MINI-SCHOOL 2025

7th edition of the Mini-school on mathematics for theoretical chemistry and physics

(organized by GDR NBODY with support from CNRS Chimie, LCT, LJLL, and ERC EMC2)

In the same spirit than the 1st edition, 2nd edition, 3rd edition, 4th edition, 5th edition, and 6th edition

• Dates: 19-21 May 2025

• Location: Sorbonne Université, Pierre et Marie Curie (or Jussieu) campus, 4 place Jussieu, 75005, Paris. Laboratoire Jacques-Louis Lions, tower/corridor 15-16, 3rd floor, room 309.

• Lecturers: Geneviève Dusson and Gabriel Stoltz.

• Organizers: Eric Cancès, Mi-Song Dupuy, Emmanuel Fromager, Pierre-François Loos, Julien Toulouse. contact email

• List of registered participants

Presentation

The lectures delivered are intended to be of interest to any person working in the field of theoretical chemistry and physics and willing to discover or deepen some mathematical aspects of the field. Master and PhD students, post-docs and any academic are welcome!

Program

Two courses will be proposed:

1 - (Un)supervised learning with applications to molecular dynamics (9 hours) by Gabriel Stoltz (École des Ponts ParisTech)

- What is machine learning? A survey of supervised and unsupervised learning

- Regression in the context of supervised learning

• K-nearest neigbors: a first method to introduce various concepts (excess risk, empirical risk, cross validation, ...)
• linear least-square predictors and the need for regularization to prevent overfitting (ridge/LASSO)
• kernel methods
• trees and ensemble methods
• neural network approaches
• a word on the training of machine learning models (SGD/Adam, minibatching, ...)

- Unsupervised learning

• Clustering
• Dimensionality reduction: linear methods (principal component analysis) and nonlinear ones (autoencoders)
• Application: finding collective variables in molecular dynamics

2 - From machine-learned wavefunctions to interatomic potentials (9 hours) by Geneviève Dusson (CNRS and Université Franche-Comté)

- From wavefunctions to interatomic potentials: What is to be learned

• Quick summary of the theory, Schrödinger equation, Wavefunction, Electronic density, Density matrix, Potential energy surface
• Data, Functionals to approximate, Objective/cost functions

- Atomic descriptors: Dealing with the symmetries, Invariance and equivariance, Review of existing descriptors

- Linear methods (MTP, PIPs, ACE, …) & Kernel methods (GAP)

- Neural networks for interatomic potentials & MACE (tensor network)

- ML wavefunctions: PINNs + PauliNet, FermiNet

Schedule

Monday 19 May Tower 15-16, room 309	Tuesday 20 May Tower 15-16, room 309	Wednesday 21 May Tower 15-16, room 309
8:45-9:00 Arrivals/Welcome
9:00-10:30 Gabriel Stoltz 1	9:00-10:30 Gabriel Stoltz 3	9:00-10:30 Geneviève Dusson 5
10:30-10:45 Coffee break	10:30-10:45 Coffee break	10:30-10:45 Coffee break
10:45-12:15 Gabriel Stoltz 2	10:45-12:15 Gabriel Stoltz 4	10:45-12:15 Geneviève Dusson 6
12:15-14:00 Lunch at L'Ardoise (Tower 25)	12:15-14:00 Lunch at L'Ardoise (Tower 25)	12:15-14:00 Lunch at L'Ardoise (Tower 25)
14:00-15:30 Geneviève Dusson 1	14:00-15:30 Geneviève Dusson 3	14:00-15:30 Gabriel Stoltz 5
15:30-15:45 Coffee break	15:30-15:45 Coffee break	15:30-15:45 Coffee break
15:45-17:15 Geneviève Dusson 2	15:45-17:15 Geneviève Dusson 4	15:45-17:15 Gabriel Stoltz 6

Practical details

Registration

To register, send an email at

minischool@lct.jussieu.fr

and indicate:
- your name and affiliation;
- whether you want to participate to the group lunches;
- whether you are a CNRS staff (either permanent or non permanent).

To facilitate the participation of young researchers, no registration fees will be asked. However, accommodation will not be provided but must be arranged independently by the participants.

Location of the mini-school

The mini-school will take place on the Pierre et Marie Curie (or Jussieu) campus of Sorbonne Université, 4 place Jussieu, 75005 Paris.

Subway (Metro) lines 7 or 10: get off at "Jussieu" station.

From the main entrance of the campus, go to Tower 16. Take the stairs or the elevator to the third level. Find corridor 15-16, and then the room 309. This is the seminar room of Laboratoire Jacques-Louis Lions. All the lectures will take place in this seminar room.

Lunches

Lunches at Restaurant L'Ardoise (Jussieu campus, entrance near Tower 25) will be offered to the first 50 registered participants to the mini-school (see the list of registered participants on the page List of registered participants).

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