USX-PGD: Uncertainty-Aware, Sparse, and Explainable Reduced-Order Modelling for Two-Phase Reservoir Simulation

High-fidelity reservoir simulation is too costly for multi-query tasks such as history matching and production optimisation. Existing reduced-order models (ROMs) mitigate this cost but generally lack uncertainty quantification, spatial sparsity, and interpretable mode-to-geology mappings. We introduce USX-PGD (Uncertainty-aware, Sparse, and eXplainable Proper Generalised Decomposition), a non-intrusive ROM for two-phase immiscible flow that addresses all three gaps within a single greedy Alternating Least Squares framework. USX-PGD is benchmarked against Proper Orthogonal Decomposition (POD), standard Proper Generalised Decomposition (PGD), and an intermediate Uncertainty-aware Sparse PGD (US-PGD) variant, on a formation-aware upscaled coarse-grid (30×110×34 cells) representation of the SPE10 Model 2 benchmark, a heterogeneous two-phase reservoir with permeability contrasts spanning six orders of magnitude. US-PGD adds sparsity-promoting thresholding and bootstrap resampling to certify a confidence interval on reconstruction accuracy; USX-PGD further adds formation energy decomposition, mode dominance mapping, breakthrough attribution, and mode sensitivity indexing, attributing the reduced-order modes to identifiable geological formations. All four methods reproduce the reference production curves to within 11.03–11.05% NRMS at online reconstruction times of 51–63 ms; the sparse and explainable variants achieve comparable accuracy while additionally providing 41.8% spatial sparsity and a certified 95% confidence interval. All four ROMs compress and replay an already-simulated trajectory, not predict new, unsimulated scenarios; USX-PGD is offered as a reproducible, physically transparent foundation for such multi-query workflows, with predictive extension identified as future work.