Gradient-Enhanced PINN Surrogate for Reliable Sensitivity Estimation in Structural Topology Optimization

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.