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

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 benchmark 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.