A Discrete Neural Operator with Adaptive Sampling for Surrogate Modeling of Parametric Transient Darcy Flows in Porous Media

2025-12-02

AI Summary

This work addresses high-fidelity surrogate modeling of transient Darcy flow fields in stochastic heterogeneous porous media. We propose a novel discrete neural operator that takes the finite-volume-derived conductance matrix—not the conventional permeability field—as input, integrating time encoding, neural operator learning, and a UNet architecture. A key innovation is a generative latent-space adaptive sampling strategy based on Gaussian mixture models, which explicitly models and optimizes the generalization error density, thereby significantly improving modeling accuracy and sampling efficiency under limited data. Evaluated on 2D/3D single-phase and two-phase Darcy flow prediction tasks, the method demonstrates robust performance with scarce training data, consistently outperforming the state-of-the-art attention-based residual UNet in predictive accuracy.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Mixed Discrete/Continuous Search

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: Web data generation and simulation
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to approximate the mapping between vector spaces of random parameter and spatiotemporal flow fields. The new discrete neural operator can achieve higher prediction accuracy than the SOTA attention-residual-UNet structure. Derived from the finite volume method, the transmissibility matrices rather than permeability is adopted as the inputs of surrogates to enhance the prediction accuracy further. To increase sampling efficiency, a generative latent space adaptive sampling method is developed employing the Gaussian mixture model for density estimation of generalization error. Validation is conducted on test cases of 2D/3D single- and two-phase Darcy flow field prediction. Results reveal consistent enhancement in prediction accuracy given limited training set.

Problem

• Develops a discrete neural operator for surrogate modeling of parametric transient Darcy flows
• Enhances prediction accuracy using transmissibility matrices and adaptive sampling
• Validates the method on 2D/3D single- and two-phase Darcy flow predictions

Innovation

• Discrete neural operator with temporal encoding and UNet
• Transmissibility matrices as inputs from finite volume method
• Generative latent space adaptive sampling with Gaussian mixture