# Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators

arXiv: https://arxiv.org/abs/2203.14396 · HTML: https://mlsanity.com/paper/2203.14396/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 57 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems](https://mlsanity.com/paper/1902.09699/) (2019)

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

- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation](https://mlsanity.com/paper/2301.11509/) (2023)
- [Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs](https://mlsanity.com/paper/2204.01205/) (2022)
- [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)
- [Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator](https://mlsanity.com/paper/2209.14291/) (2022)
- [A reduced-order derivative-informed neural operator for subsurface fluid-flow](https://mlsanity.com/paper/2509.13620/) (2025)

## Abstract (arXiv)

Seismic monitoring of carbon storage sequestration is a challenging problem involving both fluid-flow physics and wave physics. Additionally, monitoring usually requires the solvers for these physics to be coupled and differentiable to effectively invert for the subsurface properties of interest. To drastically reduce the computational cost, we introduce a learned coupled inversion framework based on the wave modeling operator, rock property conversion and a proxy fluid-flow simulator. We show that we can accurately use a Fourier neural operator as a proxy for the fluid-flow simulator for a fraction of the computational cost. We demonstrate the efficacy of our proposed method by means of a synthetic experiment. Finally, our framework is extended to carbon sequestration forecasting, where we effectively use the surrogate Fourier neural operator to forecast the CO2 plume in the future at near-zero additional cost.