What Physics-Informed Neural Networks Add to Earth Science

Neural networks can learn patterns from data, but Earth science observations are often sparse while the physical system is complex. Physics-informed neural networks, or PINNs, attempt to combine data with governing equations.

The goal is not to replace physics. It is to use physics as part of the learning process.

Adding Constraints to the Loss Function

A conventional model is trained to reduce the difference between predictions and observations. A PINN adds another penalty for violating physical relationships, such as conservation laws or differential equations.

The model is therefore asked to fit available data while remaining approximately consistent with known physics.

This can be useful when observations exist only at scattered locations. GNSS stations, for example, measure surface motion at specific points, while researchers may want to infer a continuous deformation or stress field.

Physics Does Not Guarantee Correctness

A PINN can still be wrong. The governing equations may be simplified, boundary conditions uncertain, or material properties poorly known. Different parameter combinations may explain the same sparse observations.

Adding a physical constraint can reduce impossible solutions, but it does not create missing information.

Training can also be difficult because data-fitting and physics terms may operate at different scales. The relative weights assigned to them influence the result.

Interpretability Requires Testing

A physically informed output may look more convincing than a purely statistical prediction. That appearance should not replace validation.

Researchers can compare results with withheld stations, synthetic cases with known solutions, alternative physical assumptions, and sensitivity tests.

PINNs are most valuable when they make assumptions explicit and create a bridge between equations and observations. Their promise is not that a neural network suddenly understands geology. It is that data-driven flexibility can be guided—and challenged—by the physical laws scientists already use to describe Earth.