Fiches de cours

Statistical methods in atomistic computer simulations


Lecturer(s) :

Ceriotti Michele




Every 2 years


The course gives an overview of atomistic simulation methods, combining theoretical lectures and hands-on sessions. It covers the basics (molecular dynamics and monte carlo sampling) and also more advanced topics (accelerated sampling of rare events, and non-linear dimensionality reduction).


Sampling the constant-temperature ensemble in atomistic simulations
- Canonical averages and importance sampling
- Monte Carlo, detailed balance and the Metropolis algorithm
- Molecular dynamics, integrators, energy conservation
- Autocorrelation functions, correlation time and statistical efficiency
Thermostatting molecular dynamics
- Breaking energy conservation and getting into the canonical ensemble
- Global and local thermostats, deterministic and stochastic thermostats
- Langevin dynamics. Stochastic differential equations and sampling efficiency
- Colored-noise generalized Langevin dynamics
Rare events. Getting dynamics from ensemble averages
- Rare events and time-scale separation
- Transition-state theory on the potential energy surface
- Collective coordinates. Free energy and TST on the free-energy surface
- Beyond TST. Bennett-Chandler method, committor analysis
Re-weighted sampling and adaptive biasing
- Re-weighting a trajectory to get averages in a different ensemble
- Statistics of re-weighting. Sampling efficiency of weighted averages
- Umbrella sampling and adaptive (Wang-Landau) biasing
- Metadynamics. Basics, examples and caveats
Linear and non-linear dimensionality reduction
- Dimensionality reduction -- coarse-graining the description of structurally complex systems
- Linear projection: principal component analysis; classical multidimensional scaling
- Non-linear dissimilarity reduction: ISOMAP, locally-linear embedding
- Sketch map: using proximity matching to describe atomistic problems


Introductory knowledge of statistical mechanics and probability, basic programming skills preferably in FORTRAN.  Some familiarity with working in a Linux environment is preferable. '

Learning Prerequisites

Recommended courses

Introductory knowledge of statistical mechanics and probability, basic programming skills,
preferably in FORTRAN or Python

Assessment methods

Project report



In the programs

Reference week

      Exercise, TP
      Project, other


  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German