The Brummer & Partners MathDataLab at the Department of Mathematics, KTH, is organizing online mini-courses for PhD students, postdocs, and faculty. The next course, given in January, is given by Tony Lelievre, ParisTech, on sampling problems in computational physics. Everyone is welcome.
Lecture 1. Zoom, Monday January 18, 15.15-16.15. kth-se.zoom.us/j/63389722507
Lecture 2. Zoom, Tuesday January 19, 15.15-16.15. kth-se.zoom.us/j/63389722507
Lecture 3. Zoom, Thursday January 21, 15.15-16.15. kth-se.zoom.us/j/63389722507
Computational statistical physics is typically a domain where efficient sampling methods are crucial. The objective is indeed to obtain macroscopic properties of materials starting from a microscopic description at the molecular level, using ensemble averages (thermodynamic properties) or averages over paths (dynamical properties). Applications are numerous in very different scientific fields such as molecular biology, chemistry or materials science. The objective of these lectures will be, starting from some prototypical sampling problems raised in statistical physics, to introduce general purpose algorithms which are useful to sample multimodal distributions, rare events and metastable trajectories. More precisely, the first lecture will be devoted to free energy adaptive biasing techniques, and their analysis using entropy techniques or standard methods to prove the convergence of stochastic algorithms. In the second lecture, we will present rare event sampling techniques in order to sample reactive trajectories, namely the pieces of trajectory between metastable states. Finally, the third lecture will be devoted to a discussion of the link between metastable dynamics and jump Markov processes, using the notion of quasi-stationary distribution, and associated algorithms (accelerated dynamics methods).