A symmetry-based method for constructing nonlocally related partial differential equation systems
Bibliographic record
Abstract
Nonlocally related partial differential equation (PDE) systems are important in the analysis of a given PDE system. In particular, they are useful for seeking nonlocal symmetries. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related PDE system. In this paper, a new and complementary method for constructing nonlocally related PDE systems is introduced. In particular, it is shown that each point symmetry of a PDE system systematically yields a nonlocally related PDE system. Examples include nonlinear reaction-diffusion equations, nonlinear diffusion equations, and nonlinear wave equations. The considered nonlinear reaction-diffusion equations have no local conservation laws. Previously unknown nonlocal symmetries are exhibited through our new symmetry-based method for two examples of nonlinear wave equations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".