Deterministic Numeric Simulation and Surrogate Models with White and Black Machine Learning Methods: A Case Study on Inverse Mappings
Bibliographic record
Abstract
The approximation and emulation of first principles based deterministic models are important problems in science, engineering, industrial processes, design, digital twining and other tasks. Usually these are complex systems described by partial differential/integral equations, with a broad range of initial and boundary conditions. Finding solutions is often computationally costly and time consuming. Surrogate models have been useful for constructing approximations that effectively replace the complex and costly original models. Statistical and computational intelligence based techniques have been effective for creating surrogate models, such as neural networks, support vector machines and boosted trees (labeled black box techniques). This paper approaches the problem of finding surrogate models aimed at solving inverse problems for deterministic systems described by a partial differential equation. This situation, often intractable when using first principles methods, is illustrated with a case study of heat transfer in a rectangular space. Unsupervised methods are used for gaining insight into the properties of the input/output state spaces and supervised approaches, composed of white (explainable), black box modeling methods and ensembles, explore the feasibility of retrieving the input from the system's outputs. For most input variables accurate inverse models were obtained, demonstrating the effectiveness of machine learning approaches for this problem.
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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 | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".