An End-to-End Differentiable, Graph Neural Network-Embedded Pore Network Model for Permeability Prediction

2025-09-17

AI Summary

Accurately predicting permeability in porous media is critical for subsurface flow simulation. Existing purely data-driven models suffer from poor generalizability, while conventional pore-network models (PNMs) rely on idealized geometric assumptions, limiting their accuracy for complex microstructures. This work proposes an end-to-end differentiable graph neural network (GNN)-enhanced PNM framework: GNNs replace empirical hydraulic conductance formulas, and discrete adjoint methods enable gradient backpropagation across physics-based solvers, facilitating end-to-end training without labeled flux data. By tightly integrating data-driven flexibility with physics-informed constraints, the method achieves superior accuracy, strong generalization across diverse microstructures and scales, and inherent physical interpretability. Comprehensive evaluation demonstrates significant improvements over both pure data-driven models and classical PNMs in multi-scale benchmark tasks.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Accurate prediction of permeability in porous media is essential for modeling subsurface flow. While pure data-driven models offer computational efficiency, they often lack generalization across scales and do not incorporate explicit physical constraints. Pore network models (PNMs), on the other hand, are physics-based and efficient but rely on idealized geometric assumptions to estimate pore-scale hydraulic conductance, limiting their accuracy in complex structures. To overcome these limitations, we present an end-to-end differentiable hybrid framework that embeds a graph neural network (GNN) into a PNM. In this framework, the analytical formulas used for conductance calculations are replaced by GNN-based predictions derived from pore and throat features. The predicted conductances are then passed to the PNM solver for permeability computation. In this way, the model avoids the idealized geometric assumptions of PNM while preserving the physics-based flow calculations. The GNN is trained without requiring labeled conductance data, which can number in the thousands per pore network; instead, it learns conductance values by using a single scalar permeability as the training target. This is made possible by backpropagating gradients through both the GNN (via automatic differentiation) and the PNM solver (via a discrete adjoint method), enabling fully coupled, end-to-end training. The resulting model achieves high accuracy and generalizes well across different scales, outperforming both pure data-driven and traditional PNM approaches. Gradient-based sensitivity analysis further reveals physically consistent feature influences, enhancing model interpretability. This approach offers a scalable and physically informed framework for permeability prediction in complex porous media, reducing model uncertainty and improving accuracy.

Problem

• Overcoming idealized geometric assumptions limiting pore network model accuracy
• Replacing analytical conductance formulas with GNN predictions from pore features
• Enabling physics-preserving permeability prediction without labeled conductance data

Innovation

• End-to-end differentiable hybrid framework embedding GNN
• Replacing analytical conductance formulas with GNN predictions
• Training without labeled data using permeability backpropagation