Neural networks learn to generate physics equations directly from rock data

The challenge of predicting seismic wave velocity in underground rock has traditionally forced geophysicists into a dilemma: rely on rigorous theoretical models that demand extensive physical derivation, or settle for empirical formulas that fit data but lack fundamental grounding. A new technique described in recent research on arXiv aims to transcend this trade-off entirely.

The approach#

Researchers introduced rational function neural networks (RafNN), a data-driven method designed to extract analytical rock physics models directly from observation datasets. Rather than starting with theory or pure empiricism, the system learns patterns in real seismic measurements and produces equations that both fit the data and reflect underlying physics principles. The process requires only observational records—no complex mathematical derivations or physical reasoning from researchers.

How it validates itself#

The method's credibility comes from an elegant proof: it successfully reconstructed Gassmann's equation, a foundational theoretical model in geophysics that relates how rock bulk modulus depends on mineral composition, porosity, and fluid content. The fact that the neural network "rediscovered" this well-established physics relationship from pure data suggests the approach captures genuine physical structure rather than mere statistical noise.

Why this matters#

Earth science relies on velocity models to map underground structure during seismic surveys and geological exploration. Current theoretical models often struggle in complex, heterogeneous settings found in practice. This work opens a new pathway: leveraging modern machine learning to generate physics-informed equations automatically from field measurements, potentially yielding models that work better in real-world conditions while retaining mathematical interpretability.