Rapid Permeability Upscaling of Digital Porous Media via Physics‐Informed Neural Networks
Bibliographic record
Abstract
Abstract Subsurface processes are important in solving many of the grand challenges facing our society today, including the sustainable extraction of hydrocarbons, the permanent geological sequestration of carbon dioxide, and the seasonal storage of renewable energy underground. Permeability characterization of underground rocks is the critical first step in understanding and engineering these processes. While recent advances in machine learning methods have enabled fast and efficient permeability prediction of digital rock samples, their practical use remains limited since they can only accommodate subsections of the digital rock samples, which is often not representative of properties at the core‐scale. Here, we derive a novel analytical solution that approximates the effective permeability of a three‐dimensional (3D) digital rock consisting of 2 × 2 × 2 anisotropic cells based on the physical analogy between Darcy’s law and Ohm’s law. We further develop physics‐informed neural network (PINN) models that incorporate the analytical solution and subsequently demonstrate that the PINN equipped with the physics‐informed module achieves excellent accuracy, even when used to upscale previously unseen samples over multiple levels of upscaling. Our work elevates the potential of machine learning models such as 3D convolutional neural network for rapid, end‐to‐end digital rock analysis at the core‐scale.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".