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

TL;DR

This paper introduces a hybrid solver combining IGA-ADS and CRVPINN for efficient $CO_2$ sequestration simulation, achieving over three times faster performance than traditional methods.

Contribution

The novel hybrid IGA-ADS and CRVPINN approach significantly accelerates $CO_2$ sequestration modeling compared to baseline solvers.

Findings

Hybrid solver is over 3 times faster than baseline.

CRVPINN requires only 100 Adam iterations per time step.

The method effectively simulates $CO_2$ behavior in porous media.

Abstract

This paper presents the hybrid solver for a $CO_2$ sequestration problem. The solver uses the IGA-ADS (IsoGeometric Analysis Alternating Directions solver) to compute the saturation scalar field update using the explicit method, and CRVPINN (Collocation-based Robust Variational Physics Informed Neural Networks solver) to compute the pressure scalar field. The study focuses on simulating the physical behavior of $CO_2$ in porous structures, excluding chemical reactions. The mathematical model is based on Darcy's Law. The CRVPINN is pretrained on the initial pressure configuration, and the time step pressure updates require only 100 iterations of the Adam method per time step. We compare our hybrid IGA-ADS solver, coupled with the CRVPINN method, with a baseline of the IGA-ADS solver coupled with the MUMPS direct solver. Our hybrid solver is over 3 times faster on a single computational node from the ARES cluster of ACK CYFRONET. Future work includes extensive testing, inverse problem solving, and potential application to $H_2$ storage problems.