# Discovering state-parameter mappings in subsurface models using generative adversarial networks

arXiv: https://arxiv.org/abs/1810.12856 · HTML: https://mlsanity.com/paper/1810.12856/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2018.

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

- [Attention U-Net as a surrogate model for groundwater prediction](https://mlsanity.com/paper/2204.04518/) (2022)
- [Applications of physics-informed scientific machine learning in subsurface science: A survey](https://mlsanity.com/paper/2104.04764/) (2021)
- [Deep Learning to Estimate Permeability using Geophysical Data](https://mlsanity.com/paper/2110.10077/) (2021)
- [Generation of non-stationary stochastic fields using Generative Adversarial Networks](https://mlsanity.com/paper/2205.05469/) (2022)
- [Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models](https://mlsanity.com/paper/2310.00839/) (2023)
- [Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty](https://mlsanity.com/paper/2511.16926/) (2025)
- [Machine learning for sustainable geoenergy: uncertainty, physics and decision-ready inference](https://mlsanity.com/paper/2603.14907/) (2026)

## Abstract (arXiv)

A fundamental problem in geophysical modeling is related to the identification and approximation of causal structures among physical processes. However, resolving the bidirectional mappings between physical parameters and model state variables (i.e., solving the forward and inverse problems) is challenging, especially when parameter dimensionality is high. Deep learning has opened a new door toward knowledge representation and complex pattern identification. In particular, the recently introduced generative adversarial networks (GANs) hold strong promises in learning cross-domain mappings for image translation. This study presents a state-parameter identification GAN (SPID-GAN) for simultaneously learning bidirectional mappings between a high-dimensional parameter space and the corresponding model state space. SPID-GAN is demonstrated using a series of representative problems from subsurface flow modeling. Results show that SPID-GAN achieves satisfactory performance in identifying the bidirectional state-parameter mappings, providing a new deep-learning-based, knowledge representation paradigm for a wide array of complex geophysical problems.