Tensorized Deep Physics Informed Neural Networks

This repository contains an implementation of Tensorized Physics Informed Neural Networks (TPINNs) for solving physics-based problems. TPINNs combine the power of neural networks with the physical laws governing the system to improve accuracy and generalization. 🚀

📚 Introduction

Tensorized Physics Informed Neural Networks (TPINNs) are a class of neural networks that incorporate known physical laws into their architecture. By including the governing equations of a system as constraints, TPINNs can solve complex physics-based problems more accurately than traditional neural networks. This repository provides an implementation of TPINNs using TensorFlow. ♾️

✔️ Requirements

To run the code in this repository, you need the following dependencies:

• Python (>= 3.6)
• TensorFlow (>= 2.0)
• NumPy (>= 1.18)

💾 Installation

1. Clone the repository:

   git clone git@github.com:mvanzulli/TPINN.git
   

2. Navigate to the project directory:

   cd TPINN
   

3. Install the required dependencies:

   pip install -r requirements.txt
   

💻 Usage

To utilize TPINNs in your own projects, follow these steps:

1. Import the necessary modules:

   import tensorflow as tf
   import numpy as np
   from tn_layer import TNLayer
   from tn_model import TNModel

2. Create an instance of the TNLayer class:

   tn_layer = TNLayer(input_dim, bond_dim, activation, kernel_initializer, use_bias, bias_initializer)

   Replace the arguments with the desired values. input_dim is the dimensionality of the input tensor, bond_dim is the bond dimension of the TN layer, activation is the activation function to use, kernel_initializer is the initializer for the weight matrices, use_bias specifies whether to include a bias term, and bias_initializer is the initializer for the bias term.

3. Create an instance of the TNModel class:

   tn_model = TNModel(num_layers, MPO_units, output_dim, bond_dim, activation, use_bias, kernel_initializer, bias_initializer, dif_equation)

   Replace the arguments with the desired values. num_layers is the number of TN layers, MPO_units is the number of units in the MPO tensor, output_dim is the dimension of the output, bond_dim is the bond dimension of the TN layer (optional), activation is the activation function to use, use_bias specifies whether to include a bias term, kernel_initializer is the initializer for the weight matrices, bias_initializer is the initializer for the bias term, and dif_equation is a callable representing the one-dimensional fourth-order PDE.

4. Use the TNModel to perform forward pass and compute the PDE loss:

   y_pred = tn_model.call(x)
   pde_loss = tn_model.compute_pde_loss(x)

   Replace x with the input tensor.

🚀 Examples

An example usage of TPINNs can be found in the examples directory. It demonstrates how to solve a physics-based problem using TPINNs.

👥 Contributing

Contributions to this repository are welcome. Feel free to open issues or submit pull requests.

📃 License

This project is licensed under the MIT License.