Multi-solver spectral-element and adjoint methods
Bibliographic record
Abstract
The spectral-element method (SEM) for simulating wave propagation is widely used with adjoint methods for full-waveform inversion. Typically, SEM is used to compute forward and adjoint wavefields, which is then applied to evaluate the Fréchet derivatives for updating the seismic structural model. The Hessian is rarely computed as the high computational and storage costs, although it can improve the accuracy of the model update and model convergence. Instead the approximate Hessian is determined, which is obtained with less computational effort. We present a method for simultaneously constructing Fréchet and Hessian kernels on the fly, which we call Multi-solver spectral-element and adjoint methods (Multi-SEM). Rather than storing all the wavefields, Multi-SEM is computed on the fly and requires only about a 2-fold computational cost when compared to the computation of Fréchet kernels. Numerical examples demonstrate the functionality of the method and the computer codes are provided with this contribution.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.014 | 0.005 |
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".