Accurate modeling of scattering from three-dimensional (3D) perfectly electrically conducting (PEC) targets at microwave frequencies constitutes a fundamental objective in computational electromagnetics, particularly for radar cross section (RCS) prediction and microwave scattering analysis. Classical solvers, such as the method of moments and the Multilevel Fast Multipole Algorithm (MLFMA), although provide high physical fidelity, they become costly under scenarios of repeated queries involving many incidence configurations or frequencies, whereas purely data-driven surrogates often lack accuracy on geometrically complex targets. This paper proposes a U-shaped physics-informed artificial neural network (U-PINet) for 3D microwave scattering analysis. Inspired by the near-far field decomposition of MLFMA, U-PINet combines a near-field graph encoder, parameterized by learnable univariate basis functions, with a hierarchical multi-scale fusion module organized on an octree partition. The proposed network is trained against a discretized residual of the electric-field integral equation at surface collocation points, without requiring reference current labels. Experiments on canonical and geometrically complex 3D PEC targets, conducted under multiple frequency and polarization configurations and assessed through bistatic RCS reconstruction, showcase that U-PINet outperforms representative physics-informed baselines, and yields substantial runtime savings over the classical MLFMA solver under repeated-query scenarios.