Finite-Volume-Aligned Physics Regularisation for Reservoir Pressure Surrogates under Distribution Shift: Robustness, Residual Monitoring, and Resolution-Transfer Limits
Fast reservoir surrogates are attractive for uncertainty quantification, optimisation, and repeated forecasting, yet data-only networks can lose accuracy and local conservation when geology or well controls leave the training distribution. This study isolates the marginal value of a finite-volume-aligned physics loss and then examines whether its residual can support trustworthy deployment. A 32 × 32 benchmark was generated for steady single-phase Darcy flow over heterogeneous permeability fields and variable injector-producer configurations. Identical 8089-parameter dilated convolutional networks were trained from 60 labelled simulations using pressure error alone (Data-60) or the same objective plus the normalized residual of the finite-volume stencil that generated the labels (PI-60). For the three-seed ensemble on fixed tests, PI-60 reduced mean relative pressure error by 5.3% on Test-ID and 10.4% on Fixed Compound-OOD (Test-OOD), with a 14.1% reduction on the independently regenerated Independent Combined-Shift stress test: P90 and P95 Fixed Compound-OOD errors decreased by 13.0% and 14.7%. The raw residual separated the designed ID and OOD populations extremely well (AUC = 0.997) but ranked case-wise OOD pressure error weakly (Spearman ρ = 0.148; worst-20%-error AUROC = 0.648). Stability-aware weighting materially improved this diagnostic role: a five-step Jacobi-preconditioned conjugate-gradient inverse-action score increased ρ to 0.382 and AUROC to 0.790, while the exact inverse-weighted energy score provided an analysis ceiling of ρ = 0.466 and AUROC = 0.838. In selective-simulation analysis, the preconditioned score reduced risk-coverage AURC by 4.6% relative to the raw residual; combining it with seed disagreement did not help. Continuous severity sweeps further showed that PI-60 reduced integrated pressure error by 5.7% for shortening correlation length and 6.9% for increasing well rate, while reducing linear degradation slopes by 48.3% and 27.0%. Finally, a zero-shot 16 × 16/32 × 32/64 × 64 test exposed an important limit: the finite-volume reference showed decreasing adjacent-grid discrepancy and an empirical order near 2.38, whereas both learned surrogates became less coherent under refinement. PI-60 reduced the 32-to-64 discrepancy by 4.5% relative to Data-60 but did not restore convergence. These results distinguish fixed-grid finite-volume alignment from genuine discretization consistency and support residual monitoring only when stability, calibration, and resolution limits are
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