Physical Sensitivity Kernels Can Emerge in Data-Driven Forward Models: Evidence From Surface-Wave Dispersion

arXiv cs.LG / 4/7/2026

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Key Points

The paper investigates whether data-driven neural surrogate forward models in geophysics learn only input-output mappings or also recover the underlying physical sensitivity (gradient/kernel) structure.
Using surface-wave dispersion, it compares automatically differentiated neural-network gradients with theoretical sensitivity kernels and finds that the learned gradients reproduce the main depth-dependent structure over a wide range of periods.
The findings suggest neural surrogates can provide physically meaningful differential information (not just black-box predictions), which can support inversion and uncertainty analysis.
However, the study also shows that strong structural priors embedded in the training distribution can produce systematic artifacts in the inferred sensitivities, potentially reducing physical consistency.
Overall, it clarifies the conditions under which neural forward surrogates yield physically consistent differential structure versus biased or artifact-prone results.

Abstract

Data-driven neural networks are increasingly used as surrogate forward models in geophysics, but it remains unclear whether they recover only the data mapping or also the underlying physical sensitivity structure. Here we test this question using surface-wave dispersion. By comparing automatically differentiated gradients from a neural-network surrogate with theoretical sensitivity kernels, we show that the learned gradients can recover the main depth-dependent structure of physical kernels across a broad range of periods. This indicates that neural surrogate models can learn physically meaningful differential information, rather than acting as purely black-box predictors. At the same time, strong structural priors in the training distribution can introduce systematic artifacts into the inferred sensitivities. Our results show that neural forward surrogates can recover useful physical information for inversion and uncertainty analysis, while clarifying the conditions under which this differential structure remains physically consistent.