Functionally graded (FG) materials have gained increasing attention in nano- and micro-structure design due to their ability to enhance structural performance. In particular, bi-directionally FG nano- and microbeams offer greater flexibility by enabling material gradation in multiple directions, and their bending behavior has been investigated using analytical and numerical approaches [1–3]. However, these conventional methods often require substantial computational effort. Recently, physics-informed neural networks (PINNs) have emerged as an efficient alternative for solving partial differential equations by embedding physical laws directly into the learning process. Despite their growing application in solid mechanics, only a limited number of studies have employed PINNs for the bending analysis of nano- and micro-scale beams [4,5]. In this study, a PINN-based framework is proposed to analyze the bending behavior of a bi-directionally FG cantilever microbeam subjected to a uniformly distributed load. The governing equation is formulated by coupling the Euler–Bernoulli beam theory with the modified couple stress theory. Then, a PINN model is trained to approximate the solution by minimizing a loss function that includes the governing equation residual and boundary conditions. To improve accuracy and computational efficiency, the PINN hyperparameters are optimized using a Taguchi–Grey method. The effects of geometric properties, length scale parameter, and material gradation on bending response are investigated. The results demonstrate that the proposed PINN approach provides accurate predictions for the bending behavior of bi-directionally FG microbeams and effectively captures size-dependent effects, highlighting its suitability for micro-scale structural analysis.