Towards the Automatic Discovery of Physical Laws via Accurate Machine Learning and Symbolic Regression

Supervision

Rodrigo Ibata (OBAS, Strasbourg)

Laboratory and team

OBAS, Strasbourg - Team "GALHECOS"

Subject description

This thesis proposes to develop a novel framework to automatically discover interpretable physical laws from observational data. The approach combines two methodologies: a specialized Levenberg-Marquardt optimization algorithm with analytic derivatives for fitting physical models, and a Class-Symbolic-Regression (CSR) method that enforces physical unit consistency across multiple datasets. The key innovation lies in fitting flexible neural networks with accurate derivatives across different physical scenarios, and then rendering the fits interpretable with CSR to discover underlying mathematical laws, conservation principles, and equations of motion. This will represent a significant advance toward automated scientific discovery. The methodology will be applied to study stellar dynamics in the outer Milky Way to map the dark matter distribution, utilizing two major brand new datasets: the 4MOST spectroscopic survey (providing data for over 100,000 RR Lyrae stars) and the LSST. The high-precision 6D phase-space data will enable mapping the gravitational potential and potentially discovering subtle dynamical laws or deviations from standard models.

Related mathematical skills

The ideal candidate will have a strong background in mathematics, physics and computer science, with an interest in numerical methods, optimization, machine learning, and ideally Hamiltonian dynamics. The project will be highly interdisciplinary, offering access to cutting-edge astrophysical data from the latest major observatories (4MOST, LSST).

IRMIA++ is one of the 15 Interdisciplinary Thematic Institute (ITI) of the University of Strasbourg. It brings together a research cluster and a master-doctorate training program, relying on 12 research teams and 9 master tracks.

It encompasses all mathematicians at Université de Strasbourg, with partners in computer science and physics. ITI IRMIA++ builds on the internationally renowned research in mathematics in Strasbourg, and its well-established links with the socio-economic environment. It promotes interdisciplinary academic collaborations and industrial partnerships.

A core part of the IRMIA++ mission is to realize high-level training through integrated master-PhD tracks over 5 years, with common actions fostering an interdisciplinary culture, such as joint projects, new courses and workshops around mathematics and its interactions.

Selection will rely on the professional project of the candidate, his/her interest for interdisciplinarity and academic results.