A Stochastic Porous Media Schr{ö}dinger Equation: Feynman-type Motivation, Well-Posedness and Control Interpretation
Bibliographic record
Abstract
This paper's aim is threefold. First, using Feynman's path approach to the derivation of theclassical Schr{ö}dinger's equation in [6] and by introducing a slight path (or wave) dependency ofthe action, we derive a new class of equations of Schr{ö}dinger type where the driving operatoris no longer the Laplace one but rather of complex porous media-type. Second, using suitableconcepts of monotonicity in the complex setting and on appropriate functional spaces, we showthe existence and uniqueness of the solution to this type of equation. In the formulation of ourequation, we adjoin possible measurement absolute errors translating in an additive Brownianperturbation and interactions between different waves translating in a mean-field (or McKean-Vlasov) dependency of drift coefficient. Finally, using Fitzpatrick's characterization of maximalmonotone operators (cf. [7]), we propose a Br{é}zis-Ekeland type characterization of the solutionof the deterministic equation via a control problem. This is envisaged as a possible way toovercome strict monotonicity requirements in the complex setting.
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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 | 0.001 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".