CO$_2$ sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)

A research team from AGH University of Science and Technology and ACK CYFRONET has published a novel computational method for simulating the underground storage of carbon dioxide (CO₂). Their hybrid solver, dubbed IGA-ADS-CRVPINN, ingeniously marries two distinct approaches: a classical numerical solver and a modern AI technique. The IsoGeometric Analysis Alternating-Directions Solver (IGA-ADS) handles the explicit calculation of how CO₂ saturation spreads in porous rock. Simultaneously, a Collocation-based Robust Variational Physics-Informed Neural Network (CRVPINN) is tasked with computing the complex pressure field, a task where neural networks can excel by learning the underlying physics.

This division of labor yields significant performance gains. The CRVPINN component is pre-trained on the initial pressure configuration, allowing each subsequent time-step update to be computed with remarkable efficiency—requiring only about 100 iterations of the Adam optimization algorithm. When benchmarked against a standard high-performance direct solver (MUMPS) on a single node of the ARES supercomputer cluster, the hybrid AI-physics approach proved to be over three times faster. The model focuses on the physical flow governed by Darcy's Law, deliberately setting aside chemical reactions for this stage.

The work, detailed in a preprint on arXiv, represents a promising step toward making complex geophysical simulations more tractable. The authors indicate that future development will include more extensive testing, applying the method to inverse problems (like determining underground properties from surface data), and potentially adapting it for modeling hydrogen (H₂) storage, another critical technology for the clean energy transition.