🌀 Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty

📖 Introduction

Diffusion-Inversion-Net (DIN) is a deep learning framework for probabilistic inversion of groundwater flow and solute transport processes. It utilizes diffusion models as geological priors and directly generates posterior parameter ensembles without iterative forward simulations.

DIN: Groundwater Permeability Gaussian Field Diffusion

DIN: Groundwater Permeability TI Field Diffusion

✨ Key Highlights

• 🔄 Direct Probabilistic Inversion: End-to-end framework for hydraulic conductivity field characterization
• 🎯 Conditional Diffusion Models: Incorporates sparse multi-source data (hydraulic head, concentration, conductivity)
• 📊 Uncertainty Quantification: Generates posterior ensembles for reliable uncertainty assessment
• ⚡ Computational Efficiency: Bypasses traditional iterative forward simulations

🚀 Quick Start

Installation

git clone https://github.com/your_username/Diffusion-Inversion-Net.git
cd Diffusion-Inversion-Net

Training

python main.py

Sampling

Please use "Sampling.ipynb" for field generations.

Folder Structure

Diffusion-Inversion-Net/
├── functions/
│   ├── data.py          # Data loading & preprocessing
│   └── trainer.py       # Training loops & optimization
├── models/
│   ├── model.py         # Main network architecture
│   └── ddpm.py          # Diffusion model implementation
├── main.py              # Main training & sampling script
└── sampling.ipynb       # Interactive analysis notebook

🧠 Methodology

DIN integrates diffusion models and physical constraints in a unified inversion framework:

🎯 Core Framework

• Dual Components: Geological prior (DDPM) + Data-consistency mechanism
• Conditional Guidance: Classifier-free guidance (CFG) with guidance scale λ balances geological realism and observation fidelity
• Alignment Loss: Augments diffusion loss with physical consistency term: L_total = L_denoising + ηL_alignment

🔄 Sampling Process

1. Sample initial noise m_T ~ N(0,I)
2. Progressive denoising with conditional guidance
3. Generate ensembles through stochastic sampling

📊 Uncertainty Quantification

• Implicit Bayesian inference via diffusion process
• Ensemble generation M = {m₀⁽¹⁾, m₀⁽²⁾, ..., m₀⁽Nₑ⁾}
• Statistical analysis of inversion uncertainty

🏗️ Implementation

• Modified U-Net backbone for noise prediction
• Three conditional injection strategies
• End-to-end probabilistic inversion

📝 Citation

@article{zhang2024diffusion,
  title={Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty},
  author={Zhang, Xun and Yang, Weijie and Jiang, Simin},
  year={2024}
}

📮 Contact

• Xun Zhang, College of Civil Engineering, Tongji University, Shanghai, China.
• Weijie Yang, School of Information, University of California, Berkeley, United States.
• Corresponding author: Simin Jiang (jiangsimin@tongji.edu.cn)