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  **A geometric deep learning framework for the inverse design of 3D crystal structures using E(n)-Equivariant Denoising Diffusion Probabilistic Models (DDPM).**
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- ![Streamlit Web App](cry_test.png)
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- *(CrystalDiff interactive web application generating novel Perovskite structures in real-time.)*
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  ---
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  2. **Covalent Bonding (~1.9 Å):** The first sharp peak aligns perfectly with standard Titanium-Oxygen bond lengths, demonstrating the model learned local chemical environments from scratch.
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  3. **Lattice Formation:** Secondary peaks (> 2.5 Å) confirm the generation of long-range repeating crystalline order.
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- ---
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- ## 🚀 Installation & Usage
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-
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- ### Prerequisites
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- * Python 3.8+
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- * PyTorch
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- * Materials Project API Key (`mp-api`)
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-
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- ### 1. Clone & Install
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- ```bash
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- git clone [https://github.com/YOUR_USERNAME/CrystalDiff.git](https://github.com/YOUR_USERNAME/CrystalDiff.git)
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- cd CrystalDiff
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- pip install -r requirements.txt
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- ```
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- ### 2. Fetch the Dataset
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- ```bash
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- python src/data_loader.py
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- ```
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-
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- ### 3. Train the Model
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- Train the Equivariant Diffusion model.
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- ```bash
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- python train.py
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- ```
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- ### 4. Run the Web Application
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- ```bash
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- streamlit run app.py
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- ```
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  ## 📚 References & Inspiration
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  **A geometric deep learning framework for the inverse design of 3D crystal structures using E(n)-Equivariant Denoising Diffusion Probabilistic Models (DDPM).**
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  ---
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  2. **Covalent Bonding (~1.9 Å):** The first sharp peak aligns perfectly with standard Titanium-Oxygen bond lengths, demonstrating the model learned local chemical environments from scratch.
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  3. **Lattice Formation:** Secondary peaks (> 2.5 Å) confirm the generation of long-range repeating crystalline order.
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  ## 📚 References & Inspiration
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