Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage

New Framework Enhances Carbon Capture and Storage Modeling

A novel generative framework, Fun-DDPS, aims to improve the modeling of subsurface flow in Carbon Capture and Storage (CCS) applications. This approach addresses challenges posed by inverse problems and sparse observational data, demonstrating superior performance over traditional methods.

Fun-DDPS merges function-space diffusion models with differentiable neural operator surrogates for modeling. It learns a prior distribution of geological parameters through a single-channel diffusion model and utilizes a Local Neural Operator (LNO) surrogate for physics-consistent guidance. This technique enables Fun-DDPS to recover missing information in parameter space while enhancing data assimilation.

Performance Improvements

The efficacy of Fun-DDPS was evaluated using synthetic modeling datasets for CCS, yielding two significant findings:

• Forward Modeling Efficiency: Using only 25% of available observations, Fun-DDPS achieved a relative error of 7.7%, a substantial improvement over standard surrogate models, which recorded a relative error of 86.9%.
• Inverse Modeling Validation: Fun-DDPS was validated against asymptotically exact Rejection Sampling (RS) posteriors, achieving a Jensen-Shannon divergence of less than 0.06 compared to ground truth data, and a fourfold increase in sample efficiency compared to rejection sampling.