A physics-guided symbolic regression framework for efficient and interpretable sand constitutive modeling
Bibliographic record
Abstract
Data-driven constitutive modeling for geomaterials encounters significant challenges in achieving a balance among interpretability, physical consistency, and computational efficiency. Traditional symbolic regression often struggles with extensive search spaces, slow convergence rates, and insufficient physical constraints, which limits its applicability to complex granular materials such as sands. In this context, we propose a framework for knowledge-based physically guided symbolic regression (KB-phgSR), which seamlessly integrates classical constitutive models with data-driven optimization techniques. The framework employs a two-stage approach: initially distilling Pareto-optimal equations from established physical models to establish physically consistent solutions; subsequently refining these equations using experimental data while ensuring dimensional balance and adherence to mechanical boundary conditions. Validated against triaxial tests conducted on Toyoura and Ottawa sands under various drainage conditions, KB-phgSR demonstrates enhanced convergence speed and robustness in capturing the intricate behaviors of sand. The optimized equations exhibit both high accuracy and interpretability while conforming to fundamental elastoplastic principles. By effectively combining physics-based priors with data-driven discovery methods, this framework advances constitutive modeling towards improved generalizability and engineering efficacy, positioning it as a paradigm-shifting tool with transformative potential in geomechanics and beyond.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".