ReCoDE project - Euler-Maruyama method¶

Description¶

This code is part of the Research Computing and Data Science Examples (ReCoDE) projects. The project consists of a Python class containing the Euler-Maruyama (EM) method for the numerical solution of a Stochastic Differential Equation (SDE). SDEs describe the dynamics that govern the time-evolution of systems subjected to deterministic and random influences. They arise in fields such as biology, physics or finance to model variables exhibiting uncertain and fluctuating behaviour. Being able to numerical solve an SDE is essential for these fields, especially if there is no closed-form solution. This project provides an object-oriented implementation of the EM method. Throughout the project, it is emphasised the benefits that class encapsulation provides in terms of code modularity and re-usability.

Learning Outcomes¶

This project is designed for Master's and Ph.D. students with basic Python knowledge and need to solve SDEs for their research projects. After going through this project, students will:

1. Understand how to solve an SDE using the EM method.
2. Learn to encapsulate the EM method code into a Python class.
3. Explore how to parallelise the code to improve solution speed.

Requirements¶

System¶

Dependencies¶

Project Structure¶

.
├── .github/workflows
│   └── tests_workflow.yaml
├── docs
│   ├── 1-Introduction.ipynb
│   ├── 2-Probability-Distributions.ipynb
│   ├── 3-Euler-Maruyama-Method.ipynb
│   ├── 4-Euler-Maruyama-Class.ipynb
│   └── 5-Parallel-Euler-Maruyama-Class.ipynb
├── src
│   └── euler_maruyama
│       ├── __init__.py
│       ├── coefficients.py
│       ├── euler_maruyama.py
│       └── parallel_euler_maruyama.py
├── tests
│   ├── test_coefficient.py
│   ├── test_euler_maruyama.py
│   └── test_parallel_euler_maruyama.py
├── .gitignore
├── poetry.lock
├── poetry.toml
├── pyproject.toml
├── README.md
└── requirements.txt

Getting Started¶

You can read the Jupyter notebooks non-interactively on Github. Click here to view the collection of Jupyter notebooks located in the docs folder. However, for an improved experience, we suggest cloning the Github repository and running the Jupyter notebooks on your local machine. To assist you setting up the project locally, we provide a list of steps:

1. Clone the repository¶

After installing git in your local machine, you can run the following command in a terminal:

git clone https://github.com/ImperialCollegeLondon/ReCoDe_Euler_Maruyama.git euler-maruyama
cd euler-maruyama

2. Install poetry¶

Once you have downloaded a Python version, you need to install poetry. Poetry is a dependency management and packaging tool for Python projects that simplifies the process of managing dependencies and distributing packages. It allows you to define project dependencies in a pyproject.toml file and provides commands to install, update, and remove dependencies. The main advantages of poetry include dependency resolution to ensure consistent environments, the management of virtual environments for isolation and simplified package publishing. It streamlines the development workflow and facilitates collaboration by providing a unified and straightforward approach to managing dependencies in Python projects. You can find more information in its documentation. Our main focus here is to use poetry to install the project and their dependencies locally.

pip install poetry

You can check that poetry has been successfully installed by running:

poetry --version
Poetry (version 1.4.0)

3. Install the project¶

Now, we need to install the project and its requirements. You can run the following command in the folder where you downloaded the Github repository:

poetry install

This command creates a virtual environment in the same folder you are working, as specified by the poetry.toml configuration file of the project. Then, the packages requirements are installed and finally, the project is installed locally with the name euler-maruyama version (0.1.0).

4. Activate the local environment¶

Run the following command to activate the local environment you created in the previous step:

poetry shell

5. Launch the Jupyter notebooks¶

You can run this command to launch the Jupyter notebook:

jupyter notebook

Now, you can explore and experiment with the different notebook examples we have prepared to help you understand this project.

6. Close the environment¶

If you have closed the Jupyter notebooks and want to exit from the local environment, just run:

exit