/LSN_code

Lie Symmetry Net

Primary LanguagePython

LSN: Preserving Conservation Laws in Modelling Financial Market Dynamics via Differential Equations

License: MIT arXiv

This paper introduce LSN, a symmetry-aware approach that addresses a fundamental challenge in AI-driven SDE solvers: ensuring AI models can learn and preserve intrinsic symmetries from data. By incorporating Lie symmetry principles, LSN achieves a significant reduction in test error—over an order of magnitude—compared to state-of-the-art AI-driven methods. The framework is not limited to specific equations or methods but provides a universal solution that can be applied across various AI-driven differential equation solvers.

Typing SVG

Installation

Step 1: install pytorch

 conda install pytorch==1.13.1 torchvision==0.14.1 torchaudio==0.13.1 pytorch-cuda=11.7 -c pytorch -c nvidia
 
Step 2: install pyDOE 
   
 pip install pyDOE

Schematic Diagram of Lie Symmetry Network

Run

For task start run this command from repository root directory:

python LSN.py

Citation

Please consider citing our paper if you find this repo useful in your work.

@article{jiang2024lie,
  title={Lie Symmetry Net: Preserving Conservation Laws in Modelling Financial Market Dynamics via Differential Equations},
  author={Jiang, Xuelian and Zhu, Tongtian and Wang, Can and Xu, Yingxiang and He, Fengxiang},
  journal={arXiv preprint arXiv:2406.09189},
  year={2024}
}