Deep Null Space Regularization for Seismic Inverse Problems
Why this work is in the frame
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Bibliographic record
Abstract
Summary We investigate the use of null space regularizing networks for linear ill-posed seismic inverse problems by combining a classic regularization method with the learned deep decomposition framework. This method extends the popular learned post-processing approach by learning how to improve an initial reconstruction with estimated missing components from the null space of the forward operator while naturally enforcing that the high-resolution prediction is always consistent with the low-resolution input. Unlike traditional model-based reconstruction algorithms, this approach does not make any prior explicit assumption on the solution. Employing a deep decomposition architecture, we consider the inversion of noisy data sets where an additional denoising component on the range of the pseudo-inverse is also trained. To illustrate the approach, we present two numerical examples: a single channel deconvolution and a tomographic (ray-based) inversion. By combining the classical regularization method of truncated singular value decomposition and the deep decomposition approach, we show that it is possible to achieve significant improvements upon the initial reconstruction.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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