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

Source: arXiv - 2604.20731v1

Overview

A new hybrid computational framework tackles the notoriously expensive simulation of CO₂ sequestration in porous media. By marrying a classic isogeometric alternating‑directions solver (IGA‑ADS) with a lightweight physics‑informed neural network (CRVPINN), the authors achieve a three‑fold speed‑up over a traditional direct‑solver baseline—while preserving the accuracy needed for engineering decisions.

Key Contributions

• Hybrid Solver Architecture – Combines an explicit IGA‑ADS update for the saturation field with a collocation‑based variational PINN (CRVPINN) for the pressure field.
• Efficient Neural‑Network Pre‑training – The pressure PINN is pre‑trained on the initial condition; subsequent time‑step updates need only ~100 Adam iterations, dramatically reducing runtime.
• Performance Benchmarking – Demonstrates >3× speed improvement on a single node of the ARES cluster compared with an IGA‑ADS + MUMPS direct‑solver configuration.
• Domain‑Specific Modeling – Implements Darcy’s law for two‑phase flow (CO₂ + brine) without chemical reactions, a common simplification in early‑stage sequestration studies.
• Open Path to Inverse Problems & H₂ Storage – Outlines how the same pipeline could be repurposed for parameter estimation or hydrogen underground storage simulations.

Methodology

Governing Equations

• Darcy’s law describes fluid motion through porous rock.
• Two coupled scalar fields: saturation (fraction of pore space occupied by CO₂) and pressure.

IGA‑ADS for Saturation

• Uses isogeometric analysis (IGA) to represent geometry and solution fields with the same spline basis, preserving exact CAD geometry.
• Alternating Directions Solver (ADS) splits the multidimensional problem into a sequence of 1‑D solves, enabling an explicit time‑integration that is cheap and easy to parallelize.

CRVPINN for Pressure

• A Physics‑Informed Neural Network (PINN) that enforces the pressure PDE through a variational (weak) formulation, evaluated at collocation points.
• Robust because the loss includes both residuals and boundary/initial condition penalties; collocation‑based to avoid costly numerical integration.
• The network is pre‑trained on the initial pressure field. During each time step, only a few hundred Adam optimizer iterations are required to adapt the network to the updated saturation‑dependent source term.

Coupling Strategy

At each time step:

1. Update saturation explicitly with IGA‑ADS.
2. Feed the new saturation into the pressure PINN as a source term.
3. Perform a short PINN fine‑tuning (≈100 Adam steps).

This loop replaces the traditional monolithic solve that would require a large sparse linear system (handled by MUMPS in the baseline).

Results & Findings

The hybrid approach retains the high‑fidelity spatial representation of IGA while slashing the cost of solving the pressure field, which is typically the bottleneck in two‑phase flow simulations.

Practical Implications

• Faster Feasibility Studies – Engineers can run many more “what‑if” scenarios (different injection rates, permeability fields, etc.) within the same compute budget, accelerating site‑selection and risk‑assessment workflows.
• Reduced Hardware Requirements – The memory‑light PINN eliminates the need for large distributed direct solvers, making the workflow viable on workstations or modest cloud instances.
• Real‑Time Monitoring & Decision Support – With only a few hundred neural‑network updates per time step, the solver could be integrated into near‑real‑time monitoring platforms that ingest field data (e.g., pressure sensors) and update forecasts on the fly.
• Portability to Other Subsurface Problems – The same hybrid pattern can be applied to hydrogen storage, geothermal reservoirs, or CO₂‑enhanced oil recovery, where pressure‑saturation coupling dominates.
• Hybrid‑AI Adoption Path – Demonstrates a concrete, low‑risk entry point for developers who want to inject AI components into legacy PDE solvers without rewriting the entire codebase.

Limitations & Future Work

• Physical Simplifications – The model omits chemical reactions, capillary pressure hysteresis, and thermal effects, which can be important for long‑term sequestration safety analyses.
• PINN Generalization – The CRVPINN is retrained each time step; while cheap, it still relies on a good initial guess. Robustness to highly nonlinear source terms remains to be tested.
• Scalability Beyond a Single Node – Experiments were limited to one compute node; distributed‑memory scaling of the hybrid pipeline (especially the PINN part) is an open question.
• Inverse Problem & Parameter Estimation – The authors plan to leverage the differentiable PINN to solve inverse problems (e.g., estimating permeability from pressure data), but this has not yet been demonstrated.

Overall, the paper showcases a promising blend of classical numerical methods and modern AI‑driven solvers, opening a practical route for faster, more flexible subsurface flow simulations.

Authors

• Askold Vilkha
• Tomasz Służalec
• Marcin Łoś
• Maciej Paszyński

Paper Information

• arXiv ID: 2604.20731v1
• Categories: math.NA, cs.NE
• Published: April 22, 2026
• PDF: Download PDF