This study proposes a neural network (NN)-assisted, physics-informed framework for global flow-based upscaling to accelerate reservoir simulation. While traditional global upscaling methods can accurately capture fine-scale flow characteristics, their high computational cost hinders practical application in ensemble-based uncertainty quantification and optimization workflows. Existing NN-assisted upscaling approaches predominantly rely on numerical simulation data, which remains computationally expensive and often lacks physical interpretability. Furthermore, no current method enables physics-informed training for corner-point grid (CPG) models without simulation data, limiting the application of deep learning in practical geological model upscaling. To address these limitations, we develop a finite-volume physics-informed Fourier neural operator (FV-PIFNO) as a pressure-solution surrogate model for CPG models. This physics-driven approach eliminates the need for simulation data and inherently enforces inter-grid flux continuity during inference. A flow-based numerical post-processing procedure is designed to compute coarse-grid transmissibility and well index that are strictly equivalent to fine-scale fluxes, naturally extending to non-orthogonal CPG systems. Comparisons are designed between different mapping and driving methods. Validation on synthetic models demonstrates that the fully physics-constrained approach achieves high accuracy in both single-phase and two-phase flow simulations, along with strong generalization to heterogeneous scenarios. Application to a standard SAIGUP model confirms that the framework achieves accuracy comparable to numerical upscaling while significantly improving computational efficiency, demonstrating its potential for practical, high-fidelity reservoir upscaling.

In this study, we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network (EPINN), which is applied to simulate two-phase flow in heterogeneous porous media. Specifically, we first analyze the layerwise outputs of EPINN, and identify the distinct functions across layers, including dimensionality adjustment, pointwise construction of non-equilibrium potential, extraction of high-level features, and the establishment of long-range dependencies. Then, inspired by these distinct modules, we propose a novel constraint learning strategy based on regularization approaches, which improves neural network (NN) learning through layer-specific differentiated updates to enhance cross-timestep generalization. Since different neural network layers exhibit varying sensitivities to global generalization and local regression, we decrease the update frequency of layers more sensitive to local learning under this constraint learning strategy. In other words, the entire neural network is encouraged to extract more generalized features. The superior performance of the proposed learning strategy is validated through evaluations on numerical examples with varying computational complexities. Post hoc analysis reveals that gradient propagation exhibits more pronounced staged characteristics, and the partial differential equation (PDE) residuals are more uniformly distributed under the constraint guidance. Interpretability analysis of the adaptive constraint process suggests that maintaining a stable information compression mode facilitates progressive convergence acceleration.