Fast full-field forecasting in petroleum reservoir simulation is important for field-development planning, well-control screening, uncertainty assessment, and production optimization, where many two-phase flow scenarios must be evaluated before final high-fidelity simulator verification. This study proposes a Coupled Multi-Physics Operator Learning (COMPOL)-based neural operator proxy with separate local–global Fourier neural operator branches for pressure and oil saturation, coupled through a Perceiver latent aggregation module. The model is trained on 2048 well configurations and evaluated on 512 disjoint held-out validation cases over a 20-step operational horizon generated with tNavigator. In this fixed-geology benchmark, the Coupled neural operator achieves the lowest error on three of the four reported physical metrics: well-level pressure error and both field- and well-level saturation errors. Transolver obtains the lowest full-field pressure error, indicating complementary strength on the smoother global pressure response. Qualitative maps show that the remaining errors are concentrated near wells and moving saturation fronts. A 30-case benchmark shows a $309\times$ speedup over tNavigator. These results suggest that field-specific operator branches with compact pressure–saturation coupling are a promising proxy strategy within the studied setting.

This paper presents a comprehensive analysis of training strategies for finite basis physics-informed neural networks (FBPINNs). We implement four distinct