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

This paper investigates whether natural language descriptions can serve as an effective, inference-time interface for injecting qualitative geological knowledge into learned inverse solvers. The authors focus on the Darcy-flow inverse problem, where the goal is to reconstruct hydraulic conductivity fields from sparse hydraulic head observations—a task that is inherently ill-posed and highly sensitive to the choice of prior.

Using a U-Net architecture, the authors implement a text-conditioning mechanism via Feature-wise Linear Modulation (FiLM) at the bottleneck layer. They test this on a synthetic dataset of six distinct geological classes (e.g., Band, Circle, Layered) and a benchmark reservoir model (SPE10). The core of the study is a controlled audit where the researchers vary the specificity of the text input—ranging from generic class labels to detailed, latent-derived geometric descriptions—to isolate which information the solver actually utilizes. They also introduce a paraphrase-ensemble method as a low-cost proxy for sensitivity analysis, allowing them to measure how reconstruction stability changes with linguistic variation.

The study finds that text conditioning provides an 81% reduction in reconstruction error compared to a no-text baseline. Crucially, the authors demonstrate that the majority of this performance gain is derived from the categorical, class-level information rather than fine-grained geometric details. While the text-based prior is highly effective at resolving ambiguities where hydraulic head observations are uninformative, it offers diminishing returns for dense-observation regimes. Furthermore, the embedding interface enables open-vocabulary inputs and provides a stable, paraphrase-based mechanism for assessing model sensitivity, which is not possible with simple discrete class labels.