# Geological text descriptions in ill-posed inverse problems: insights from learned hydraulic-conductivity inversion

arXiv: https://arxiv.org/abs/2606.24967 · HTML: https://mlsanity.com/paper/2606.24967/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [Training-image based geostatistical inversion using a spatial generative adversarial neural network](https://mlsanity.com/paper/1708.04975/) (2017)
- [Future-proofing geotechnics workflows: accelerating problem-solving with large language models](https://mlsanity.com/paper/2312.12411/) (2023)
- [Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties](https://mlsanity.com/paper/2110.12367/) (2021)

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

- [Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEs](https://mlsanity.com/paper/2609.32941/) (2026)

## Abstract (arXiv)

Hydraulic-conductivity inversion is ill posed: even complete head observations can leave structural ambiguity. Geological text descriptions can supply additional information about subsurface structure to constrain reconstruction. However, it remains unclear when descriptions improve reconstruction and how solvers use their stated content. We examine these questions in learned inversion using a synthetic Darcy-flow dataset with idealised descriptions, varying observation density and flow direction. After sparse-observation training, descriptions can improve reconstruction over models trained without them when observations leave structural ambiguity, though gains vary across conditions and runs. Instance-specific content can improve reconstruction beyond field-type information. Editing this content shifts reconstructions toward the stated geometry of selected features, less strongly as observations become more informative about those features. We do not establish a reconstruction advantage of text over numerical inputs encoding the same geological information. Finally, we discuss how this complementarity could guide the joint design of measurements and geological knowledge acquisition in site investigations.