Extreme events are of primarily importance for understanding the impact of climate change. However, because they are too rare and realistic models are too complex, traditional deep neural networks are inefficient for predictions. We cope with this lack of data using rare event simulations. From the best climate models, we oversample extremely rare events and obtain several hundreds more events than with usual climate runs, at a fixed numerical cost. Coupled with deep neural networks this approach improves drastically the prediction of extreme heat waves.[-]

We will present sampling algorithms which are used in computational statistical physics to sample multimodal measures and metastable dynamics. More precisely, we will focus on free energy adaptive biasing techniques to approximate thermodynamic quantities, and accelerated dynamics methods to sample the state-to-state dynamics of a metastable trajectory. The mathematical analysis of these algorithms relies on entropy techniques, and quasi-stationary distributions.[-]

The two workhorses of molecular simulation are molecular dynamics and Markov-chain Monte Carlo. In this talk we compare them with an alternative: 'Event chain Monte Carlo' in which detailed balance is replaced by the weaker balance condition. We characterise the large scale dynamics of each method pointing out where event chains can give rise to more efficient or more accurate calculations. By optimising the splitting of interactions in event chain methods we show (in hard sphere systems) that we are able to further accelerate the sampling of density modes.[-]

RBMs are generative models capable of fitting complex dataset's probability distributions. Thanks to their simple structure, they are particularly well suited for interpretability and pattern extraction, a feature particularly appealing for scientific use. In this talk, we show that RBMs operate in two distinct regimes, depending on the procedure followed to estimate the log-likelihood gradient during the training. Short sampling times fit machines that are trained to reproduce exactly the dynamics followed to train them, long samplings (as compared to the MCMC mixing time) are need to learn a good model for the data. The non-equilibrium regime should be used to generate high quality samples in short learning and sampling times, but cannot be used to extract the unnormalized data probability of the data necessary for interpretability. In practice, it is hard to extract good equilibrium models for structured datasets (which is the typical case in biological applications) due to a divergence of the Monte Carlo mixing times. In this work, we show this barrier can be surmounted using biased Monte Carlo methods. [-]

Computer simulations give unique insights into the microscopic behavior of dense liquids approaching a glass transition. A major computational problem is that these systems take a very long time to reach thermal equilibrium. Monte Carlo approaches appear as a possible tool to produce very fast equilibrium glassy configurations by developing unphysical but smart algorithms to move the particles. I will review some possible solutions to this problem, and will emphasize a recent 'swap' Monte Carlo algorithm which dramatically speeds up the equilibration in realistic models of glasses. [-]