What Do Language Priors Contribute to Darcy-Flow Inversion? A Mechanistic Audit

Researchers demonstrate that natural language descriptions can significantly improve machine learning models solving inverse problems in hydrogeology, reducing reconstruction error by 81% compared to models without text conditioning. The study reveals that categorical geological classifications carry the most value, while detailed geometric descriptions provide secondary benefits, establishing language as a practical interface for encoding domain expertise into learned solvers.

This research addresses a fundamental challenge in applied machine learning: how to incorporate qualitative engineering knowledge into quantitative models. Inverse problems in hydrogeology require inferring underground properties from observable data, a task where prior knowledge substantially influences outcomes. Traditional approaches rely on formal mathematical priors, but much geological expertise exists only as descriptive text in reports and documentation. The researchers tested whether sentence embeddings—dense vector representations of text—could bridge this gap by conditioning a neural network trained on Darcy-flow simulations. The 81% error reduction demonstrates that language can effectively encode domain constraints that guide model inference. The mechanistic audit reveals the actual contribution mechanisms: categorical information (rock type, formation class) provides the dominant signal, concentrating its impact precisely where measurements leave the problem underdetermined. Fine-grained geometric details add less value but improve training stability. Sentence embeddings outperform discrete labels by enabling continuous variation and paraphrase robustness, though dense-observation accuracy gains remain modest. This finding has broader implications for inverse modeling across geosciences, petroleum engineering, and medical imaging, where qualitative expert knowledge vastly exceeds formal mathematical specifications. The work establishes language processing as a practical engineering-informatics interface rather than merely a curiosity. For practitioners, this suggests substantial value in digitizing unstructured geological reports and integrating them into learned solvers. The results also highlight important limitations: language priors work best for categorical constraints rather than geometric precision, indicating where human expertise can most productively augment machine learning.

• →Text conditioning reduces Darcy-flow inverse problem reconstruction error by 81% relative to no-text baselines
• →Categorical geological classifications provide the primary value, concentrating benefits where data is most underdetermined
• →Sentence embeddings add training stability and paraphrase robustness compared to discrete class labels
• →Language priors perform best for constraint specification rather than geometric detail recovery
• →The approach establishes a practical framework for injecting unstructured domain expertise into learned inverse solvers