Divide-and-conquer DNN approach for the inverse point source problem using a few single frequency measurements
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We consider the inverse problem to determine the number and locations of acoustic point sources from single low-frequency partial data. The problem is particularly challenging in the sense that the data is available only at a few locations which span a small aperture. Integrating the deep neural networks (DNNs) and Bayesian inversion, we propose a divide-and-conquer approach by dividing the inverse problem into three subproblems. The first subproblem is to determine the number of point sources, which is formulated as a common machine learning task—classification. A simple DNN is proposed and trained to predict the numbers of the point sources. The second subproblem is to reconstruct the (approximate) locations of the point sources. We formulate the problem as a nonlinear function with the input being the measured data and the output being a carefully elaborated location vector. Then a second DNN is proposed to learn the mapping and predict the location vector effectively. The location vector is post-processed to provide an indicator (image) function for the (approximate) locations of the point sources. The third subproblem is to improve the accuracy of the location prediction, for which we employ a Bayesian inversion algorithm. This divide-and-conquer approach can effectively treat both phase and phaseless data as demonstrated by various examples.
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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