Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage
This work addresses the ill-posed inverse problem in CCS modeling, offering a novel method for handling extreme data sparsity, which is incremental in applying diffusion models to this domain.
The paper tackled the challenge of accurately characterizing subsurface flow for Carbon Capture and Storage (CCS) with sparse observations by introducing Fun-DDPS, a generative framework combining function-space diffusion models with neural operator surrogates. It achieved a 7.7% relative error in forward modeling with only 25% observations (an 11x improvement over standard methods) and produced physically consistent realizations with 4x improved sample efficiency in inverse modeling.
Accurate characterization of subsurface flow is critical for Carbon Capture and Storage (CCS) but remains challenged by the ill-posed nature of inverse problems with sparse observations. We present Function-space Decoupled Diffusion Posterior Sampling (Fun-DDPS), a generative framework that combines function-space diffusion models with differentiable neural operator surrogates for both forward and inverse modeling. Our approach learns a prior distribution over geological parameters (geomodel) using a single-channel diffusion model, then leverages a Local Neural Operator (LNO) surrogate to provide physics-consistent guidance for cross-field conditioning on the dynamics field. This decoupling allows the diffusion prior to robustly recover missing information in parameter space, while the surrogate provides efficient gradient-based guidance for data assimilation. We demonstrate Fun-DDPS on synthetic CCS modeling datasets, achieving two key results: (1) For forward modeling with only 25% observations, Fun-DDPS achieves 7.7% relative error compared to 86.9% for standard surrogates (an 11x improvement), proving its capability to handle extreme data sparsity where deterministic methods fail. (2) We provide the first rigorous validation of diffusion-based inverse solvers against asymptotically exact Rejection Sampling (RS) posteriors. Both Fun-DDPS and the joint-state baseline (Fun-DPS) achieve Jensen-Shannon divergence less than 0.06 against the ground truth. Crucially, Fun-DDPS produces physically consistent realizations free from the high-frequency artifacts observed in joint-state baselines, achieving this with 4x improved sample efficiency compared to rejection sampling.