Geometry-Aware Physics-Informed PointNets for Modeling Flows Across Porous Structures

2026-02-15

AI Summary

This work addresses the challenge of modeling coupled flow inside and outside porous media by proposing Physics-Informed PointNets (PIPN) and a Geometry-Aware Neural Operator (PI-GANO). These frameworks embed the incompressible Navier–Stokes equations and the Darcy–Forchheimer model into a unified loss function, conditioned on geometric and material parameters to enable end-to-end prediction. The study presents the first systematic evaluation of neural operators’ generalization capability in simultaneously resolving both external flow around and internal flow through porous structures, demonstrating adaptability to unseen geometries, boundary conditions, and parameter configurations without retraining. Validated on 2D channel and 3D windbreak scenarios, the models accurately reproduce wake vortex structures with low velocity and pressure errors, exhibiting only minor performance degradation near sharp interfaces and regions of high gradients.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Deep Neural Architectures and Foundation Models

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
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Predicting flows that occur both through and around porous bodies is challenging due to coupled physics across fluid and porous regions and the need to generalize across diverse geometries and boundary conditions. We address this problem using two Physics Informed learning approaches: Physics Informed PointNets (PIPN) and Physics Informed Geometry Aware Neural Operator (P-IGANO). We enforce the incompressible Navier Stokes equations in the free-flow region and a Darcy Forchheimer extension in the porous region within a unified loss and condition the networks on geometry and material parameters. Datasets are generated with OpenFOAM on 2D ducts containing porous obstacles and on 3D windbreak scenarios with tree canopies and buildings. We first verify the pipeline via the method of manufactured solutions, then assess generalization to unseen shapes, and for PI-GANO, to variable boundary conditions and parameter settings. The results show consistently low velocity and pressure errors in both seen and unseen cases, with accurate reproduction of the wake structures. Performance degrades primarily near sharp interfaces and in regions with large gradients. Overall, the study provides a first systematic evaluation of PIPN/PI-GANO for simultaneous through-and-around porous flows and shows their potential to accelerate design studies without retraining per geometry.

Problem

• porous flow
• geometry generalization
• boundary conditions
• Navier-Stokes equations
• Darcy-Forchheimer

Innovation

• Physics-Informed Neural Networks
• Geometry-Aware Learning
• Porous Media Flow
• Neural Operators
• Navier-Stokes-Darcy Coupling