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

2026-04-23 · Source: cs.NE updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Environmental Science & Earth Systems, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

A new hybrid solver, IGA-ADS-CRVPINN, has been developed for simulating $CO_{2}$ sequestration in porous structures, excluding chemical reactions. This solver combines the IsoGeometric Analysis Alternating Directions solver (IGA-ADS) for saturation scalar field updates with the Collocation-based Robust Variational Physics Informed Neural Networks (CRVPINN) solver for pressure scalar field computation. The CRVPINN is pretrained on the initial pressure configuration and requires only 100 iterations of the Adam method per time step for subsequent updates. Benchmarking against a baseline IGA-ADS solver coupled with the MUMPS direct solver on an ARES cluster computational node demonstrated that the hybrid IGA-ADS-CRVPINN solver is over 3 times faster, achieving a total time of 3,400 seconds compared to 10,800 seconds for the MUMPS-based approach for a $128^{2}$ mesh. The method shows good agreement with the baseline, with relative errors typically below 5% for uniform permeability and around 15-20% for complex non-uniform permeability maps.

Key takeaway

For AI Scientists and Research Scientists developing computational fluid dynamics models for subsurface flow, adopting hybrid solvers like IGA-ADS-CRVPINN can drastically reduce simulation times for problems such as $CO_{2}$ sequestration. You should consider integrating Physics-Informed Neural Networks (PINNs) for computationally intensive components, especially where direct solvers are bottlenecks, to achieve significant speedups without substantial accuracy loss. This approach also enables simulations on more accessible hardware, including laptops or cloud-based GPUs.

Key insights

Hybridizing IGA-ADS with CRVPINN significantly accelerates $CO_{2}$ sequestration simulations while maintaining accuracy.

Principles

• Combine specialized solvers for different field types.
• Pre-training can reduce iterative computational cost.
• Robust loss functions improve PINN stability.

Method

The IGA-ADS-CRVPINN method uses IGA-ADS for saturation updates and a pre-trained CRVPINN for pressure updates, minimizing a robust loss function with Kronecker delta test functions and an inverse Gram matrix.

In practice

• Pre-train CRVPINN for initial pressure configuration.
• Perform 100 Adam iterations for time step pressure updates.
• Utilize GPU for CRVPINN to accelerate computations.

Topics

• CO2 Sequestration
• Isogeometric Analysis
• Physics-Informed Neural Networks
• Collocation Method
• Robust Loss Function

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.