DualMaxwell: Hybrid Dual-Network PINN for Maxwell's Equations

This repository provides the official Python implementation for the paper: "A Novel, Hybrid, Dual-Network PINN Framework for Solving Maxwell's Equations: Overcoming Numerical Instabilities, Scale Imbalance, and Sharp Geometries".

This package implements a framework for simulating electromagnetic (EM) fields by solving the full, 4D, vector Maxwell's equations using Physics-Informed Neural Networks (PINNs).

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Key Features & Challenges Addressed

This framework is specifically engineered to solve critical failure modes in standard PINN implementations:

1. The Scale Challenge: Overcomes the inherent "Scale Imbalance" (up to $10^9$) between Electric ($E$) and Magnetic ($B$) fields using non-dimensionalization.
2. The Geometry Challenge: Utilizes GeoNet (a Multi-Resolution Hash Grid) to learn "sharp" geometry SDFs, avoiding the smoothing bias of standard MLPs.
3. The Training Challenge: Implements a dual-network strategy with aggressive weight balancing to prevent "Catastrophic Forgetting" and trivial solutions.

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Installation

You can install and run this framework on a local machine or in cloud environments like Google Colab.

Note: This repository contains large model files (.pth). If running locally, ensure you have Git LFS installed.

Option 1: Google Colab (Recommended for Testing)

If you are running this on Google Colab, copy and paste the following commands into a code cell:

# 1. Clone the repository from Hugging Face
!git clone https://huggingface.co/ayda138000/DualMaxwell

# 2. Enter the directory
%cd DualMaxwell

# 3. Install the package and dependencies
!pip install .
!pip install torch numpy matplotlib huggingface_hub

Option 2: Local Machine (Terminal)

# Install Git LFS if you haven't already
git lfs install

# Clone the repository
git clone https://huggingface.co/ayda138000/DualMaxwell

# Navigate to the folder
cd DualMaxwell

# Install the package
pip install .

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Running the Simulation

The repository includes an example_usage.py script that loads the pre-trained models (GeoNet and PhysNet) and visualizes the results.

CRITICAL: Prepare Your Data (ground_truth.npz)

Before running the example, provide your own data file:

• The script expects a file named ground_truth.npz in the root DualMaxwell directory.
• Google Colab: Upload your .npz file into the DualMaxwell folder via the "Files" tab on the left sidebar.
• Local: Place the file in the cloned directory.

Required Data Structure

Your ground_truth.npz file must contain the following NumPy arrays:

• coords: Shape (N, 3). Spatial coordinates $(x, y, z)$ used to normalize the geometry inputs.
• t: Shape (T_steps,) or (N, 1). Time data, used to determine the maximum simulation time ($T_{max}$).

Note: If this file is missing or the keys coords and t do not exist, the script will exit with an error.

Execution

Once the file is uploaded/placed, run the script:

In Google Colab:

!python example_usage.py

In Terminal:

python example_usage.py

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Expected Output

The script performs the following actions:

1. Loads GeoNet (geonet_real_v30.pth) to handle geometry boundaries.
2. Loads PhysNet (physnet_v31_real.pth) to predict EM fields.
3. Visualizes the $E_x$ field at time $t = 0.75 \times T_{max}$.
4. Saves the result as an image: v35_final_plot_defense.png.

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Models Included

• GeoNetHash: Pre-trained on the geometry SDF using Multi-Resolution Hash Grids.
• MaxwellPINN: The physics-informed network trained to solve Maxwell's equations.

License

This project is licensed under the MIT License.