Stratified Autoregressive Generation Framework for Reservoir Characterization: Bridging Multiple-Point Geostatistics and Transformer

To address the mode collapse and artifacts encountered in deep generative models under hard data constraints, this study proposes a Stratified Autoregressive Generation (SAG) method, aiming to develop a robust reservoir characterization approach. The method utilizes an offline-trained Transformer architecture as a conditional distribution estimator to replace the computationally expensive online "search and count" process of MPS. A three-level, coarse-to-fine strategy is adopted to define global structures at large scales first and subsequently propagates constraints to finer scales, thereby avoiding the quadratic computational complexity on large grids. Multiple sets of experiments as well as multidimensional scaling and variogram analyses indicate that the generated realizations possess diversity and accurately reproduce the global statistics and spatial continuity of the training data. Quantitative assessment using histogram intersection further confirms high local pattern fidelity without artifacts. Uncertainty assessment reveals that uncertainty increases outward from hard data points, showing a convergence pattern consistent with geological laws. The results indicate that the proposed method maintains spatial continuity and realization diversity under varying amounts of hard data constraints, which achieves the accurate characterization of complex reservoir structures and properties.