# Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage

arXiv: https://arxiv.org/abs/2410.15302 · HTML: https://mlsanity.com/paper/2410.15302/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 51 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [A Deep Learning-Accelerated Data Assimilation and Forecasting Workflow for Commercial-Scale Geologic Carbon Storage](https://mlsanity.com/paper/2105.09468/) (2021)
- [Deep Learning-Accelerated 3D Carbon Storage Reservoir Pressure Forecasting Based on Data Assimilation Using Surface Displacement from InSAR](https://mlsanity.com/paper/2201.08543/) (2022)
- [AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage](https://mlsanity.com/paper/2402.06110/) (2024)
- [Parameterizations for Ensemble Kalman Inversion](https://mlsanity.com/paper/1709.01781/) (2017)
- [History Matching for Geological Carbon Storage using Data-Space Inversion with Spatio-Temporal Data Parameterization](https://mlsanity.com/paper/2310.03228/) (2023)

## Built on by (most cited first, 3 of 3)

- [3D latent diffusion models for parameterizing and history matching multiscenario facies systems](https://mlsanity.com/paper/2508.16621/) (2025)
- [Integrating Score-Based Diffusion Models with Machine Learning-Enhanced Localization for Advanced Data Assimilation in Geological Carbon Storage](https://mlsanity.com/paper/2511.05266/) (2025)
- [PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers](https://mlsanity.com/paper/2609.20794/) (2026)

## Abstract (arXiv)

Data assimilation will be essential for the management and expansion of geological carbon storage operations. In traditional data assimilation approaches a fixed set of geological hyperparameters, such as mean and standard deviation of log-permeability, is often assumed. Such hyperparameters, however, may be highly uncertain in practical CO2 storage applications where measurements are scarce. In this study, we develop a hierarchical data assimilation framework for carbon storage that treats hyperparameters as uncertain variables characterized by hyperprior distributions. To deal with the computationally intractable likelihood function in hyperparameter estimation, we apply a likelihood-free (or simulation-based) inference algorithm, specifically sequential Monte Carlo-based approximate Bayesian computation (SMC-ABC), to draw posterior samples of hyperparameters given dynamic monitoring well data. In the second step we use an ensemble smoother with multiple data assimilation (ESMDA) procedure to provide posterior realizations of grid-block permeability. To reduce computational costs, a 3D recurrent R-U-Net deep learning-based surrogate model is applied for forward function evaluations. A rejection sampling (RS) procedure for data assimilation is applied to provide reference posterior results. Detailed posterior results from SMC-ABC-ESMDA are compared to those from the reference RS method. Close agreement is achieved with 'converged' RS results, for two synthetic true models, in all quantities considered. Importantly, the SMC-ABC-ESMDA procedure provides speedup of 1-2 orders of magnitude relative to RS for the two cases. A modified standalone ESMDA procedure is introduced for comparison purposes. For the same number of function evaluations, the hierarchical approach is shown to provide superior results for posterior hyperparameter distributions and monitoring well pressure predictions.