TEDEouS - Torch Exhaustive Differential Equation Solver

The purpose of the project

1. Make equation discovery more transparent and illustrative
2. Combine power of pytorch, numerical methods and math overall to conquer and solve ALL XDEs(X={O,P}). There are some examples to provide a little insight to an operator form

Table of Contents

• Core features
• Installation
• Examples
• Project Structure
• Documentation
• Getting started
• License
• Contacts
• Citation

Core features

• Solve ODE initial- or boundary-value problems
• Solve PDE initial-boundary value problems
• Use variable models and their differentiation methods
• Faster solution using cache

Installation

TEDEouS can be installed with pip:

$ git clone https://github.com/ITMO-NSS-team/torch_DE_solver.git
$ cd torch_DE_solver
$ pip install -r requirements.txt

Examples

After the TEDEouS is installed the user may refer to various examples that are in examples forlder.

$ cd examples

Every example is designed such that the boxplots of the launches are commented and the preliminary results are not shown, but stored in separate folders.

• Legendre polynomial equation

$ python example_ODE_Legendre.py

or

$ python example_ODE_Legendre_autograd.py

• Panleve transcendents (others are placed in 'examples\to_renew' folder due to the architecture change)

$ python example_Painleve_I.py

• Wave equation (non-physical conditions for equation discovery problem)

$ python example_wave_paper_autograd.py

• Wave equation (initial-boundary value problem)

$ python example_wave_physics.py

• Heat equation

$ python example_heat.py

• KdV equation (non-physical conditions for equation discovery problem)

$ python example_KdV.py

• KdV equation (solitary solution with periodic boundary conditions)

$ python example_KdV_periodic.py

• Burgers equation and DeepXDE comparison

$ python example_Burgers_paper.py

Project Structure

Stable version is located in the master branch.

Documentation

https://torch-de-solver.readthedocs.io/en/docs/index.html

Getting started

Schroedinger equation example step-by-step https://torch-de-solver.readthedocs.io/en/docs/tedeous/examples/schrodinger.html

License

TEDEouS is distributed under BSD-3 licence found in LICENCE file

Contacts

• Feel free to make issues or contact @SuperSashka directly

Citation

@article{hvatov2023solver,
AUTHOR = {Hvatov, Alexander},
TITLE = {Automated Differential Equation Solver Based on the Parametric Approximation Optimization},
JOURNAL = {Mathematics},
VOLUME = {11},
YEAR = {2023},
NUMBER = {8},
ARTICLE-NUMBER = {1787},
URL = {https://www.mdpi.com/2227-7390/11/8/1787},
ISSN = {2227-7390},
DOI = {10.3390/math11081787}
}