A Multi-Model Non-Intrusive Reduced-Order Framework for Parametric Erosion Prediction via Kinematic Cross-Moment Compression

High-fidelity Eulerian--Lagrangian simulations of solid particle erosion in curved pipes require hours of compute per operating point, preventing rapid parameter sweeps and real-time wear assessment. Existing reduced-order models (ROMs) speed up these evaluations, yet they are typically trained on a single, fixed empirical erosion formula (e.g., Oka or Finnie). Changing the material law or target hardness then requires a complete retrain of the surrogate. Here, we present a non-intrusive reduced-order framework that avoids this model-locking by approximating the underlying particle collision kinematics instead of scalar wear rates. Specifically, we project and compress 23 Eulerian boundary cross-moments ($\mathbb{E}[V_p^u \sin^vα_p \cos^wα_p]$) across the pipe surface. Using 372 high-fidelity CFD-DPM cases of $90^\circ$ elbows over three bend ratios ($R/D \in \{1.5, 2.0, 5.0\}$), five Reynolds numbers, five density ratios, and six particle diameters in the inertial regime ($St > 1$), we evaluate a hybrid compression scheme. Linear Proper Orthogonal Decomposition (POD) and Mode-1 tensor unfolding SVD are combined with block-wise Convolutional Autoencoders (CNN-AE) to handle both broad convective transport and localized impact craters. An anisotropic Gaussian Process Regression (GPR) surrogate maps four dimensionless $Π$-groups to the compressed latent space, evaluating full 2D wear topographies in roughly $2\,\mathrm{ms}$ ($R^2 > 0.99$ on primary kinematic fields). Because kinematics are decoupled from material damage laws, the resulting surrogate evaluates multiple empirical models post-hoc exactly matching Finnie and closely approximating Oka, McLaury, and Arabnejad without retraining.