Data-driven deep neural network approach for magnetoelectric effects in functionally graded piezoelectric/piezomagnetic spherical shells with material parameters uncertainties

Analyzing the magnetoelectric (ME) effect and optimal design of layered functionally graded piezoelectric/piezomagnetic (FGPEPM) structures are important in applications. This study addresses the issue of material parameter uncertainties related to the ME effect in layered FGPEPM spherical shells characterized by volume fraction gradients. Closed-form expressions for the magneto-electro-elastic fields and the ME effect are derived under the power-law gradient model, providing benchmark solutions for spherical structures. For cases involving arbitrary property gradients, the finite difference method (FDM) is employed to investigate magneto-electro-elastic multi-field coupling responses and the associated ME effect. To address uncertainties in material properties, an interval random uncertainty model is newly proposed. More significantly, a data-driven deep neural network (NN) framework is developed as a computationally efficient surrogate to achieve rapid uncertainty quantification and optimization of the ME effect, overcoming the high computational cost of traditional FDM. The findings demonstrate that material parameter uncertainties significantly alter the ME coupling behavior, with the NN approach achieving high-precision predictions while dramatically improving computational efficiency. This work makes four primary contributions: establishing novel analytical solutions for FGPEPM spherical shells; developing a generalized numerical framework for arbitrary gradients; introducing an efficient NN-based uncertainty quantification method; and enabling optimal design under material uncertainties.