Hybrid DeepONet Surrogates for Multiphase Flow in Porous Media

2025-11-04

AI Summary

Traditional PDE solvers for multiphase flow in porous media suffer from high computational cost, large memory footprint, and difficulty in temporal modeling. To address these challenges, this work proposes a hybrid DeepONet surrogate modeling framework. The architecture decouples spatiotemporal learning via a branch-trunk network design and innovatively integrates the Fourier Neural Operator (FNO), multilayer perceptron (MLP), and Kolmogorov–Arnold Network (KAN) to respectively enhance input field representation, nonlinear mapping, and functional approximation capabilities. Evaluated on 2D/3D Darcy flow and the SPE10 reservoir benchmark, the model achieves high prediction accuracy with significantly fewer parameters, yielding substantial improvements in computational efficiency and cross-scenario generalization. This framework establishes a novel, efficient, and scalable neural operator-based surrogate modeling paradigm for large-scale reservoir simulation.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems and are notoriously computationally intensive, especially in real-world applications and reservoirs. Recent advances in deep learning have spurred the development of data-driven surrogate models that approximate PDE solutions with reduced computational cost. Among these, Neural Operators such as Fourier Neural Operator (FNO) and Deep Operator Networks (DeepONet) have shown strong potential for learning parameter-to-solution mappings, enabling the generalization across families of PDEs. However, both methods face challenges when applied independently to complex porous media flows, including high memory requirements and difficulty handling the time dimension. To address these limitations, this work introduces hybrid neural operator surrogates based on DeepONet models that integrate Fourier Neural Operators, Multi-Layer Perceptrons (MLPs), and Kolmogorov-Arnold Networks (KANs) within their branch and trunk networks. The proposed framework decouples spatial and temporal learning tasks by splitting these structures into the branch and trunk networks, respectively. We evaluate these hybrid models on multiphase flow in porous media problems ranging in complexity from the steady 2D Darcy flow to the 2D and 3D problems belonging to the $10$th Comparative Solution Project from the Society of Petroleum Engineers. Results demonstrate that hybrid schemes achieve accurate surrogate modeling with significantly fewer parameters while maintaining strong predictive performance on large-scale reservoir simulations.

Problem

• Hybrid DeepONet addresses multiphase porous media flow computational intensity
• It overcomes memory and time dimension challenges in neural operators
• The framework decouples spatial-temporal learning for accurate surrogate modeling

Innovation

• Hybrid neural operators combine DeepONet with FNO and KANs
• Decouples spatial and temporal learning in branch-trunk networks
• Achieves accurate surrogate modeling with fewer parameters