A Physics-aware Bayesian Vision Transformer for Seismic AVO Inversion: Towards an Embodied Structural Intelligence Framework with Structure-aware Uncertainty Modeling

Traditional seismic inversion frameworks struggle to preserve spatial structure and to quantify model reliability. We present a next-generation pathway that progresses from a convolutional Physics-Informed Neural Network (PINN) to a Bayesian PINN (BPINN) with uncertainty modeling, and culminates in a Bayesian Physics-Informed Vision Transformer (BPI-ViT) that enables structure-level uncertainty quantification. In our formulation, PINN “training data” are equation-domain samples used to minimize physical residuals—supporting physics-driven, data-agnostic generalization—while BPI-ViT integrates multi-layer self-attention and Bayesian inference to transition from pixel-level optimization to structure-aware collaboration. Consistent evaluation on the Marmousi2 benchmark and validation on field-scale CO₂ EOR monitoring data show that BPI-ViT outperforms prior methods in target-horizon recovery, fault and anomaly detection, spatial continuity, and uncertainty quantification, while maintaining physical consistency. These results establish a structural-intelligent paradigm that moves seismic inversion beyond error minimization toward structure-aware, reliable, and cognitively informed modeling, and provide a foundation for future multi-physics and complex-geology applications.