Design-GenNO: Physics-Informed Generative Neural Operator for Inverse Microstructure Design

This repository provides the official implementation of Design-GenNO, a novel physics-informed generative model based on neural operators for inverse microstructure design.

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🌟 Overview

Design-GenNO is a physics-informed deep generative neural operator framework for inverse microstructure design. It unifies generative modeling, operator learning, and physics-informed training to design microstructures that meet user-specified targets such as effective properties or microscopic field responses.

✨ Key Features

• Generative Neural Operator framework combining MultiONet decoders with a structured latent space
• Physics-informed training using PDE residuals, reducing reliance on costly labeled data
• Normalizing Flow prior for efficient sampling and robust optimization
• Supports diverse inverse design tasks:
  • Property-matching problems
  • Microstructure recovery from field measurements
  • Maximization of anisotropic conductivity ratios
• Demonstrates strong out-of-distribution generalization beyond training data

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🎯 Inverse Microstructure Design Problems

This framework addresses three key inverse design problems:

Problem 1: Property-Targeted Design

Objective: Given a target region $\mathcal{T}d$ in the effective property space, design microstructures $\mu$ whose effective property $\kappa{\text{eff}}$ lies within $\mathcal{T}_d$.

Applications: Materials with specified thermal/electrical conductivity, stiffness, or other bulk properties.

Problem 2: Field Response Matching

Objective: Given a target field $u_d$ on domain $\Omega$, identify microstructure(s) $\mu$ such that the corresponding field prediction satisfies $u \approx u_d$.

Applications: Temperature distribution matching, stress field engineering, wave propagation control.

Problem 3: Property Optimization

Objective: Given a utility function $F$, design microstructures $\mu$ that maximize the objective $F(\kappa_{\text{eff}})$.

Applications: Maximizing anisotropic conductivity ratios, optimizing thermal performance, enhancing mechanical properties.

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⚙️ Dependencies

The implementation relies on the following Python packages:

torch==2.2.0
scipy==1.12.0
tqdm==4.66.1
h5py==3.10.0
matplotlib==3.8.2
scikit-learn==1.7.2
scienceplots==2.1.1

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📂 Datasets and Trained Models

All datasets and trained models are publicly available on Kaggle: Design-GenNO Dataset

📦 Data Structure

• Dataset/ - Training and testing datasets
• saved_models/ - Pretrained Design-GenNO models

Download these folders and place them in the same directory as the training scripts.

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🚀 Usage Instructions

Step 1. Configure the Environment

Install the required Python packages:

pip install torch==2.2.0 scipy==1.12.0 tqdm==4.66.1 h5py==3.10.0 matplotlib==3.8.2 scikit-learn scienceplots

Step 2. Prepare Data and Models

Download the datasets and pretrained models from the Kaggle dataset and place them in the project directory.

Step 3. Train Design-GenNO Model

Mixed-driven training (using both labeled data and PDE residuals):

nohup python3 -u DesignGenNO_MixedDriven.py > out_mixed &

Physics-driven training (using only PDE residuals):

nohup python3 -u DesignGenNO_PhysicsDriven.py > out_physics &

Step 4. Solve Inverse Design Problems

Navigate to the corresponding Jupyter Notebook for your problem of interest and execute it to reproduce the numerical results.

Example notebooks:

• InverseDesign_P1_region_case1.ipynb - Design microstructures with target effective properties (in-distribution)
• InverseDesign_P1_region_case2.ipynb - Design microstructures with target effective properties (out-of-distribution)
• InverseDesign_P2_target_T.ipynb - Microstructure recovery from field measurements
• InverseDesign_P3_maximize.ipynb - Maximize anisotropic conductivity ratios

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📄 Citation

If you use this work in your research, please cite:

@article{zang2026design,
  title={Design-GenNO: A physics-informed generative model with neural operators for inverse microstructure design},
  author={Zang, Yaohua and Koutsourelakis, Phaedon-Stelios},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={450},
  pages={118597},
  year={2026},
  publisher={Elsevier}
}