Numerical simulations for reservoir management for energy recovery optimization involve solving partial differential equations across numerical grids, providing detailed insights into fluid flow, heat transfer, and other critical reservoir behaviors. However, their computational demands often hinder practical implementation due to lengthy runtimes and resource-intensive processes. In this paper, we propose a deep learning methodology to address these challenges. Our approach leverages a neural operator that directly parameterizes the integral kernel in Fourier space. By doing so, we facilitate swift and efficient predictions, effectively reducing the computational burden associated with multiple numerical simulations.The robustness of the proposed approach has been evaluated for simulations of the steam injection process in high-viscosity oil reservoirs, an advanced thermal recovery method used to extract heavy oil from underground reservoirs. Key features of the proposed methodology are that it slashes computational time from hours to seconds, making it feasible for real-time reservoir management decisions. We use input data and corresponding output fields from five numerical models for the steam injection process as training data. This allows the ML model to learn from the complete evolution of the process across diverse simulations.During inference, the ML model relies on the first 10 time steps of numerical simulation results. It then predicts the subsequent 40 time steps in an autoregressive manner, capturing temporal dependencies effectively.The ML model accurately forecasts simulation outcomes at the numerical grid level, with error rates consistently below 10 percent.Beyond reservoir simulation, our approach holds promise for other fields, including computational fluid dynamics (CFD), structural engineering, and weather forecasting.