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# QUNOM23 inverse problems tutorial # Solving high-dimensional inverse problems with tensor compression
## Tutorial summary
Solving inverse problems using the Bayesian framework to allow not only parameter determination but also quantification of parameter uncertainties is a well established principle.
## Getting started In optical applications, the forward model used to simulate the scattering process is often computationally very demanding, which renders determining the shape of the parameter distribution through standard methods such as MCMC prohibitively time consuming.
In these cases the forward model is typically bypassed by some kind of surrogate, i.e., an approximation that can be evaluated efficiently such as polynomial chaos, Gaussian processes or neural networks.
To make it easy for you to get started with GitLab, here's a list of recommended next steps. When the number of sought after parameters gets sufficiently large, however, computing such surrogates becomes difficult and often requires even more time and storage than the original MCMC run.
Already a pro? Just edit this README.md and make it your own. Want to make it easy? [Use the template at the bottom](#editing-this-readme)! As an alternative to alleviate this problem, we will discuss how tensor formats can be used to compress the required surrogate to keep things computationally feasible.
Moreover, these formats potentially allow us to construct a functional representation of the Bayesian posterior, which yields the possibility to compute quantities of interest such as mean, variance, higher-order moments and marginals analytically without the need for sampling.
## Add your files
## Setup
- [ ] [Create](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#create-a-file) or [upload](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#upload-a-file) files After cloning the repository, you need to ensure all required python packages are installed.
- [ ] [Add files using the command line](https://docs.gitlab.com/ee/gitlab-basics/add-file.html#add-a-file-using-the-command-line) or push an existing Git repository with the following command: A specification of all requirements and their respective versions are listed in the `environment.yml` file.
You can use this file to create a new conda environment called `qunom23`, which is ready to execute the files of this repository.
To do so, run the following line in the repositry root (where this README is located):
```sh
conda env create -f environment.yml
``` ```
cd existing_repo Then start the environment using `conda activate qunom23`.
git remote add origin https://gitlab1.ptb.de/ptb-843/qunom23-inverse-problems-tutorial.git
git branch -M main
git push -uf origin main
```
## Integrate with your tools
- [ ] [Set up project integrations](https://gitlab1.ptb.de/ptb-843/qunom23-inverse-problems-tutorial/-/settings/integrations)
## Collaborate with your team
- [ ] [Invite team members and collaborators](https://docs.gitlab.com/ee/user/project/members/)
- [ ] [Create a new merge request](https://docs.gitlab.com/ee/user/project/merge_requests/creating_merge_requests.html)
- [ ] [Automatically close issues from merge requests](https://docs.gitlab.com/ee/user/project/issues/managing_issues.html#closing-issues-automatically)
- [ ] [Enable merge request approvals](https://docs.gitlab.com/ee/user/project/merge_requests/approvals/)
- [ ] [Automatically merge when pipeline succeeds](https://docs.gitlab.com/ee/user/project/merge_requests/merge_when_pipeline_succeeds.html)
## Test and Deploy
Use the built-in continuous integration in GitLab.
- [ ] [Get started with GitLab CI/CD](https://docs.gitlab.com/ee/ci/quick_start/index.html)
- [ ] [Analyze your code for known vulnerabilities with Static Application Security Testing(SAST)](https://docs.gitlab.com/ee/user/application_security/sast/)
- [ ] [Deploy to Kubernetes, Amazon EC2, or Amazon ECS using Auto Deploy](https://docs.gitlab.com/ee/topics/autodevops/requirements.html)
- [ ] [Use pull-based deployments for improved Kubernetes management](https://docs.gitlab.com/ee/user/clusters/agent/)
- [ ] [Set up protected environments](https://docs.gitlab.com/ee/ci/environments/protected_environments.html)
*** ## How to use this repository
**TODO:** describe which scripts to run and how.
# Editing this README
When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!). Thank you to [makeareadme.com](https://www.makeareadme.com/) for this template.
## Suggestions for a good README
Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
## Name
Choose a self-explaining name for your project.
## Description
Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
## Badges
On some READMEs, you may see small images that convey metadata, such as whether or not all the tests are passing for the project. You can use Shields to add some to your README. Many services also have instructions for adding a badge.
## Visuals
Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
## Installation
Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
## Usage
Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
## Support
Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc.
## Roadmap
If you have ideas for releases in the future, it is a good idea to list them in the README.
## Contributing
State if you are open to contributions and what your requirements are for accepting them.
For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
You can also document commands to lint the code or run tests. These steps help to ensure high code quality and reduce the likelihood that the changes inadvertently break something. Having instructions for running tests is especially helpful if it requires external setup, such as starting a Selenium server for testing in a browser.
## Authors and acknowledgment ## Authors and acknowledgment
Show your appreciation to those who have contributed to the project. This repository has been created and is maintained by N. Farchmin, PTB Group 8.43.
TODO: Acknowledge funding from ATMOC
## License
For open source projects, say how it is licensed.
## Project status
If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.
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