Designing thin-walled plate structures is challenging due to their susceptibility to various forms of structural instability. In addition, the substantial computational cost of finite element analyses, especially in optimization scenarios, underscores the need for efficient and reliable surrogate models. To address this challenge, the present study employs machine learning (ML) techniques to predict the buckling response of thin plates under complex boundary conditions. Four ML models, including XGBoost, CatBoost, Light GBM, and Random Forest, are developed to predict the buckling coefficient based on input features, including aspect ratio, boundary condition, and compressive loading pattern. The training data for these models is generated using the finite integral transform method. Model performance is rigorously evaluated, with all four algorithms demonstrating strong predictive capabilities. Among them, XGBoost demonstrates the superior predictive performance, achieving an R2 value of 0.99. To gain deeper insights into feature influence, SHAP analysis is conducted, revealing that the aspect ratio has the greatest influence on buckling coefficient, followed by boundary conditions and compressive loading. By adopting gradient-boosting approaches, the proposed framework demonstrates improved generalization and reduced overfitting, with potential applicability to structural optimization. The results suggest that integrating machine learning with structural analysis can serve as a computationally efficient approach for the design and optimization of thin-walled plates.

Structural topology optimization of large-scale engineering systems requires repeated compliance evaluations, making conventional finite element solvers computationally prohibitive in iterative design workflows. Physics-informed neural networks (PINNs) offer a mesh-free, differentiable surrogate alternative, but standard PINNs yield unstable sensitivity fields due to error amplification in higher-order automatic differentiation, undermining optimization reliability. This paper introduces a gradient-enhanced PINN surrogate (gSurrogate) that incorporates a residual-gradient penalty into the total potential energy loss, directly regularizing displacement field derivatives and stabilizing compliance sensitivities for practical structural design. The surrogate is validated on cantilever, simply supported, and fixed–fixed beam configurations and embedded within a SIMP-based topology optimization pipeline driven by the Method of Moving Asymptotes. Over 200 optimization iterations, the proposed surrogate reduces unfiltered sensitivity variance by 94.35\% and filtered variance by 81.74\% relative to a standard PINN, with variance standard deviation reduced by 97.16\%. Three-dimensional topology optimization across mesh resolutions of 120×20×20 and 60×60×20 demonstrates that the gSurrogate achieves displacement errors of 1.81\% and 1.63\% with respect to FEM (Abaqus), compared to 3.75\% and 3.45\% for a standard PINN, a consistent twofold accuracy improvement. These results establish the proposed surrogate as a computationally efficient and numerically reliable alternative to finite element solvers for compliance-driven topology optimization of structural systems.