[Paper] Surrogate models for Rock-Fluid Interaction: A Grid-Size-Invariant Approach

Source: arXiv - 2602.22188v1

Overview

The paper presents a suite of eight surrogate models that can predict fluid flow in porous rock without the massive computational cost of traditional high‑fidelity PDE solvers. By introducing a grid‑size‑invariant neural‑network framework, the authors enable accurate inference on domains larger than those seen during training—a breakthrough for tasks that require many repeated simulations such as uncertainty quantification, optimization, and real‑time decision support.

Key Contributions

• Eight surrogate models: four reduced‑order models (ROMs) that separate compression and prediction, and four end‑to‑end image‑to‑image networks that are invariant to the computational grid size.
• Grid‑size‑invariant architecture: a novel training strategy that lets a single neural network generalize to larger (or differently shaped) simulation domains without retraining.
• UNet++ vs. UNet comparison: systematic benchmarking shows UNet++ consistently outperforms the classic UNet for surrogate modeling of rock‑fluid interaction.
• Memory‑efficient training: the invariant approach reduces GPU memory footprints, making it feasible to train on modest hardware while still delivering high‑quality predictions.
• Application to reactive dissolution: the models handle the challenging case where the solid matrix evolves over time, demonstrating robustness in non‑static scenarios.

Methodology

1. Data Generation – High‑resolution PDE simulations of fluid flow and rock dissolution were run on a set of training domains (various permeability fields, reaction rates, etc.). The resulting pressure and concentration fields serve as ground truth.
2. Model Families
   • ROMs: A first neural network (autoencoder) compresses the high‑dimensional field into a low‑dimensional latent vector; a second network maps simulation parameters to this latent space, and the decoder reconstructs the full field.
   • Grid‑size‑Invariant Networks: Single convolutional encoder‑decoder models (UNet and UNet++) are trained on patches of the simulation domain. During inference, the network processes the entire domain, regardless of its size, thanks to fully convolutional layers and adaptive padding.
3. Training Tricks – Random cropping, data augmentation, and a loss function that combines mean‑squared error with a physics‑informed regularizer (encouraging mass conservation) help the models learn robust representations.
4. Evaluation – The authors compare predictions against unseen high‑fidelity simulations using correlation coefficients, relative error metrics, and visual inspection of flow patterns.

Results & Findings

• Prediction Accuracy: Grid‑size‑invariant UNet++ achieved an average Pearson correlation of 0.96 with the ground‑truth fields, surpassing the best ROM (0.91) and the standard UNet (0.93).
• Speedup: Inference time dropped from several hours per simulation (full PDE solve) to under 2 seconds on a single GPU, a >10,000× speedup.
• Memory Savings: Training on 64 × 64 patches required ~4 GB GPU memory, whereas a naïve full‑domain training would exceed 24 GB.
• Robustness to Domain Size: Models trained on 128 × 128 grids accurately predicted on 256 × 256 and 512 × 512 domains, preserving flow structures and dissolution fronts.
• UNet++ Advantage: The nested skip connections in UNet++ reduced checkerboard artifacts and improved fine‑scale detail recovery, especially near reactive interfaces.

Practical Implications

• Rapid Scenario Exploration: Engineers can now run thousands of “what‑if” simulations for reservoir management, CO₂ sequestration, or geothermal projects in minutes rather than days.
• Real‑Time Monitoring: Coupling the surrogate with sensor data enables near‑real‑time updates of subsurface flow predictions, supporting adaptive drilling or injection strategies.
• Cost‑Effective Uncertainty Quantification: Monte‑Carlo analyses that were previously prohibitive become tractable, allowing more rigorous risk assessments.
• Integration into Optimization Loops: Gradient‑based or evolutionary optimizers can query the surrogate directly, accelerating design of injection schedules, fracture placements, or chemical additives.
• Hardware Accessibility: Because the approach works on modest GPUs, smaller companies and academic labs can adopt high‑fidelity‑level modeling without massive HPC allocations.

Limitations & Future Work

• Training Data Dependence: The surrogate’s accuracy hinges on the diversity of the high‑fidelity training set; extreme permeability contrasts or novel reaction kinetics outside the training envelope may degrade performance.
• Physics Guarantees: While a physics‑informed loss helps, the models are not strictly mass‑conservative; post‑processing steps may be needed for safety‑critical applications.
• Extension to 3‑D: Current experiments are 2‑D; scaling the grid‑size‑invariant framework to full 3‑D reservoirs will demand additional memory‑efficient tricks and possibly hybrid physics‑ML schemes.
• Dynamic Boundary Conditions: The study assumes static inlet/outlet conditions; handling time‑varying boundary conditions remains an open challenge.

Overall, the grid‑size‑invariant surrogate models open a practical pathway for developers and industry practitioners to embed high‑resolution rock‑fluid physics into fast, data‑driven workflows.

Authors

• Nathalie C. Pinheiro
• Donghu Guo
• Hannah P. Menke
• Aniket C. Joshi
• Claire E. Heaney
• Ahmed H. ElSheikh
• Christopher C. Pain

Paper Information

• arXiv ID: 2602.22188v1
• Categories: cs.LG, cs.AI, physics.flu-dyn
• Published: February 25, 2026
• PDF: Download PDF