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

Luigi Ciceri, Corrado Mio, Jianyi Lin, Gabriele Gianini

TL;DR

This 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.

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.

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

TL;DR

This 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.

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.
Paper Structure (23 sections, 10 equations, 8 figures, 6 tables)

This paper contains 23 sections, 10 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Fluid Motion Equations and Problem Setup
  3. Navier--Stokes and Darcy--Forchheimer Models
  4. 2D study cases
  5. Manufactured solution test.
  6. Case studies.
  7. 3D study cases
  8. Numerical Data Generation
  9. CFD Simulations in OpenFOAM
  10. Point Cloud Representation
  11. Physics-Informed and Geometry-Aware ANNs
  12. Physics-Informed Neural Networks
  13. Physics-informed PointNets
  14. Architecture
  15. Physics-Informed Geometry-Aware Neural Operator
  16. ...and 8 more sections

Figures (8)

  • Figure 1: Some 2D porous geometries: (a--c) from training set, (d) unseen composite.
  • Figure 2: 2D domains generated with snappyHexMesh, boundary conditions: inlet, outlet, wall.
  • Figure 3: 3D domains with tree canopies, boundary conditions: inlet, outlet, wall.
  • Figure 4: Architectures modified to take into account porous medium.
  • Figure 5: MAE obtained from the PIPN prediction on the unseen geometry in Fig. \ref{['fig:2d-geometries']}.
  • ...and 3 more figures