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

  • Materials Science and Engineering (edoc), 2019-2020
    • Semester
    • Exam form
      Project report
    • Credits
    • Subject examined
      Statistical methods in atomistic computer simulations
    • Number of places
    • Lecture
      14 Hour(s)
    • Practical work
      14 Hour(s)

Reference week

Exercise, TP
Project, other


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