Anand Singh

Pankaj K Mishra, Sanni Laaksonen, Jochen Kamm et al.

Inversion of gravity data is an important method for investigating subsurface density variations relevant to diverse applications including 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. Positional 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 Gaussian random fields, representing realistic geological complexity, and a dipping block model to assess recovery of blocky structures. The INR framework reconstructs detailed structure and geologically plausible boundaries without explicit regularisation or depth weighting, while significantly reducing the number of inversion parameters. 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.

Dieuwke Hupkes, Anand Singh, Kris Korrel et al.

While neural network models have been successfully applied to domains that require substantial generalisation skills, recent studies have implied that they struggle when solving the task they are trained on requires inferring its underlying compositional structure. In this paper, we introduce Attentive Guidance, a mechanism to direct a sequence to sequence model equipped with attention to find more compositional solutions. We test it on two tasks, devised precisely to assess the compositional capabilities of neural models, and we show that vanilla sequence to sequence models with attention overfit the training distribution, while the guided versions come up with compositional solutions that fit the training and testing distributions almost equally well. Moreover, the learned solutions generalise even in cases where the training and testing distributions strongly diverge. In this way, we demonstrate that sequence to sequence models are capable of finding compositional solutions without requiring extra components. These results helps to disentangle the causes for the lack of systematic compositionality in neural networks, which can in turn fuel future work.