Autoregressive Inverse Design of Disordered Metamaterials for Target Nonlinear Response

Dazhi Zhao¹, Yujie Xiang¹, Peng Zhang¹, Ning Liu¹, Xianqiao Wang², Keke Tang^1,3*
1School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
²School of ECAM, College of Engineering, University of Georgia, Athens, GA 30602, USA
³Key Laboratory of AI-aided Airworthiness of Civil Aircraft Structures, Civil Aviation Administration of China, Tongji University, Shanghai 200092, China
^*Corresponding author: kktang@tongji.edu.cn (Keke Tang)

Abstract

The pursuit of novel mechanical metamaterials faces a core dilemma: while introducing architectural disorder unlocks unprecedented design space, it jeopardizes the structural connectivity essential for mechanical integrity. We introduce a data-driven framework to resolve this critical trade-off in programming nonlinear responses. Our approach pairs a generative autoregressive model for inverse design with a surrogate model for rapid forward prediction. The autoregressive model learns implicit connectivity rules from data to sequentially build valid structures targeting specific performances. We demonstrate that this method successfully designs disordered metamaterials with target nonlinear properties on demand. Analysis of the model's internal mechanism reveals its learned strategies for maintaining connectivity, highlighting a critical yet controllable trade-off between performance and connectivity. The framework exhibits strong interpolation and extrapolation capabilities, generating novel designs that outperform those in the training set. By providing a powerful and generalizable design tool, this work establishes a pathway to reliably meet complex functional requirements with disordered metamaterials, moving them from conceptual appeal toward practical viability.
Keywords: Data-Driven Design, Disordered Metamaterials, Structural Connectivity, Autoregressive Model, Inverse Design, Nonlinear Response

Environment Setup

Clone this repository to your local machine, and install the dependencies.

git clone git@github.com:dazhizhao/Autoregressive-Inverse-Design-for-Disordered-Metamaterials.git 
pip install -r requirements.txt

Dataset & Checkpoints

You can find the all the dataset and checkpoints we adopted in this paper from Google Drive.
To remind you, our metamaterial structures are stored through .mat format and nonlinear responses are stored through .xlxs format. Plz prepare the correct software/tool to open it.

Usage

Autoregressive Transformer Model for Inverse Design

If you wanna see more details about the autoregressive process, play the gif below:

Training Stage

To train the autoregressive transformer model, run this code:

  cd inverse
  python inverse.py

Inference Stage

Plz carefully check your own weight path path_to_the_weight below.
For inversely designing the target obtained from disordered structures, run this code:

  cd inverse
  python post_process.py --ckpt_path path_to_the_weight --top_p 0.95 --temperature 1.0

For inversely designing the target obtained from periodic structures, run this code:

  cd inverse
  python post_process_base.py --ckpt_path path_to_the_weight --top_p 0.95 --temperature 1.0

Fourier Neural Operator for Forward Prediction

Training Stage

To train the forward Fourier Neural Operator, run this code:

  cd forward
  python train_fno.py

Inference Stage

For forward predicting the nonlinear response from certain structures, run this code:

  cd forward
  python inference.py

Citation

If you find our work helpful for you, plz cite and have a star for us! 😊

@article{zhao2025ardisorder,
  title={Autoregressive Inverse Design of Disordered Metamaterials for Target Nonlinear Response},
  author={Zhao, Dazhi and Xiang, Yujie and Zhang, Peng and Liu, Ning and Wang, Xianqiao and Tang, Keke},
  booktitle={Thin-Walled Structures},
  year={2025}
}

Computing Resource Report

We report that all training and inference procedures for both models were conducted on a single NVIDIA RTX 4090 (24GB) GPU with the platform Openbayes.

License

This project is licensed under the MIT License, see the LICENSE file for details.