Physics-informed convolutional neural networks for fluid flow through porous media

• URL: http://arxiv.org/abs/2605.20250v1
• Date: Mon, 18 May 2026 08:02:28 GMT
• Title: Physics-informed convolutional neural networks for fluid flow through porous media
• Abstract summary: We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry.<n>We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.

Related papers

• Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching [60.37045080890305]
  We provide the first analysis of the sample complexity for flow-matching based generative models.<n>We decompose the velocity field estimation error into neural-network approximation error, statistical error due to the finite sample size, and optimization error due to the finite number of optimization steps for estimating the velocity field.
  arXiv  Detail & Related papers  (2025-12-01T05:14:25Z)
• Integrating Newton's Laws with deep learning for enhanced physics-informed compound flood modelling [0.8999666725996978]
  Coastal communities increasingly face compound floods, where multiple drivers like storm surge, high tide, heavy rainfall, and river discharge occur together or in sequence.<n>Traditional hydrodynamic models can provide accurate physics-based simulations but require substantial computational resources for real-time applications or risk assessments.<n>This study addresses these challenges by developing ALPINE, a physics-informed neural network framework to enforce complete shallow water dynamics in compound flood modeling.
  arXiv  Detail & Related papers  (2025-07-20T16:06:10Z)
• LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE [8.014720523981385]
  We propose LaPON, an operator network inspired by the Lagrange's mean value theorem.<n>It embeds prior knowledge directly into the neural network architecture instead of the loss function.<n>LaPON provides a scalable and reliable solution for high-fidelity fluid dynamics simulation.
  arXiv  Detail & Related papers  (2025-05-18T10:45:17Z)
• MultiPDENet: PDE-embedded Learning with Multi-time-stepping for Accelerated Flow Simulation [48.41289705783405]
  We propose a PDE-embedded network with multiscale time stepping (MultiPDENet)<n>In particular, we design a convolutional filter based on the structure of finite difference with a small number of parameters to optimize.<n>A Physics Block with a 4th-order Runge-Kutta integrator at the fine time scale is established that embeds the structure of PDEs to guide the prediction.
  arXiv  Detail & Related papers  (2025-01-27T12:15:51Z)
• Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks [44.99833362998488]
  Navier-Stokes equations may exhibit a highly nonlinear behavior. The system of nonlinear equations resulting from the discretization of the Navier-Stokes equations can be solved using nonlinear iteration methods, such as Newton's method. In this paper, pseudo-transient continuation is employed in order to improve nonlinear convergence.
  arXiv  Detail & Related papers  (2023-10-10T15:45:19Z)
• Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes [37.69303106863453]
  We present a hybrid quantum physics-informed neural network that simulates laminar fluid flows in 3D Y-shaped mixers. Our approach combines the expressive power of a quantum model with the flexibility of a physics-informed neural network, resulting in a 21% higher accuracy compared to a purely classical neural network.
  arXiv  Detail & Related papers  (2023-04-21T20:49:29Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• A predictive physics-aware hybrid reduced order model for reacting flows [65.73506571113623]
  A new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. The number of degrees of freedom is reduced from thousands of temporal points to a few POD modes with their corresponding temporal coefficients. Two different deep learning architectures have been tested to predict the temporal coefficients.
  arXiv  Detail & Related papers  (2023-01-24T08:39:20Z)
• Emulating Spatio-Temporal Realizations of Three-Dimensional Isotropic Turbulence via Deep Sequence Learning Models [24.025975236316842]
  We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The accuracy of the model is assessed using statistical and physics-based metrics.
  arXiv  Detail & Related papers  (2021-12-07T03:33:39Z)
• Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS [1.6274397329511197]
  This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner.
  arXiv  Detail & Related papers  (2021-09-04T08:43:19Z)
• A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries [62.28265459308354]
  Network learns end-to-end mapping between spatial positions and CFD quantities. Incompress laminar steady flow past a cylinder with various shapes for its cross section is considered. Network predicts the flow fields hundreds of times faster than our conventional CFD.
  arXiv  Detail & Related papers  (2020-10-15T12:15:02Z)
• ML-LBM: Machine Learning Aided Flow Simulation in Porous Media [0.0]
  Direct simulation of fluid flow in porous media requires significant computational resources to solve within reasonable timeframes. An integrated method combining predictions of fluid flow with direct flow simulation is outlined. Deep Learning techniques based on Convolutional Neural Networks (CNNs) are shown to give an accurate estimate of the steady state velocity fields.
  arXiv  Detail & Related papers  (2020-04-22T01:55:59Z)

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.