Physical Law Learning
Master's thesis / Bachelor's thesis / guided research
Strongly dependent on the specific topic.
For the most time of the history of humankind, scientists had to discover physical laws on their own using observations. However, the increase of available data and computing power and the general advance of artificial intelligence recently triggered the idea to automate this search for physical laws. Physical law learning aims to learn the function governing a (physical) phenomenon exactly, such that they are interpretable and offer more insight than black box prediction solutions. Possible thesis topics range from applying existing algorithms to new fields or devising new algorithms to tackling theoretical questions about PDE learning.
- Review paper: https://arxiv.org/abs/2211.10873
- Seminal work in phyiscal law learning using genetic programming: https://www.science.org/doi/abs/10.1126/science.1165893
- Introducing SINDy (a form of sparse regression) to compute physical laws: https://www.pnas.org/doi/10.1073/pnas.1517384113
- Modelling the physical law as a neural network: http://proceedings.mlr.press/v80/sahoo18a.html
- Using transformers to compute physical laws: https://arxiv.org/abs/2204.10532
- Theoretical work tackling the uniqueness problem: https://arxiv.org/abs/2210.08342