Deterministic Numeric Simulation and Surrogate Models with White and Black Machine Learning Methods: A Case Study on Direct Mappings
Bibliographic record
Abstract
The approximation and emulation of first principles based deterministic models are important problems in many disciplines, like physical and natural sciences, as well as in engineering (industrial design, creation of digital twins and other tasks). Typically they involve complex systems, described by partial differential or integral equations which must be solved for a variety of space and time boundary conditions. Finding these solutions is usually costly in terms of both computational resources and time. Surrogate models are an effective way of building approximations that may replace the use of the compled/costly original models, expediting and speeding operations. Computational intelligence techniques have proven suitable for surrogating purposes and this paper explores the characterization of a relatively simple deterministic system described by a partial differential equation, using white as well as black box approaches for direct supervised mappings (inverse mappings are explored elsewhere). In addition, unsupervised methods are used for gaining insight into the properties of the input and output state spaces. White-box ML techniques exposed the nature of the inter-dependencies and the importance of the predictor variables. Individually, support vector regression outperformed all other models for the fixed-location, fixed time and also for the fixedlocation, time dependent scenario. However, performance-wise, the ensemble composed of white-box techniques outperformed the one integrated by black-box methods from the point of view of error and correlation measures.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 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".