  Gravity inversion is a commonly applied data analysis technique in the field
of geophysics. While machine learning methods have previously been explored for
the problem of gravity inversion, these are deterministic approaches returning
a single solution deemed most appropriate by the algorithm. The method
presented here takes a different approach, where gravity inversion is
reformulated as a Bayesian parameter inference problem. Samples from the
posterior probability distribution of source model parameters are obtained via
the implementation of a generative neural network architecture known as
Normalising Flows. Due to its probabilistic nature, this framework provides the
user with a range of source parameters and uncertainties instead of a single
solution, and is inherently robust against instrumental noise. The performance
of the Normalising Flow is compared to that of an established Bayesian method
called Nested Sampling. It is shown that the new method returns results with
comparable accuracy 200 times faster than standard sampling methods, which
makes Normalising Flows a suitable method for real-time inversion in the field.
When applied to data sets with high dimensionality, standard sampling methods
can become impractical due to long computation times. It is shown that
inversion using Normalising Flows remains tractable even at 512 dimensions and
once the network is trained, the results can be obtained in $O(10)$ seconds.

Geophysics;Computational Physics;Data Analysis, Statistics and Probability