The Transfer Matrix Metamodel for Dynamic Systems With Arbitrary Time-Variant Inputs
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Bibliographic record
Abstract
This paper addresses the problem of mapping a vector of input variables (corresponding to discrete samples from a time-varying input) to a vector of output variables (discrete samples of the time-dependent response). This mapping is typically performed by a mechanistic model. However, when the mechanistic model is complex and dynamic, the computational effort to iteratively generate the response for design purposes can be burdensome. Metamodels (or, surrogate models) can be computationally efficient replacements, especially when the input variables have some amplitude and frequency bounds. Herein, a simple metamodel in the form of a transfer matrix is created from a matrix of a few training inputs and a corresponding matrix of matching responses provided by simulations of the dynamic mechanistic model. A least-squares paradigm reveals a simple way to link the input matrix to the columns of the response matrix. Application of singular value decomposition (SVD) introduces significant computational advantages since it provides matrices whose properties give, in an elegant fashion, the transfer matrix. The efficacy of the transfer matrix is shown through an investigation of a nonlinear, underdamped, double mass–spring–damper system. Arbitrary excitations and selected sinusoids are applied to check accuracy, speed and robustness of the methodology. The sources of errors are identified and ways to mitigate them are discussed. When compared to the ubiquitous Kriging approach, the transfer matrix method shows similar accuracy but much reduced computation time.
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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 | 0.011 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 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 it