# AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage

arXiv: https://arxiv.org/abs/2402.06110 · HTML: https://mlsanity.com/paper/2402.06110/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 64 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Multimodal Learning with Transformers: A Survey](https://mlsanity.com/paper/2206.06488/) (2022)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [Combining data assimilation and machine learning to infer unresolved scale parametrisation](https://mlsanity.com/paper/2009.04318/) (2020)
- [A Deep Learning-Accelerated Data Assimilation and Forecasting Workflow for Commercial-Scale Geologic Carbon Storage](https://mlsanity.com/paper/2105.09468/) (2021)
- [Use of low-fidelity models with machine-learning error correction for well placement optimization](https://mlsanity.com/paper/2111.02960/) (2021)
- [Attention U-Net as a surrogate model for groundwater prediction](https://mlsanity.com/paper/2204.04518/) (2022)

## Built on by (most cited first, 7 of 7)

- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification](https://mlsanity.com/paper/2406.02204/) (2024)
- [Accelerated training of deep learning surrogate models for surface displacement and flow, with application to MCMC-based history matching of CO2 storage operations](https://mlsanity.com/paper/2408.10717/) (2024)
- [Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage](https://mlsanity.com/paper/2410.15302/) (2024)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers](https://mlsanity.com/paper/2609.20794/) (2026)
- [Mitigating loss of variance in ensemble data assimilation: machine learning-based and distance-free localization](https://mlsanity.com/paper/2506.13362/) (2025)

## Abstract (arXiv)

This study investigates the integration of machine learning (ML) and data assimilation (DA) techniques, focusing on implementing surrogate models for Geological Carbon Storage (GCS) projects while maintaining high fidelity physical results in posterior states. Initially, we evaluate the surrogate modeling capability of two distinct machine learning models, Fourier Neural Operators (FNOs) and Transformer UNet (T-UNet), in the context of CO2 injection simulations within channelized reservoirs. We introduce the Surrogate-based hybrid ESMDA (SH-ESMDA), an adaptation of the traditional Ensemble Smoother with Multiple Data Assimilation (ESMDA). This method uses FNOs and T-UNet as surrogate models and has the potential to make the standard ESMDA process at least 50% faster or more, depending on the number of assimilation steps. Additionally, we introduce Surrogate-based Hybrid RML (SH-RML), a variational data assimilation approach that relies on the randomized maximum likelihood (RML) where both the FNO and the T-UNet enable the computation of gradients for the optimization of the objective function, and a high-fidelity model is employed for the computation of the posterior states. Our comparative analyses show that SH-RML offers better uncertainty quantification compared to conventional ESMDA for the case study.