Populating Cellular Metamaterials via Neuroevolution

Research code for the paper "Populating cellular metamaterials on the extrema of attainable elasticity through neuroevolution".

This repository explores metamaterial unit-cell design with CPPNs (Compositional Pattern-Producing Networks) and a modified NEAT-based multi-objective evolutionary pipeline. The framework generates diverse cellular geometries, evaluates their homogenized elastic properties, and pushes the search toward the empirical bounds of attainable elasticity.

Overview

Designing architected materials often requires navigating strong trade-offs between mechanical properties such as stiffness, shear response, and Poisson's ratio. Instead of optimizing a single hand-crafted topology, this project treats metamaterial discovery as a search problem over geometry generators:

• CPPNs encode geometry compactly and generate structured, highly regular patterns.
• Modified NEAT evolves both weights and topology of the CPPNs.
• Finite-element homogenization evaluates the effective properties of each generated unit cell.
• Multi-objective selection and diversity mechanisms help populate the Pareto frontier instead of converging to a single design.

Highlights

• CPPN-based generation of 2D unit-cell topologies on structured point clouds
• Multiple point-cloud symmetries: nosym, sym2, sym4, rotate, parallel
• Customized neat-python fork with archive-based multi-objective behavior and novelty-related utilities
• FEniCS / Dolfin-based periodic homogenization for effective elastic-property evaluation
• Utilities for geometry extraction, contour interpolation, meshing, constraint checking, and visualization

Method Pipeline

flowchart LR
    A[Initialize population] --> B[Decode genome to CPPN]
    B --> C[Sample structured point cloud]
    C --> D[Threshold and extract geometry]
    D --> E[Build mesh]
    E --> F[Evaluate effective properties]
    F --> G[Assign fitness / constraints]
    G --> H[Evolve next generation]

Loading

At the repository level, the main metamaterial workflow is:

1. Generate a structured point cloud for the chosen symmetry class.
2. Evaluate a CPPN on the point cloud.
3. Convert scalar outputs into material/void regions.
4. Construct a triangular mesh and enforce geometric constraints.
5. Solve periodic homogenization problems to compute effective properties.
6. Feed the results back into the evolutionary loop.

Repository Layout

.
├── main.py                     # Main entry for metamaterial evolution
├── config.ini                  # Core NEAT and experiment configuration
├── multi_task.py               # Batch task definitions across symmetries/trade-offs
├── gen_pcd.py                  # Point-cloud generation utilities
├── tools/                      # Geometry, meshing, homogenization, constraints, utils
├── neat/                       # Modified local neat-python implementation
├── test/                       # Utility and exploratory test scripts
└── output/                     # Generated results, checkpoints, figures

Main Components

Core metamaterial workflow

• main.py: experiment entry point and genome evaluation loop
• gen_pcd.py: structured point-cloud generation for different symmetry assumptions
• tools/shape.py: contour extraction, triangulation, and geometry handling
• tools/read_mesh.py: conversion from generated geometry to FEniCS meshes
• tools/period.py: periodic homogenization and effective-property computation
• tools/handle_constraints.py: connectivity and validity checks

Evolution engine

• neat/: local fork of neat-python
• neat/population.py: modified population flow for this research setup

Requirements

The main metamaterial pipeline was developed around the following stack:

• Python 3.8
• NumPy
• SciPy
• Matplotlib
• FEniCS / Dolfin
• cvxopt (for some homogenization utilities)

Because this is a research codebase with several experimental branches, dependency management is partly workflow-specific. For the metamaterial experiments, the most important requirement is a working FEniCS/Dolfin environment.

Installation

git clone https://github.com/mh-yan/evo_cppn_material.git
cd evo_cppn_material

Then install the dependencies required by your target workflow:

• Metamaterial pipeline: Python scientific stack + FEniCS/Dolfin

Quick Start

Run the main metamaterial experiment

python main.py

This uses the settings in config.ini and the default trade-off defined in main.py.

Customize the experiment

Edit config.ini to control parameters such as:

• population size
• number of generations
• point-cloud density
• symmetry type (pcdtype)
• novelty/archive parameters

Batch experiments

For multiple experiment definitions, inspect and edit multi_task.py, then enable task collection in main.py.

Output and Data

Typical outputs include:

• evolved genomes (.pkl)
• generated meshes and contours
• fitness distribution plots
• intermediate geometry visualizations

The paper-related metamaterial database is publicly available here:

• Metamaterial Database

Documentation

• DOCUMENTATION.md: detailed Chinese walkthrough of the project structure and workflow

If you are onboarding to the codebase for development or reproducibility work, DOCUMENTATION.md is the best starting point after this README.

Notes on Project Status

This repository combines:

• the main research code used for neuroevolutionary metamaterial discovery
• modified optimization infrastructure built on top of neat-python
• several engineering and downstream exploratory workflows

As a result, some directories are more polished than others; the metamaterial pipeline centered around main.py, config.ini, tools/, and neat/ is the primary reference implementation.

Citation

If you use this repository in academic work, please cite the associated paper:

Maohua Yan, Ruicheng Wang, Ke Liu
Populating cellular metamaterials on the extrema of attainable elasticity through neuroevolution

License

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