Hybrid Two-Stage Reconstruction of Multiscale Subsurface Flow with Physics-informed Residual Connected Neural Operator

2025-01-22

AI Summary

To address low prediction accuracy and severe physical inconsistency in Darcy pressure field modeling for high-contrast fractured porous media, this paper proposes a two-stage hybrid reconstruction framework. In the first stage, a data-driven multiscale basis function construction method is developed to achieve feature-preserving dimensionality reduction of permeability fields. In the second stage, a physics-informed neural network (PINN) is integrated with a Transformer architecture, incorporating strong enforcement of the Darcy equation and a novel physics-guided residual connection neural operator to jointly ensure multiscale representational capacity and strict physical consistency. Evaluated on multiple heterogeneous permeability datasets, the framework achieves R² > 0.9 for both basis function fitting and pressure field reconstruction, with physical residuals as low as 1×10⁻⁴. It significantly improves predictive accuracy, generalizability, and physical fidelity compared to existing methods.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate reconstruction capability and strict adherence to physical laws. In this study, we proposed a hybrid two-stage framework that uses multiscale basis functions and physics-guided deep learning to solve the Darcy flow problem in high-contrast fractured porous media. In the first stage, a data-driven model is used to reconstruct the multiscale basis function based on the permeability field to achieve effective dimensionality reduction while preserving the necessary multiscale features. In the second stage, the physics-informed neural network, together with Transformer-based global information extractor is used to reconstruct the pressure field by integrating the physical constraints derived from the Darcy equation, ensuring consistency with the physical laws of the real world. The model was evaluated on datasets with different combinations of permeability and basis functions and performed well in terms of reconstruction accuracy. Specifically, the framework achieves R2 values above 0.9 in terms of basis function fitting and pressure reconstruction, and the residual indicator is on the order of $1 imes 10^{-4}$. These results validate the ability of the proposed framework to achieve accurate reconstruction while maintaining physical consistency.

Problem

• Neural Network Design
• Subsurface Flow Prediction
• Physical Rule Compliance

Innovation

• Two-step Method
• Deep Learning with Transformer
• Physical Consistency in Prediction