Learning to model geophysical processes with NNs

Scientific machine learning (SML) is an emerging field focused on leveraging machine learning across different sciences whose natural processes are governed by well-established physical equations. Early successes have been reported by the geophysical community in terms of modelling various wave phenomena by means of PINNS, e.g. eikonal equation (bin Waheed et al., 2021) and wave equation (Alkhalifah et al., 2021). Alternative solutions have recently emerged in the SML community with the aim of overcoming some of the limitations of PINNs and extending applicability from functionals to operators. This project will investigate such approaches in the context of geophysical modelling and inversion and identify the benefits and limitations when compared to traditional modelling methods as well as PINNs. References: - U. bin Waheed, E. Haghighat, T. Alkhalifah, C Song, Q Hao, 2021, PINNeik: Eikonal solution using physics-informed neural networks, Computers & Geosciences. - T. Alkhalifah, C. Song, U. Waheed, Q. Hao, 2021, Wavefield solutions from machine learned functions, arXiv preprint arXiv:2106.01433.

The candidate will be tasked with: - Literature review of ML methods for learning physical phenomena governed by PDEs. - Develop and implement one of the methods for a geophysical PDE of choice. - Compare pros and cons of the developed method against state-of-the art numerical modelling methods and PINNs.