Abstract

Finite element analysis remains standard for structural verification, but repeated full-field simulations are costly for geometry exploration and monitoring. This work introduces GeoPINONet, a geometry-conditioned physics-informed neural operator for three-dimensional linear elasticity under sparse finite-element (FEM) supervision. It combines a PointNet geometry encoder, multiscale Fourier features, a mixed displacement-stress decoder, and Active Critical Selective Validation (ActiveCSV), which reallocates supervised anchors toward mechanically critical and persistently difficult nodes. Training uses 64 Latin hypercube geometries per family on 3D lug and plate-with-hole benchmarks with moving stress concentrations. On dense FEM meshes for 16 unseen geometries, including interpolative and controlled near-boundary cases, GeoPINONet achieves mean R-u(2) = 0.996-0.999 and p95(sigma vM,ip )< 8% across both families and load modes. For a characterized target and fixed 50,000-point grid, prepared-operator deployment executes both learned output projections and reconstructs physical fields in 2.60 ms on average (2.89 ms at the 95th percentile). Including device-to-host transfer and visualization-field replacement requires 3.70 ms on average (4.14 ms at the 95th percentile). Relative to the reported 44 s two-load finite-element solver boundary, the ratio is approximately 1.1 & times; 10(4); offline FEM generation, training, one-time invariant-feature preparation, and rendering are reported separately. Ablations show that stress reconstruction depends on spectral enrichment, adaptive supervision, and constitutive consistency: removing Fourier features reduces R-sigma vM,ip(2) from 0.90 to 0.16, while removing Hooke consistency increases the lateral-bending tensor Frobenius error from 9.8% to 133.4%.