# Three-dimensional inversion of gravity data using implicit neural representations and scientific machine learning

arXiv: https://arxiv.org/abs/2510.17876 · HTML: https://mlsanity.com/paper/2510.17876/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [Investigation of the Robustness of Neural Density Fields](https://mlsanity.com/paper/2305.19698/) (2023)
- [Towards Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields](https://mlsanity.com/paper/2503.17503/) (2025)

## Abstract (arXiv)

Inversion of gravity data is an important method for investigating subsurface density variations relevant to mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here we present a scientific machine-learning approach for three-dimensional gravity inversion that represents subsurface density as a continuous field using an implicit neural representation (INR). The method trains a deep neural network directly through a physics-based forward-model loss, mapping spatial coordinates to a continuous density field without predefined meshes or discretisation. Spatial encoding enhances the network's capacity to capture sharp contrasts and short-wavelength features that conventional coordinate-based networks tend to oversmooth due to spectral bias. We demonstrate the approach on synthetic examples including smooth models, representing realistic geological complexity, and a dipping block model to assess recovery of structures at different depths. The INR framework reconstructs detailed structure and geologically plausible boundaries without explicit regularisation or depth weighting, while reducing the number of inversion parameters as the problem size grows bigger. These results highlight the potential of implicit representations to enable scalable, flexible, and interpretable large-scale geophysical inversion. This framework could generalise to other geophysical methods and for joint/multiphysics inversion.