Researchers from the California Institute of Technology, including Xin Ju and Jiachen Yao, alongside Anima Anandkumar and collaborators from Stanford University and Imperial College London, have introduced a groundbreaking approach to modeling subsurface fluid flow for Carbon Capture and Storage (CCS). Their study, published recently, unveils the Fun-DDPS framework, which synergizes function-space diffusion models with differentiable neural operator surrogates. This innovation seeks to enhance both forward and inverse modeling capabilities, addressing the challenges posed by limited observational data in CCS applications.
Effective and safe carbon dioxide storage necessitates precise characterization of subsurface processes, a task complicated by the opaque nature of geological formations and sparse data availability. The Fun-DDPS framework stands out by decoupling the learning of geological characteristics from the physics governing fluid flow, a limitation often encountered in traditional methods. By training a diffusion model to understand a realistic range of geological parameters and using a separate neural operator to simulate fluid dynamics, the framework claims an impressive eleven-fold reduction in relative error—down to 7.7%—when utilizing just 25% of the typical observational data.
This advancement is particularly relevant for large-scale CCS projects, where comprehensive data collection is costly and laborious. The study also marks the first rigorous validation of diffusion-based inverse solvers against the accepted gold standard known as Rejection Sampling, achieving a Jensen-Shannon divergence of less than 0.06, indicating high statistical accuracy. Notably, the generated geological models maintain physical consistency and require four times less computational effort compared to Rejection Sampling.
At the heart of Fun-DDPS is a single-channel function-space diffusion model tasked with learning the prior distribution over geological parameters. By progressively adding noise to training data until it becomes indistinguishable from random noise, the model learns to reverse this process, generating new, realistic geological samples. This innovative approach circumvents the pitfalls of traditional methods that struggle with high-dimensional, non-Gaussian parameters, allowing for direct modeling of continuous fields representing geological properties.
To effectively guide the diffusion process during inverse modeling, the researchers trained a Local Neural Operator (LNO) surrogate that approximates the physics of carbon dioxide plume migration. Neural operators, as a subset of deep learning models, facilitate rapid prediction of dynamic states based on geological parameter fields. The LNO excels at capturing local dependencies within the flow field, thereby enhancing both accuracy and computational efficiency. This methodological separation enables the diffusion model to recover missing information robustly while leveraging the surrogate’s gradient-based guidance for data assimilation.
During inference, the framework uses sparse observational data to compute gradients that are backpropagated through the LNO into the diffusion model. This strategic steering helps align the generation of geological parameters with the observed data. The researchers rigorously tested the entire framework using synthetic CCS modeling datasets designed to mirror real-world subsurface conditions, thus enabling strict control over parameters and quantitatively assessing performance.
The results of forward modeling with Fun-DDPS reveal its relative error of just 7.7% under limited observational data, a stark contrast to the 86.9% error rate exhibited by standard surrogate models under identical conditions. This dramatic improvement underscores Fun-DDPS’s efficacy, especially in scenarios where deterministic methods typically falter. Both Fun-DDPS and its joint-state baseline counterpart, Fun-DPS, demonstrated comparable success in approximating true posterior distributions, validated by the low Jensen-Shannon divergence values.
This research signifies a noteworthy evolution in the pursuit of accurate subsurface modeling, as traditional models have historically grappled with insufficient data. The Fun-DDPS framework moves away from seeking a single deterministic answer, instead generating a distribution of plausible subsurface scenarios. This approach not only enhances prediction confidence amidst uncertainty but also gains credibility through validation against Rejection Sampling, a benchmark in probabilistic inference.
Despite these advancements, the research does face limitations, primarily the reliance on synthetic datasets, which may not fully encapsulate the complexities of real-world geological formations. The statistical hyperparameters used for generating synthetic fields could fall short of representing the full spectrum of geological variability. Furthermore, the computational demands of the framework, even with high-performance GPUs, raise concerns about scalability for extensive CCS projects.
Looking ahead, the integration of this generative framework with real-world data streams, such as seismic surveys and well logs, holds exciting potential for improving dynamic reservoir management. By leveraging observational data alongside the diffusion prior, operators could adapt carbon injection strategies in real-time to maximize storage capacity. The implications extend beyond CCS, presenting a powerful tool for groundwater modeling, geothermal energy exploration, and even volcanic activity prediction.
👉 More information
🗞Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage
🧠 ArXiv: https://arxiv.org/abs/2602.12274
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