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

2026-02-12

AI Summary

This work addresses the ill-posedness of subsurface flow inversion in carbon capture and storage caused by sparse observations by proposing the Fun-DDPS framework. For the first time, it decouples the parameter field from the dynamic field in modeling, integrating function-space diffusion priors, a local neural operator (LNO) surrogate, and gradient-guided data assimilation to jointly optimize forward and inverse models. Under only 25% observational coverage, the method reduces the relative error of forward modeling to 7.7%—an 11-fold improvement—and achieves an inverse solution with Jensen–Shannon divergence below 0.06, while enhancing sample efficiency by fourfold. The reconstructions exhibit no high-frequency artifacts and, notably, the study provides the first rigorous validation based on rejection sampling to guarantee physical consistency and high-fidelity recovery.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 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.

Problem

• Carbon Capture and Storage
• inverse problem
• subsurface flow
• data sparsity
• ill-posedness

Innovation

• function-space diffusion
• neural operator surrogate
• inverse modeling
• data sparsity
• carbon capture and storage