Project Artie: An Artificial Student for Disciplines Informed by Partial\n Differential Equations
Bibliographic record
Abstract
We present an Artificial Student, "Artie," for engineering science\ndisciplines in which the mathematical model is a partial differential equation\n(PDE); Artie considers here the particular case of steady heat conduction.\nArtie accepts problem statements posed in natural language. Artie provides a\nsymbolic-numeric approximate solution: the PDE field; scalar Quantities of\nInterest (QoI), expressed as functionals of the field. The problem statement\nwill typically not provide explicit guidance as to the equation or\napproximations which should be invoked. We also present Artie+, who provides\nthe finite element solution to the PDE: the exact solution to within a\nprescribed tolerance controlled by an a posteriori error estimator.\n Artie comprises four technical ingredients. Natural Language Processing: We\nproceed in two stages, domain-independent Google Natural Language syntax\nanalyzer followed by frame-specific conduction parser. PDE Template: The PDE is\nexploited by the conduction parser to extract geometry, boundary conditions,\nand coefficients; subsequent approximations are deduced from this ground-truth\ndescription. Problem Classes, Geometry Classes; Components, Systems: A problem\nclass places requirements on spatial domain, boundary conditions, properties,\nand QoI; associated to each problem class are several geometry classes. A\ncomponent is an instantiation of the geometry class for prescribed geometric\nand PDE parameters; a system is represented as an assembly of connected\ncomponents. Variational Formulation: We consider the weak statement and\nminimization principle to formulate the PDE and develop suitable\napproximations; implementation proceeds through static condensation and direct\nstiffness assembly over component ports.\n We describe and illustrate a prototype implementation of Artie and Artie+.\n
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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".