Physics-informed neural networks for solving steady-state temperature field in artificial ground freezing
Bibliographic record
Abstract
Artificial ground freezing (AGF) is a widely used technique for soil stabilization and waterproofing. Numerous studies have been devoted to solving the heat transfer problems in AGF while encountering limitations in handling complex geometries and boundary conditions and being computationally intensive. Recently, using machine learning methods to predict temperature fields has gained attention, demonstrating the potential to achieve higher accuracy than conventional models. However, these methods are typically limited by the need for large, labeled datasets, which are time-consuming and difficult to obtain. In this study, we address these challenges by applying physics-informed neural networks (PINNs) to solve the steady-state heat transfer problem in AGF, focusing on the temperature distribution around a single freezing pipe. By embedding the heat conduction equation into the loss function, PINNs reduce the need for extensive labeled data. To enhance accuracy and efficiency, transfer learning is employed, and results are compared against the finite element method. Results show that PINNs achieve high accuracy, particularly in larger domains with moderate temperature gradients, while providing competitive performance in more complex configurations involving steeper gradients. This approach offers a promising alternative for modeling temperature fields in geotechnical applications, with implications for reducing computational costs in AGF design.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 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".