Applying Two-Grid Preconditioner for Subsurface Flow Simulation using Attention-enhanced Hybrid Network to Accelerate Multiscale Discretization in High-contrast Media

• URL: http://arxiv.org/abs/2606.02582v1
• Date: Wed, 15 Apr 2026 10:36:55 GMT
• Title: Applying Two-Grid Preconditioner for Subsurface Flow Simulation using Attention-enhanced Hybrid Network to Accelerate Multiscale Discretization in High-contrast Media
• Abstract summary: We study the efficient numerical solution of Darcy equations in strongly heterogeneous media with high-contrast permeability.<n>We propose a hybrid framework that combines learning with multiscale numerical methods.
• Score: 5.481597473968779
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the efficient numerical solution of Darcy equations in strongly heterogeneous media with high-contrast permeability and propose a hybrid framework that combines learning with multiscale numerical methods. The learning component is used for the prediction of multiscale basis functions in the mixed generalized multiscale finite element method (mixed GMsFEM), with the goal of reducing the repeated local computations required in the offline stage. Once these basis functions are predicted, the global system is assembled and the pressure field is computed by a two-grid preconditioned solver. The resulting method accelerates the costly local basis-construction stage while retaining the multiscale discretization and preconditioned iterative structure of the underlying solver. Numerical experiments on two-dimensional heterogeneous Darcy problems show that the proposed framework yields more accurate final pressure reconstruction than several representative learning-based methods and remains stable under strong heterogeneity and high-contrast coefficients. In comparison with the traditional mixed GMsFEM, its main advantage lies in the efficiency of the basis-generation stage, while the quality of the global solve is still ensured by the two-grid preconditioner. These results indicate that accelerating multiscale basis construction through learning, while preserving a mature numerical solver for the global problem, provides a viable approach for high-resolution Darcy-type simulations.

Related papers

• Fitting Unknown Number of Hyperplanes with Manifold Optimization [57.48093263119306]
  Fitting unknown number of linearplanes to data is a fundamental yet challenging problem in machine learning.<n>Existing approaches often struggle with optimum optima or lack geometric consistency.
  arXiv  Detail & Related papers  (2026-05-27T14:02:20Z)
• Parallel Diffusion Solver via Residual Dirichlet Policy Optimization [88.7827307535107]
  Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature.<n>Existing solver-based acceleration methods often face significant image quality degradation under a low-dimensional budget.<n>We propose the Ensemble Parallel Direction solver (dubbed as EPD-EPr), a novel ODE solver that mitigates these errors by incorporating multiple gradient parallel evaluations in each step.
  arXiv  Detail & Related papers  (2025-12-28T05:48:55Z)
• Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networks [0.3499870393443268]
  Inverse uncertainty quantification (UQ) tasks are computationally demanding when dealing with physics-based models.<n>Data-driven surrogate models may help reduce evaluation costs, but their utility is often limited by the expense of generating high-fidelity data.<n>We propose a Multi-Fidelity Delayed Acceptance scheme for Bayesian inverse problems.
  arXiv  Detail & Related papers  (2025-12-18T11:32:16Z)
• Dual-Domain Deep Learning Method to Accelerate Local Basis Functions Computation for Reservoir Simulation in High-Contrast Porous Media [6.1607662231604445]
  Darcy flow in heterogeneous porous media is a central problem in reservoir sim-ulation.<n>The Mixed Generalized Multiscale Finite Element Method (MGMsFEM) provides an effective framework for addressing these challenges.<n>We propose a dual-domain deep learning framework to accelerate the computation of multiscale basis functions.
  arXiv  Detail & Related papers  (2025-11-18T02:55:59Z)
• Neural Optimal Transport Meets Multivariate Conformal Prediction [58.43397908730771]
  We propose a framework for conditional vectorile regression (CVQR)<n>CVQR combines neural optimal transport with quantized optimization, and apply it to predictions.
  arXiv  Detail & Related papers  (2025-09-29T19:50:19Z)
• FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming [52.52020895303244]
  Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems.<n>We propose Joint Continuous-Integer Flow for Mixed-Integer Linear Programming (FMIP), which is the first generative framework that models joint distribution of both integer and continuous variables for MILP solutions.<n>FMIP is fully compatible with arbitrary backbone networks and various downstream solvers, making it well-suited for a broad range of real-world MILP applications.
  arXiv  Detail & Related papers  (2025-07-31T10:03:30Z)
• Data-Driven Adaptive Gradient Recovery for Unstructured Finite Volume Computations [0.0]
  We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws.<n>Our approach extends previous structured-grid methodologies to unstructured meshes through a modified DeepONet architecture.<n>The proposed algorithm is faster and more accurate than the traditional second-order finite volume solver.
  arXiv  Detail & Related papers  (2025-07-22T13:23:57Z)
• Hybrid Two-Stage Reconstruction of Multiscale Subsurface Flow with Physics-informed Residual Connected Neural Operator [6.1607662231604445]
  We propose a hybrid two-stage framework that uses multiscale basis functions and physics-guided deep learning to solve the Darcy flow problem.<n>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 $1times 10-4$.
  arXiv  Detail & Related papers  (2025-01-22T23:28:03Z)
• Differentiable DG with Neural Operator Source Term Correction [0.0]
  We introduce an end-to-end differentiable framework for solving the compressible Navier-Stokes equations.<n>This integrated approach combines a differentiable discontinuous Galerkin solver with a neural network source term.<n>We demonstrate the performance of the proposed framework through two examples.
  arXiv  Detail & Related papers  (2023-10-29T04:26:23Z)
• A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution [50.13564338607482]
  We propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix.<n>It consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module.<n>This work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• AI-enhanced iterative solvers for accelerating the solution of large scale parametrized linear systems of equations [0.0]
  This paper exploits up-to-date ML tools and delivers customized iterative solvers of linear equation systems. The results indicate its superiority over conventional iterative solution schemes.
  arXiv  Detail & Related papers  (2022-07-06T09:47:14Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• Cogradient Descent for Bilinear Optimization [124.45816011848096]
  We introduce a Cogradient Descent algorithm (CoGD) to address the bilinear problem. We solve one variable by considering its coupling relationship with the other, leading to a synchronous gradient descent. Our algorithm is applied to solve problems with one variable under the sparsity constraint.
  arXiv  Detail & Related papers  (2020-06-16T13:41:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.