## Data Assimilation and Reduced Modeling for High Dimensional Problems

##### CIRM, Luminy, France

##### July 19-August 27, 2021

#### Sampling rare events with generative models

**Supervisors:**T. LeliÃ¨vre, G. Robin, G. Stoltz (Ecole des Ponts ParisTech)

**Students:**Open to 2 students

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Project Description:
**
The dynamics of many molecular systems of interest are metastable, i.e. they spend a lot of time in some regions of the
phase space before hopping to another (free) energy basin. The transition from one basin to another is rare but fast.
The aim of this project would be to generate trajectories which transition between basins, so-called "reactive
trajectories" [1], using generative models such as Variational Auto-Encoders (VAEs) or Generative Adversarial Networks
(GANs) [2]. This would be done in the framework of supervised learning to start with, using a database of reactive
trajectories, and for low dimensional model systems, in order to identify promising learning models. Various extensions
will then be considered in a second step, concerning both the extension to more challenging molecular systems and/or
more challenging learning frameworks (for instance, no use of a database of reactive trajectories).

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References:
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[1] T. LeliÃ¨vre, Two mathematical tools to analyze metastable stochastic processes , in Numerical Mathematics and
Advanced Applications 2011, A. Cangiani, R.L. Davidchack, E. Georgoulis, A.N. Gorban, J. Levesley, M.V. Tretyakov, eds.,
Springer, p. 791-810, (2013)

[2] P. Mehta, M. Bukov, C.-H. Wang, A. G. R. Day, C. Richardson, C. K. Fisher, D. J. Schwab, A high-bias, low-variance
introduction to Machine Learning for physicists, Physics Reports, 810, 1-124 (2019)