Data-Driven On/Off Topology Optimization of Electromagnetic Devices Based on Graph Physics-Informed Neural Networks and Physics-Guided Reinforcement Learning

Abstract

Topology optimization of electromagnetic devices is computationally formidable owing to the combinatorial on/off material distribution on unstructured finite element meshes and repeated Maxwell equation solves. This paper develops GPRL-TO, a data-driven framework addressing both difficulties through three synergistic components. First, a graph physics-informed neural network (G-PINN) reformulates the finite element mesh as a graph and predicts element-wise magnetic flux densities under embedded magnetoquasistatic constraints, with two to three orders of magnitude speedup over finite element analysis. Second, as the central methodological contribution, a physics residual-driven curiosity mechanism converts the Maxwell residual into an intrinsic reward of a reinforcement learning agent, steering exploration toward physically unreliable design regions; the residual also indicates surrogate reliability. Third, a Gumbel–Softmax relaxation with temperature annealing renders the binary design variables differentiable, so the discrete on/off decisions relax to a continuous reparameterization driven by energy-type design sensitivities evaluated on the surrogate-predicted fields, instead of adjoint solves. A layered bridge-prescribed refinement fixes an iron skeleton that closes the magnetic circuit and guarantees manufacturable multi-layer barriers by construction. On a synchronous reluctance motor rotor, the G-PINN attains a relative L2 error of 9.51%, and the layered optimization improves the objective by 16.7% while raising the saliency difference from essentially zero to +0.017165.