A numerical framework is developed for simulating coupled two-phase flow and poroelastic deformation in porous media, motivated by subsurface applications where saturation changes and mechanical compaction jointly control porosity and permeability. The method combines Enriched Galerkin (EG) discretization for the flow variables with continuous Galerkin discretization for mechanical equilibrium, and couples the two-phase Darcy system to Biot poroelasticity through a Bishop-type effective stress for unsaturated conditions. Dynamic porosity and permeability updates are incorporated through a linearized porosity law and the Kozeny–Carman relation. Two fully implicit coupling strategies are presented: a staggered approach with pointwise constitutive updates, and a monolithic approach that promotes porosity and permeability to Newton unknowns. The poroelasticity component is verified against Mandel’s analytical solution, reproducing the Mandel–Cryer effect. The two-phase flow solver and the fully coupled system are verified via the Method of Manufactured Solutions. Diagnostic tests identify the Darcy-velocity pathway as the mechanism limiting saturation convergence in the fully coupled setting, and an H(div) -conforming reconstruction of the transport velocity is shown to recover near-optimal rates. Element-wise mass conservation is verified directly, and a heterogeneous quarter-five-spot benchmark demonstrates that the enriched discretization conserves mass locally to solver tolerance where an equivalent continuous discretization does not, despite producing saturation fields that differ by less than one percent.
Predicting key hydraulic fracturing parameters is critical for efficiency optimization and safety assurance. However, fracturing time-series data exhibit non-stationary and highly dynamic characteristics, which static loss functions such as MSE and Huber cannot capture. Inspired by the recursive estimation principle of the Kalman filter, this paper proposes Kalman Adaptive Loss–a dynamic loss function that embeds online uncertainty estimation into the training objective. The loss dynamically adjusts per-sample weights through an adaptive temperature, an exponentially-smoothed sample variance, and an entropy-floor uniform mixing, while maintaining a non-trainable uncertainty state P_t together with adaptive process and observation noise variances Q and R . We provide an analytical gradient derivation showing that the proposed loss performs implicit learning-rate rescaling on hard samples. On the fracturing pressure prediction task, Kalman Adaptive Loss reduces MAE from 0.257 to 0.075 and RMSE from 0.445 to 0.186, while converging 4 × faster than Huber. Evaluated on the ECL and Weather benchmarks, the proposed loss improves accuracy in most settings. A controlled ablation study with 23 configurations validates each component, and empirical results confirm that P_t is well-calibrated ( r = 0.77 with the observed error). The source code of this work can be available online at https://github.com/Yihan-Zhang1230/KalmanAdaptiveLoss.
Accurate petrogenetic discrimination of oceanic basalts is important for tracing mantle evolution and tectono-magmatic processes. This study compiled approximately 13,000 MORB, OIB, and IAB samples from the GEOROC and PetDB databases using 18 major-element, trace-element, and elemental-ratio variables to capture basaltic discrimination characteristics. After leakage-free Z-score standardization, the variables were organized into a 3 × 6 matrix for 2D-CNN modeling. Sensitivity tests using 3 × 6, 6 × 3, 2 × 9, and 9 × 2 configurations produced comparable results, with the 3 × 6 arrangement yielding the highest mean Accuracy (0.8267 ± 0.0020) and Macro-F1 (0.8258 ± 0.0020). A heterogeneous ensemble combining structurally diverse CNN sub-models through validation-performance-weighted soft voting was evaluated against RF, SVM, MLP, 1D-CNN, a Transformer-based model, TabNet, and a single 2D-CNN under the same protocol. The heterogeneous 2D-CNN achieved the highest mean Accuracy (0.8273 ± 0.0014) and Macro-F1 (0.8263 ± 0.0016), although its overall advantage over SVM was modest. It also yielded the highest mean F1-scores for MORB (0.7964 ± 0.0025) and OIB (0.8996 ± 0.0010) and reduced class-specific variability relative to the single 2D-CNN. Ensemble-level global and class-specific signed SHAP analyses revealed distinct multivariate geochemical patterns. Specifically, IAB was associated with subduction-related HFSE depletion together with higher SiO2 and Al2O3 and lower MgO feature values, MORB exhibited broad depletion of incompatible elements together with higher MgO and lower SiO2 and Al2O3 feature values, and OIB displayed a coherent enrichment in P2O5, K2O, Nb, and Zr. These results demonstrate the value of integrating structured geochemical representation, systematic benchmarking, and ensemble-level interpretation for multidimensional oceanic-basalt discrimination.
This article presents a mathematical framework for evaluating dual-phase electroosmotic flow in a vertical annulus partially filled with a porous material, consisting of immiscible fluid. Phase one occupies the inner porous region with crude oil, while phase two occupies the outer region as a clear Newtonian fluid. The model incorporates electrokinetic effects through linearized Poisson–Boltzmann equations, slip boundary conditions at the oil–water interface with shear stress jump, and Brinkman-Darcy flow in the porous phase. Exact solutions are obtained for both regions in terms of modified Bessel functions of first and second kinds. For optimization purpose, such solutions are tailored to oil enhancement applications to ascertain the role of each parameter entering flow formation. Findings demonstrate that negative values of the electric field parameter (Ezp<0) actively assist flow formation, eliminate boundary flow stagnation, and accelerate crude oil mobilization, whereas positive values retard transport. Furthermore, quantitative sensitivity analyses reveal that the outer radius ratio, the porous-fluid interface position, and the viscosity parameter exert dominant control over the system pressure gradient and interfacial velocity. Parametric evaluations confirm that optimized electrokinetic configurations yield substantial enhancements in core fluid discharge and production efficiency, providing a robust predictive foundation for designing electro-assisted enhanced oil recovery in vertical annular wellbores.
Uranium mineral prospectivity mapping is of great significance for uranium exploration and the identification of prospective mineralized areas. Hard labels constructed from buffer zones around known uranium occurrences tend to discretize continuously varying mineralization responses, making it difficult to adequately characterize the continuous variation in mineral prospectivity and the uncertainty associated with mineralization boundaries. To address this issue, this study focuses on sandstone-hosted uranium deposits in the Beverley–Four Mile area, South Australia, and introduces a self-distillation strategy into the ResNet50 model. Soft labels generated by the model are employed to supplement the differences in mineral prospectivity and spatial transitional information that are difficult to represent using hard labels, thereby enhancing the model’s ability to learn mineralization-related features. Experimental results show that, after incorporating the self-distillation strategy, ACC, AUC, F1, and PR-AUC are improved by 3.13
