CO2 sequestration hybrid solver using isogeometric alternating-directions and collocation-based robust variational physics informed neural networks (IGA-ADS-CRVPINN)

In this paper we present how Physics Informed Neural Networks augmented with robust loss function computed at collocation points can speed up the explicit dynamics simulations of time-dependent problems. We develop and apply our hybrid solver on a practical yet challenging example - the CO 2 sequestration problem. In this example, we compute the scalar saturation field from the non-stationary solver, and the pressure scalar field from the stationary solver executed in every time step. We show that the non-stationary saturation solver can be sped up using the IGA-ADS method (IsoGeometric Analysis Alternating Directions) using the explicit method and Kronecker product structure of matrices. We also show that the pressure solver can be sped up using the CRVPINN (Collocation-based Robust Variational Physics Informed Neural Networks solver) that computes the pressure update with neural network training. The study focuses on simulating the physically plausible behavior of CO 2 in porous structures, excluding chemical reactions. The mathematical model is based on two-phase Darcy’s Law. The CRVPINN is pretrained on the initial pressure configuration, and the subsequent 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, to a baseline of the IGA-ADS saturation solver coupled with the MUMPS direct pressure solver. Our CRVPINN pressure solver itself is 9.2 times faster than the MUMPS direct solver. Future work includes extensive testing, inverse problem solving, and potential application to H 2 storage problems.