# Dual-Domain Deep Learning Method to Accelerate Local Basis Functions Computation for Reservoir Simulation in High-Contrast Porous Media

arXiv: https://arxiv.org/abs/2511.20685 · HTML: https://mlsanity.com/paper/2511.20685/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 18 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Mitigating spectral bias for the multiscale operator learning](https://mlsanity.com/paper/2210.10890/) (2022)
- [Generalized Multiscale Finite Element Methods (GMsFEM)](https://mlsanity.com/paper/1301.2866/) (2013)
- [TeLU Activation Function for Fast and Stable Deep Learning](https://mlsanity.com/paper/2412.20269/) (2024)

## Abstract (arXiv)

In energy science, Darcy flow in heterogeneous porous media is a central problem in reservoir sim-ulation. However, the pronounced multiscale characteristics of such media pose significant challenges to conventional numerical methods in terms of computational demand and efficiency. The Mixed Generalized Multiscale Finite Element Method (MGMsFEM) provides an effective framework for addressing these challenges, yet the construction of multiscale basis functions remains computationally expensive. In this work, we propose a dual-domain deep learning framework to accelerate the computation of multiscale basis functions within MGMsFEM for solving Darcy flow problems. By extracting and decoding permeability field features in both the frequency and spatial domains, the method enables rapid generation of numerical matrices of multiscale basis functions. Numerical experiments demonstrate that the proposed framework achieves significant computational acceleration while maintaining high approximation accuracy, thereby offering the potential for future applications in real-world reservoir engineering.