# Deep operator network for surrogate modeling of poroelasticity with random permeability fields

arXiv: https://arxiv.org/abs/2509.11966 · HTML: https://mlsanity.com/paper/2509.11966/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 78 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media](https://mlsanity.com/paper/1807.00882/) (2018)
- [On the training and generalization of deep operator networks](https://mlsanity.com/paper/2309.01020/) (2023)
- [A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks](https://mlsanity.com/paper/2105.13136/) (2021)
- [Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training](https://mlsanity.com/paper/2110.03049/) (2021)
- [Neural Chaos: A Spectral Stochastic Neural Operator](https://mlsanity.com/paper/2502.11835/) (2025)
- [Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification](https://mlsanity.com/paper/2402.15115/) (2024)
- [Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties](https://mlsanity.com/paper/2111.14984/) (2021)
- [Surrogate Model for Geological CO2 Storage and Its Use in Hierarchical MCMC History Matching](https://mlsanity.com/paper/2308.06341/) (2023)
- [Deep-learning-based coupled flow-geomechanics surrogate model for CO2 sequestration](https://mlsanity.com/paper/2105.01334/) (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)
- [Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data. Part I: Maximum A Posteriori Estimate](https://mlsanity.com/paper/2002.10706/) (2020)
- [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)
- [Bayesian Poroelastic Aquifer Characterization from InSAR Surface Deformation Data Part II: Quantifying the Uncertainty](https://mlsanity.com/paper/2102.04577/) (2021)

## Built on by (most cited first, 1 of 1)

- [Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fields](https://mlsanity.com/paper/2608.09071/) (2026)

## Abstract (arXiv)

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for probabilistic analysis, uncertainty quantification, and inverse problems. These simulations require repeated forward solves that are often prohibitively expensive, motivating the development of efficient surrogate models. However, efficient surrogate modeling techniques for poroelasticity with random permeability fields remain scarce. In this study, we propose a surrogate modeling framework based on the deep operator network (DeepONet), a neural architecture designed to learn mappings between infinite-dimensional function spaces. The proposed surrogate model approximates the solution operator that maps random permeability fields to transient poroelastic responses. To enhance predictive accuracy and stability, we integrate three strategies: nondimensionalization of the governing equations, input dimensionality reduction via Karhunen--Lo'eve expansion, and a two-step training procedure that decouples the optimization of branch and trunk networks. The methodology is evaluated on two benchmark problems in poroelasticity: soil consolidation and ground subsidence induced by groundwater extraction. In both cases, the DeepONet achieves substantial speedup in inference while maintaining high predictive accuracy across a wide range of permeability statistics. These results highlight the potential of the proposed approach as a scalable and efficient surrogate modeling technique for poroelastic systems with random permeability fields.