NNODE

A Data-Free Framework for Solving Ordinary Differential Equations and Refining Trajectories with Neural Networks.

Introduction

NNODE (Neural Network for Ordinary Differential Equations) is a novel data-free learning framework for solving Ordinary Differential Equations (ODEs) and refining trajectories using neural networks. The framework eliminates the need for ground truth by embedding differential equations into the loss functions via automatic differentiation. By introducing boundary conditions as network inputs, the framework is capable of solving ODEs under varying boundary conditions through one-shot training. In addition, it provides a concise and efficient method for trajectory refinement by utilizing the gradients of outputs with respect to the boundary conditions.

Model

Demos

Applications

Dependencies

1. Create a conda environment.

   conda create -n nnode python=3.12
   conda activate nnode

2. Install dependencies.

   pip install torch

   NOTE: install gpu version of PyTorch if needed.

   pip install matplotlib scipy loguru tqdm tensorboard tensorboardX

3. Download the repository.

   git clone git@github.com:ZhanyuGuo/NNODE.git

Run

1. Update the options in src/NNODE/options.py.

   NOTE: set num_workers to 0 if you are using Windows.

2. Run the training script.

   source scripts/train.sh

3. Run the testing script.

   source scripts/test.sh

4. (optional) Use convert script to convert into scripted model which can be used in libtorch (Pytorch C++ API).

   source scripts/convert.sh

   More details will be available in the open source repository soon.