Extended-Lagrangian-SINDy-xL-SINDy-

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Extended-Lagrangian-SINDy-xL-SINDy-

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Repository for xL-SINDy, a robust algorithm to extract Lagrangian of nonlinear dynamical systems from noisy measurement data.

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# Extended-Lagrangian-SINDy-xL-SINDy-

## Overview
Extended Lagrangian SINDy (xL-SINDy) is a learning based algorithm designed to obtain Lagrangian function of nonlinear dynamical systems from noisy measurement data. This method is inspired by [SINDy](https://www.pnas.org/content/113/15/3932) (the Sparse identification of Nonlinear Dynamics). The Lagrangian function is modeled as a linear combination of nonlinear candidate functions, and Euler-Lagrange’s equation is used to formulate the objective cost function. The optimization of the learning process is done with proximal gradient method.

![overview](https://raw.githubusercontent.com/AdamPurnomo/Extended-Lagrangian-SINDy-xL-SINDy-/main/images/overview.png)

## Examples
The effectiveness of xL-SINDy  is demonstrated against different noise levels in physical simulation with four dynamical systems: A single pendulum, a cart-pendulum, a double pendulum, and a spherical pendulum.

## Installation
* Clone this repository `git clone https://github.com/AdamPurnomo/Extended-Lagrangian-SINDy-xL-SINDy-.git`
* Install the environment and dependencies `conda env create -f environment.yml`

## How to Use
Please take a look at `Source/Notebook/[System Name] - Train.ipynb` or `Source/Python Script/[System Name]_Train.py` and run the code.

## Dependencies
* numpy 1.19.2
* scipy 1.6.1
* pytorch 1.9.0
* sympy 1.7.1

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