PS structures and has significant practical value in engineering applications.