TITLE:
Beyond Physics Residuals: Local Conservation, Symmetry and Physics-Distance Reliability in Two-Phase Reservoir Surrogates under Distribution Shift
AUTHORS:
Franck-Hilaire Essiagne, Moussa Camara, Kouassi Louis Kra
KEYWORDS:
Reservoir Surrogate, Two-Phase Flow, Finite-Volume Conservation, Symmetry Canonicalization, Physics-Informed Machine Learning, Out-of-Distribution, Reliability
JOURNAL NAME:
Journal of Analytical Sciences, Methods and Instrumentation,
Vol.16 No.2,
June
29,
2026
ABSTRACT: Physics-informed reservoir surrogates are often evaluated by state error or equation residual alone, although neither establishes local conservation, symmetry consistency, or reliability under distribution shift. We separate these properties in a controlled two-dimensional incompressible oil-water benchmark. A flux-predictive U-Net outputs pressure, saturation increment, and oriented intercell total fluxes. Soft finite-volume residual regularization, exact minimum-norm cellwise flux projection, and horizontal/vertical reflection canonicalization are varied in a three-seed 2 × 2 × 2 factorial design across seven IID/OOD regimes. Exact local projection reduces saturation error in every regime and enforces cellwise balance to numerical precision but does not guarantee accurate pressure or long-horizon dynamics. Canonicalization gives large additional gains only for symmetry-equivalent well shifts: under combined geology plus symmetry OOD, saturation nRMSE decreases from 0.0216 without canonicalization to 0.00994 with the full method, whereas its incremental benefit is not significant for non-symmetry well or hard compound OOD after Holm correction. Converged FNO and PINO-style baselines remain less accurate in saturation/front metrics. Projector-forensics controls show learned fluxes reduce saturation error by 25% - 56% relative to a zero-flux projector-only baseline, while reference simulator fluxes require only approximately 10−6 relative correction. On a separately generated 56-case holdout, pre-projection correction magnitude predicts failure (Spearman rho = 0.648; AUROC = 0.894 for saturation nRMSE > 0.025; severe-OOD AUROC = 0.971). The results establish that conservation, symmetry, and residual consistency address distinct failure modes, and that conservation correction provides an interpretable physics-distance reliability signal.