Machine learned Green's functions that approximately satisfy the wave equation
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Bibliographic record
Abstract
Green’s functions are wavefield solutions for a particular point source. They form basis functions to build wavefields for modeling and inversion. However, calculating Green’s functions are both costly and memory intensive. We formulate frequency-domain machine-learned Green’s functions that are represented by neural networks (NN). This NN outputs a complex number (two values representing the real and imaginary part) for the scattered Green’s function at a location in space for a specific source location (both locations are input to the network). Considering a background homogeneous medium admitting an analytical Green’s function solution, the network is trained by fitting the output perturbed Green’s function and its derivatives to the wave equation expressed in terms of the perturbed Green’s function. The derivatives are calculated through the concept of automatic differentiation. In this case, the background Green’s function absorbs the point source singularity, which will allow us to train the network using random points over space and source location using a uniform distribution. Thus, feeding a reasonable number of random points from the model space will ultimately train a fully connected 8-layer deep neural network, to predict the scattered Green’s function. Initial tests on part of the simple layered model (extracted from the left side of the Marmousi model) with sources on the surface demonstrate the successful training of the NN for this application. Using the trained NN model for the Marmousi as an initial NN model for solving for the scattered Green’s function for a 2D slice from the Sigsbee model helped the NN converge faster to a reasonable solution. Presentation Date: Wednesday, October 14, 2020 Session Start Time: 1:50 PM Presentation Time: 2:15 PM Location: 360A Presentation Type: Oral
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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 | 0.000 | 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 | 0.000 | 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) | 0.005 | 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