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.
Multimodal Scientific Learning Beyond Diffusions and Flows
Graduate Group in Applied Mathematics and Computational Science（应用数学与计算科学联合研究生组）；Department of Computer and Information Science（计算机与信息科学系）；Department of Mechanical Engineering and Applied Mechanics（机械工程与应用力学系）
Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity
State Key Laboratory of Deep Earth Exploration and Imaging（深部地球探测与成像国家重点实验室）；College of GeoExploration Science and Technology, Jilin University（吉林大学地球探测科学与技术学院）；Petroleum Exploration and Production Research Institute, Sinopec（中石油石油勘探生产研究院）
ADEPTS: An auto-differentiable framework for time-dependent nonlinear thermo-chemical mantle convection inversion
Southern University of Science and Technology（南方科技大学）；Guangdong Provincial Key Laboratory of Geophysical High-resolution Imaging Technology, Southern University of Science and Technology（南方科技大学地球物理高分辨率成像技术广东省重点实验室）
