meshgraphnet 0.1.1

Graph neural network surrogates for FEA on arbitrary geometries

Introduction

Presented here is a PyTorch implementation of mesh graph networks (MGNs) for predicting von Mises stress fields in 2D structural components with arbitrary hole geometries.

This repository accompanies the paper:

Kunz, J. & Choudhary, K. (2026). "Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries." [Journal TBD].

Key Features

• Geometry-agnostic: Generalizes to unseen hole shapes without retraining
• Translation/rotation invariant: Uses relative edge features and node-type embeddings rather than absolute coordinates
• Clean, high-level API: Go from geometry to trained surrogate model with simplicity
• Fast inference: Sub-second predictions compared to minutes for FEM

Installation

Google Colab (recommended)

# Install FEniCS for Colab
!wget "https://fem-on-colab.github.io/releases/fenics-install-release-real.sh" -O "/tmp/fenics-install.sh" && bash "/tmp/fenics-install.sh"
!apt-get install -y libglu1-mesa -q

# Install meshgraphnet
!pip install meshgraphnet -q

Local (conda)

# FEniCS must be installed via conda
conda install -c conda-forge fenics

# Then install meshgraphnet
pip install meshgraphnet

Package Structure

meshgraphnet/
├── mesh_object/            # Geometry loading & meshing (STEP -> Dolfin)
├── fem_object/             # FEM problem setup, solving, and visualization
│   ├── material.py         # Linear-elastic material properties
│   ├── load_types.py       # VolumeLoad, SurfaceLoad, EdgeLoad, PointLoad
│   ├── load_collection.py  # Housing for various load types
│   ├── fixed_boundary.py   # FEM boundary condition (only fixed is currently supported)
│   └── fem_object.py       # Main FEMObject class
├── ml_object/              # ML training & evaluation on FEM results
│   ├── ml_object.py        # MLObject wrapper (sklearn + GNN)
│   ├── gnn.py              # Graph Neural Network (GNN)
│   ├── mgn.py              # Mesh Graph Network (MGN); main result
│   ├── basic_gcn.py        # Basic graph convolution network (GCN)
│   └── relative_gcn.py     # GCN that uses differences
├── units/                  # Unit system management (Pint-based)
│   └── unit_system.py      # UnitSystem, Units presets
└── common_utils/           # Shared formatting helpers

Key Classes

MeshObject

Represents a mesh. Loads a geometry file (e.g. STEP), runs Gmsh auto-meshing, and produces a Dolfin mesh ready for FEniCS. Usage snippet (see examples folder for more):

mesh = MeshObject("bracket.step", mesh_size=5, units=Units.SI_MM)
mesh.summary()      # prints statistics: vertices, cells, extents
mesh.visualize()    # matplotlib plot of the mesh

FEMObject

Represents a finite element method (FEM) simulation object. Combines a mesh, loads, boundary conditions, and material into a complete linear-elastic FEM problem. Solves with FEniCS and exposes results as NumPy arrays. Usage snippet (see examples folder for more):

fem = FEMObject(
    mesh=mesh,
    loads=loads,
    boundaries=[FixedBoundary("left")],
    material=Material.steel(),
    name="Cantilever bracket"
)

fem.visualize_setup()       # preview loads & BCs
fem.solve()                 # run FEniCS solver
fem.plot_displacement()     # displacement field
fem.plot_stress()           # von Mises stress
fem.save_results("out.csv") # export nodal results

MLObject

Represents a machine learning (ML) model object. Trains sklearn or GNN surrogate models on FEM result CSV data, with built-in cross-validation, feature analysis, and visualization. Usage snippet (see examples folder for more):

ml = MLObject(
    data="fem_results.csv",
    features=["x (m)", "y (m)"],
    objectives=["von_mises (GPa)"],
)

ml.summary()
ml.analyze_features(plot=True)
ml.train(model=GradientBoostingRegressor())
ml.evaluate_on_unseen_data()
ml.plot_predictions()

GNN/MGN

Represents either a graph neural network (GNN) model or a mesh graph network (MGN) model that uses node-level regression on FEMObjects.

• GNN: standard GCN operating on (X, y) feature matrices with an explicit edge CSV
• MGN: geometry-agnostic model inspired by Pfaff et al. 2021. Uses relative edge features and learned node-type embeddings (such as hole or fixed) so it can generalize across different geometries. Usage snippet (see examples folder for more):

mgn = MGN(hidden_channels=64, num_layers=20, global_features=["load"], epochs=5000)

ml = MLObject(
    train_fem=train_fems,   # list of solved FEMObjects
    test_fem=test_fem,
    objectives=["von_mises"],
)
ml.train(model=mgn, model_name="MGN")
mgn.save("model.pt")

# Load and reuse later:
mgn = MGN.load("model.pt")

Dependencies

Library	Purpose
fenics / dolfin	FEM solver
gmsh	Auto-meshing from STEP/geometry files
meshio	Mesh format conversion
pint	Unit arithmetic and conversion
torch / torch_geometric	Graph neural networks
scikit-learn	Classical ML models
numpy, pandas	Numerics and data handling
matplotlib	Visualization

See also requirements.txt.

Correspondence

• [e-mail]
• [e-mail]

License

Apache License 2.0