Inversion problems occur frequently in computational science, such as (a) inferring the geological subsurface from observations of the potential in response to a source of current (a process known as electrical resistivity inversion); (b) inferring the geological subsurface from observations of the amplitude of sound waves (seismic inversion). We present here a novel integrated framework which couples (a) a generative neural network to produce improved estimates of the subsurface geology with (b) a forward model that calculates the solution field (potential or wave amplitude); (c) a data assimilation approach to minimise the difference between the observations and the solution with respect to the hidden or latent variables of the generative network. What makes the framework efficient is that the forward model, based on a finite-element discretisation, is expressed as a neural network by using pre-defined weights rather than training [1, 2]. Thus, every part of the calculation is a neural network and the back-propagation functions from within machine learning libraries can be used to perform the inversion. Another advantage of using this approach is that the generative network will produce an estimation of the geology that is realistic (i.e. “close”, in some way, to the geologies that were used to train the network). REFERENCES [1] B. Chen, C. E. Heaney and C. C. Pain. Using AI libraries for Incompressible Com- putational Fluid Dynamics, in preparation (2024). [2] B. Chen, C. E. Heaney, J. L. M. A. Gomes, O. K. Matar and C. C. Pain. Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries, arXiv preprint (2024). arxiv.org/abs/2401.06755