Topics in the Stochastic Modeling and Simulations (2017)

Instructor: Tiejun Li (PKU Math)
The purpose of this course is to give an in-depth overview to the theory and computational methods for the rare event studies. Some open issues will also be discussed. The students are required to have basic knowledge on stochastic ordinary differential equations.


Lect01 Introduction: Formulation, examples and issues

Transition State Theory: RMP review 1990

Transition State Theory: Review 2005

Transition Path Theory: Review 2010

Part 1: Zero temperature regime

Lect02 Gradient system: LDT and transition path computation

NEB paper

String method

Simplified String


Accelerated MD by OM functional

Lect03 Transition rate asymptotics: 1D and Multi-D

Kramers 1940 paper

1D Rate formula by exit problem

Multi-D Rate formula by exit problem

Schuss Review

Lect04 Saddle points finding: Dimer, GAD etc.

Dimer method


Shrining dimer method

Climb image NEB

Climb string method

Lect05 Non-gradient sytems: CKS, Large volume limit and LDT

Rare Events for CKS by Dykman

Doi-Peliti formalism

Application in phenotype switching

Two-scale LDT by path integral

Lect06 Energy landscape and gMAM

Energy Landscape paper 1

Energy Landscape paper 2

gMAM paper

PLoS one paper

Landscape Review paper

Lect07 Non-gradient systems: Difficulties and unsolved issues

Maier-Stein PRE paper

Maier-Stein PRL: non-Arrhenius law

Maier-Stein PRL: Limit cycle

Maier-Stein JSP

Lect08 Onsager-Machlup and Freidlin-Wentzell dilemma

Durr-Bach CMP paper

Andrew's JCP paper

Andrew's JSP paper

Lect09 Spectral theory approach and applications

Schuette's LAA paper

Network Reduction paper

Spectral theory paper

Bovier's CMP paper

Part 2: Finite temperate case

Lect10 Potential theory for Markov processes: I

Doyle and Snell's paper

Lect11 Potential theory for Markov processes: II

Syski's book: Passage times for Markov chains

Lect12 Transtion path theory: Diffusion and jump models

TPT for diffusion processes

Illustration of TPT

TPT for jump processes

Lect13 Finite temperature string method

JPCB paper

JCP paper

CPL paper

Science paper

Lect14 Markov state modeling: Formulation and computation

JCP MSM paper

JCP Milestoning MSM paper

Entropy Review paper

PNAS paper

Lect15 Markov state modeling: Analysis and applications

MMS paper 1

MMS paper 2

Part 3: Sampling approach

Lect16 Accelerated MD, TAMD, AFED etc.

Lect17 Umbrella sampling, meta-dynamics, replica exchange etc