ChebyKAN-DEM

PyTorch implementation of Chebyshev KAN networks for a deep energy method (DEM) solving phase-field fracture (AT2, spectral split) on Gmsh triangle meshes.

This repository is organized as a compact research-code release accompanying the paper. It exposes the model structure, training workflow, benchmark entry points, and result layout in a form that is easy to inspect and adapt.

Repository Overview

The repository contains:

• the ChebyKAN-DEM solver implementation,
• a self-contained homogeneous SENT benchmark,
• several heterogeneous benchmark entry points,
• a template entry point for user-defined heterogeneous material layouts,
• result files consistent with the paper.

The homogeneous SENT example can generate its mesh directly in the repository. The heterogeneous benchmark examples read their geometry from a benchmark mesh file named:

shared_mesh.msh

Material fields and heterogeneous layouts can be adapted through the case-specific input structure and the provided template utilities.

Install

python -m venv .venv
source .venv/bin/activate   # Windows: .venv\Scripts\activate
pip install -e .

A working Gmsh installation is required. The Python package gmsh wraps the Gmsh library, but the underlying Gmsh runtime must still be available on your machine.

Quick Start

Run the homogeneous SENT benchmark first:

python examples/run_sent_homogeneous.py

or equivalently:

python -m chebykan_dem --case sent_homogeneous
chebykan-dem --case sent_homogeneous

This is the simplest entry point and is the recommended first check for a new environment.

Geometry and Input Conventions

The heterogeneous benchmark examples use a shared convention:

• geometry is read from shared_mesh.msh,
• case results are written to a dedicated output directory,
• material information can be adapted through user-editable inputs or template files.

Typical command pattern:

chebykan-dem --case layered_bimaterial --output ./results_layered_bimaterial

Supported case ids:

• sent_homogeneous
• layered_bimaterial
• circular_inclusion
• three_inclined_cracks
• fgm_threephase
• heterogeneous_user

For heterogeneous_user, the CLI points you to examples/run_heterogeneous_user.py, which creates the placeholder material input file.

Example Entry Points (examples/)

Script	Role
run_sent_homogeneous.py	Homogeneous SENT benchmark with in-repo mesh generation.
run_layered_bimaterial.py	Layered bimaterial benchmark entry point using the standard benchmark mesh convention.
run_circular_inclusion.py	Circular inclusion benchmark entry point using the standard benchmark mesh convention.
run_three_inclined_cracks.py	Three inclined cracks benchmark entry point using the standard benchmark mesh convention.
run_fgm_threephase.py	Three-phase FGM-style benchmark entry point using the standard benchmark mesh convention.
run_heterogeneous_user.py	Writes results_heterogeneous_user/material_template.json as a starting point for custom heterogeneous material inputs.

Output Layout

Each case directory follows the naming convention used in the paper:

<case_dir>/
├── config.json
├── case_summary.json
├── shared_mesh.msh
├── mesh_coordinates.npz
├── quick_preview.png
└── chebykan/
    ├── results.csv
    ├── alpha_profile_y0.csv
    ├── timing.csv
    ├── step_{NNN}.npz
    ├── frame_{NNN}.png
    ├── force_displacement.png
    ├── model.pth
    ├── chebyshev_coeffs.npz
    └── learned_activations.npz

results.csv columns:

• step
• disp
• force
• E_elastic
• E_fracture
• E_total
• alpha_max

timing.csv columns:

• step
• epochs
• time_step
• time_cumulative

Displacement written to CSV is in metres. Most figures convert the horizontal axis to micrometres (μm) for presentation.

Configuration

The main runtime configuration lives in:

• chebykan_dem/config.py

This file controls geometry dimensions, loading schedule, network widths, Chebyshev degree, optimizer settings, and output locations.

Notes For Users

• Start with sent_homogeneous to confirm your environment is working.
• Use the heterogeneous examples as benchmark-specific entry points following the same output and mesh conventions.
• If you want a custom heterogeneous setup, start from examples/run_heterogeneous_user.py and extend the material handling in the solver / physics layer.
• The repository is intentionally structured so that benchmark geometry, solver configuration, and material customization remain easy to inspect and modify.

Citation

If you use this code, please cite:

P. Zhang, K. Tang, B.-X. Xu. ChebyKAN-enhanced deep energy method for phase field fracture: From homogeneous to heterogeneous materials. Journal of the Mechanics and Physics of Solids 214, 106693 (2026). https://doi.org/10.1016/j.jmps.2026.106693

@article{Zhang2026ChebyKANDEM,
  author  = {Zhang, Peng and Tang, Keke and Xu, Bai-Xiang},
  title   = {{ChebyKAN}-enhanced deep energy method for phase field fracture: From homogeneous to heterogeneous materials},
  journal = {Journal of the Mechanics and Physics of Solids},
  volume  = {214},
  pages   = {106693},
  year    = {2026},
  doi     = {10.1016/j.jmps.2026.106693}
}

License

This project is released under the MIT License. See LICENSE for details.