The reduction of energy carbon footprint justifies the recent major programs launched on CO2 storage in existing reservoirs known to geologists. Numerical simulation plays a key role in their implementation by providing a low-cost means of monitoring. This is a global concern that explains the use of open-source software platforms facilitating knowledge sharing and collaborations. Regarding monitoring aspects, Full Waveform Inversion (FWI) has demonstrated its ability in probing the subsurface accurately. FWI is an iterative process in which we need to solve forward problems in large-scale propagation domains whose discretization involves more than 108 cells each. Implementing an FWI algorithm needs thus an optimized architecture in terms of memory management and GPU-CPU computation. Among the existing open-source platforms, GEOSX targets such architecture. Moreover, GEOSX offers a multi-physics approach ready for reservoir simulation and offers the perspective of coupling with seismic. In this work, we propose to design an optimized FWI workflow for GEOSX equipped with recent numerical approaches targeting large-scale simulations for which there is still a clear need of reducing the computational burden. For that purpose, we investigate the opportunity of using Reduced Order Models (ROM) that are low-dimensional problems for fast simulations providing accurate solutions to the original problem. This approach has been widely used in computational fluid dynamics and seems to be gaining the interest of geophysicists as recent papers testify. However, the construction of ROM using for example Krylov subspace method or Propper Orthogonal Decomposition (POD) requires solving an eigenvalue problem, which tends to be computationally expensive. Hence, there are some new ideas that have been proposed in the literature as Physics-informed Machine Learning. As a first step in the design of an optimized FWI in GEOSX, state-of-the-art of the most advanced methods for solving wave equations will be presented.