Proper orthogonal decomposition methods typically rely on uniformly distributed snapshots, which may lead to inefficiencies and reduced accuracy in reduced-order modeling. To address this limitation, this paper proposes an adaptive sampling strategy based on interval bisection, aimed at improving the quality and efficiency of snapshot selection in nonlinear magnetic field modeling. Snapshots are generated through finite element analysis, and representative sampling points are then adaptively selected on a coarse mesh using the proposed strategy. These selected time instances are subsequently re-evaluated on a fine mesh to assess the robustness and accuracy of the constructed reduced-order model in both magnetic field distribution and electromagnetic force prediction. Simulation results on a E-core transformer demonstrate that the proposed method significantly accelerates the modeling process while maintaining high prediction accuracy for both the magnetic field and electromagnetic forces, confirming its potential and computational advantages in complex multiphysics problems. This work provides a practical and efficient snapshot optimization framework for fast and accurate multiphysics simulations, with potential value for real-world electromagnetic system modeling and design.