Reconstruction Training Increases Linear Accessibility of Global Geometry in a Particle Transport Surrogate

Scientific simulations increasingly rely on reduced representations that preserve reconstruction-relevant physical structure while reducing computational cost for calculations. Monte Carlo (MC) particle transport provides a setting for studying learned representations, as the dependence of spatial mesh tallies on geometry and particle distribution statistics are well-defined. This work uses a residual 3D U-Net to map paired simulation data consisting of low-sample mesh tallies (e.g., $16^3$, $10^5$) and their relative fractional statistical uncertainties to fine, high-sample predictions (e.g., $64^3$, $10^8$). The dataset is generated with the MCNP\textsuperscript{\textregistered} code, a production-grade particle transport simulator, and contains 943 cases, with each case consisting of a water object with either a box, cylinder, or sphere as the outer geometry, and an embedded lead inclusion defined as the internal geometry, irradiated by two orthogonal photon cone-beam sources. Linear probes and matched representation controls test whether physical attributes become more accessible in U-Net's bottleneck after reconstruction training. Matched linear-readouts compare the raw input, PCA/POD, an untrained U-Net, and the trained representation. Latent encoding of the outer geometry rises from $0.909$ balanced accuracy in the raw input and $0.884$ in the untrained bottleneck to $0.992$ in the trained U-Net bottleneck. This finding suggests U-Net reorganizes pre-existing global geometry information and motivates direct comparisons between learned and prescribed reduced coordinates in future simulation studies.