# Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operators

arXiv: https://arxiv.org/abs/2210.17051 · HTML: https://mlsanity.com/paper/2210.17051/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 13 references that are in the map.
- First posted on arXiv 31 Oct 2022.

## Built on by (most cited first, 30 of 47)

- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [Calibrated Uncertainty Quantification for Operator Learning via Conformal Prediction](https://mlsanity.com/paper/2402.01960/) (2024)
- [Probabilistic neural operators for functional uncertainty quantification](https://mlsanity.com/paper/2502.12902/) (2025)
- [Stochastic Process Learning via Operator Flow Matching](https://mlsanity.com/paper/2501.04126/) (2025)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Fourier Neural Operator Surrogate Model to Predict 3D Seismic Waves Propagation](https://mlsanity.com/paper/2304.10242/) (2023)
- [Uncertainty Quantification of Surrogate Models using Conformal Prediction](https://mlsanity.com/paper/2408.09881/) (2024)
- [Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration](https://mlsanity.com/paper/2409.16572/) (2024)
- [Solving multiphysics-based inverse problems with learned surrogates and constraints](https://mlsanity.com/paper/2307.11099/) (2023)
- [Learned multiphysics inversion with differentiable programming and machine learning](https://mlsanity.com/paper/2304.05592/) (2023)
- [PI-MFM: Physics-informed multimodal foundation model for solving partial differential equations](https://mlsanity.com/paper/2512.23056/) (2025)
- [Enabling Automatic Differentiation with Mollified Graph Neural Operators](https://mlsanity.com/paper/2504.08277/) (2025)
- [When is a System Discoverable from Data? Discovery Requires Chaos](https://mlsanity.com/paper/2511.08860/) (2025)
- [Multi-fidelity Fourier Neural Operator for Fast Modeling of Large-Scale Geological Carbon Storage](https://mlsanity.com/paper/2308.09113/) (2023)
- [Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks](https://mlsanity.com/paper/2306.09648/) (2023)
- [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)
- [Fourier Neural Operator based surrogates for CO2 storage in realistic geologies](https://mlsanity.com/paper/2503.11031/) (2025)
- [A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling](https://mlsanity.com/paper/2506.07969/) (2025)
- [Decodable and Sample Invariant Continuous Object Encoder](https://mlsanity.com/paper/2311.00187/) (2023)
- [NOBLE -- Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models](https://mlsanity.com/paper/2506.04536/) (2025)
- [An effective physics-informed neural operator framework for predicting wavefields](https://mlsanity.com/paper/2507.16431/) (2025)
- [Locally Adaptive Conformal Inference for Operator Models](https://mlsanity.com/paper/2507.20975/) (2025)
- [Delay compensation of multi-input distinct delay nonlinear systems via neural operators](https://mlsanity.com/paper/2509.17131/) (2025)
- [PDE Solvers Should Be Local: Fast, Stable Rollouts with Learned Local Stencils](https://mlsanity.com/paper/2509.26186/) (2025)
- [Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage](https://mlsanity.com/paper/2602.12274/) (2026)
- [STONet: A neural operator for modeling solute transport in micro-cracked reservoirs](https://mlsanity.com/paper/2412.05576/) (2024)
- [A Benchmark Dataset for Machine Learning Surrogates of Pore-Scale CO2-Water Interaction](https://mlsanity.com/paper/2503.17592/) (2025)

## Abstract (arXiv)

Carbon capture and storage (CCS) plays an essential role in global decarbonization. Scaling up CCS deployment requires accurate and high-resolution modeling of the storage reservoir pressure buildup and the gaseous plume migration. However, such modeling is very challenging at scale due to the high computational costs of existing numerical methods. This challenge leads to significant uncertainties in evaluating storage opportunities, which can delay the pace of large-scale CCS deployment. We introduce Nested Fourier Neural Operator (FNO), a machine-learning framework for high-resolution dynamic 3D CO2 storage modeling at a basin scale. Nested FNO produces forecasts at different refinement levels using a hierarchy of FNOs and speeds up flow prediction nearly 700,000 times compared to existing methods. By learning the solution operator for the family of governing partial differential equations, Nested FNO creates a general-purpose numerical simulator alternative for CO2 storage with diverse reservoir conditions, geological heterogeneity, and injection schemes. Our framework enables unprecedented real-time modeling and probabilistic simulations that can support the scale-up of global CCS deployment.