Course Title

Computational Approaches for Complex Molecular Systems

Course Code

COS 510

Course Type

Elective

Level

PhD

Instructor’s Name

Prof. Vangelis Harmandaris (Lead Instructor)

ECTS

5

Lectures / week

2 (90 min. each)

Laboratories / week

 - 

Course Purpose and Objectives

The students will learn fundamental techniques of molecular, primarily classical, simulations (Monte Carlo and Molecular Dynamics), which are used in order to understand and predict properties of microscopic systems in materials science, physics, biology, and chemistry. All students will obtain experience on multi-scalemodelling, as well as on synergistic approaches between simulations and dataanalytics methods. A simulation project composed of scientific research, algorithmdevelopment, and presentation is required.

Learning Outcomes

By the end of the course students will acquire knowledge on the state-of-the-art mathematical and computational methodologies and algorithms across diverse fields.

By the end of the course all students expect to:

Prerequisites

None

Background Requirements

Knowledge of a programming language

Course Content

Week 1: Introduction to Statistical Mechanics: ensembles, thermodynamic averages, time correlation functions and transport coefficients; Model systems and interaction potentials: constructing an intermolecular potential, initial/boundary conditions.

Week 2: Advanced numerical algorithms: classical many-particle Molecular Dynamics simulations, Monte Carlo methods; Molecular dynamics in various ensembles: constant pressure and temperature.

Week 3: Data analytics methods: Probability, stochastic processes, and stochastic differential equations; Statistical inference: Frequentist, Bayesian, Variational inference, Inference for SDEs. Machine learning: A probabilistic perspective, main algorithms.

Week 4: Free energy calculations: tackling time-scale and rare events problems, biased and constrained simulations, thermodynamic integration,Bennett-Chandler approach, searching for the saddle points; random walk simulations).

Week 5: Multi-scale simulations: Coarse-grained techniques, rigorous potential of mean force based methods, dissipative particle dynamics, Lattice Boltzmann method.

Week 6: Analysing results of simulations: equilibrium averages, fluctuations, structural quantities, real-time correlation functions; Data analysis: data structures, data management; Uncertainty quantification: error estimates, sensitivity analysis.

Week 7: Synergistic approaches between molecular simulations and data analytics methods: Developing molecular (atomistic and coarse-grained models) via Machine Learning algorithms.

Project and essay write-up (weeks 4-7): An individual simulation project composed of scientific research, algorithm development, and presentation for a given problem.

Guest lectures: There will be the possibility for quest lectures from experts in multi-scale modelling and simulations and in data analytics methods for studying complex systems.

Teaching Methodology

Bibliography

-  Course notes, research articles
-  “Understanding Molecular Simulation. From Algorithms to Applications” by D. Frenkel and B. Smit, (Academic Press: New York, 2002).
-  “Introduction to Practice of Molecular Simulation” by A. Satoh, (Elsevier: London, 2011).
-  Statistical Mechanics: Theory and Molecular Simulation” by M. Tuckerman (Oxford, 2010).
-  “Machine Learning: a Probabilistic Perspective” by K. Murphy (MIT Press, 2012).

Assessment

The following assessment methods will be combined for the final grade:

Language

English