Understanding what lies beneath the surface of the Earth or other planets is important for exploring natural resources and studying planetary formation. One way scientists do this is by measuring small changes in gravity, which can reveal variations in underground materials. However, turning gravity measurements into accurate pictures of underground layers is a complex challenge.

In this study, we introduce a new method that uses mathematical curves and a machine learning approach to create detailed models of what lies beneath the surface. Our technique works by representing underground boundaries with smooth waves, and then improving the model step-by-step using a smart sampling process that mimics how particles move.

We tested our method on several examples, including a simulated region on the Moon known for its complex structure. The results show that our approach can accurately identify underground features, such as the depth of buried layers and the boundaries between rock types. When actual drilling data is available, the method becomes even more precise.

This work provides a new tool for planetary science and geology, helping researchers make better use of gravity data to study the hidden structures of Earth and beyond.