Nonlinear Electrical Resistivity Tomography with a Fourier Neural Operator Surrogate Model
Bibliographic record
Abstract
Electrical resistivity tomography (ERT) is commonly applied for shallow subsurface imaging. Inversion techniques generate images of the subsurface resistivity structure to interpret the data, with applications including the imaging of permafrost soils. While linearized inversion is a common method, nonlinear treatment provides advantages in terms of parametrization and model selection. However, it often incurs prohibitive computational costs. Markov Chain Monte Carlo (MCMC) methods offer nonlinear uncertainty quantification for ERT, where the computational cost is dominated by the forward model evaluations. Surrogate models advance the physics forward model with a considerable speedup; therefore, they have the potential to enable MCMC applications for inverse problems that were not previously possible. We introduce a surrogate forward model for 2D ERT based on a Fourier Neural Operator (FNO). This model leverages the FNO's capability to learn and generalize mappings between infinite-dimensional function spaces, making it particularly suitable for solving PDE-driven problems like ERT. Based on the inputs of electrode geometry and subsurface resistivity distribution, FNO predicts potentials from which apparent resistivities are computed. This process reduces evaluation times of a subsurface resistivity distribution from seconds to milliseconds with prediction errors below 5%. This efficiency gain enables applying the FNO in MCMC sampling. We show several examples of MCMC sampling results with simulated data for pole-dipole arrays and realistic subsurface models. The subsurface parametrization of resistivity considers irregular grids based on Gaussian random fields or Voronoi cells. The results demonstrate that nonlinear inversion and uncertainty quantification are computationally feasible for typical field survey scales.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".