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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Takabe Satoshi
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(W834) Thr3-4(W834)
- Group
- -
- Course number
- MCS.M422
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
Statistical mechanics is a field of theoretical physics, which has been constructed to understand macroscopic thermodynamics from the microscopic viewpoint. Similar to other fields of physics, statistical mechanics has been developed to treat materials. However, interestingly, statistical mechanics also has been known as a powerful tool for information science treating non-material things from 1970s. In this course, the basic knowledge of equilibrium statistical mechanics will be taught in a way that is as easy to understand as possible for students who have not studied physics. In particular, Markov-chain Monte-Carlo method and mean-field approximation called belief propagation will be taught as statistical-mechanical tools related to information science. In addition, applications of statistical mechanics to various fields of information science, e.g., random graph theory, error-correcting codes, and combinatorial optimization, will be introduced.
Student learning outcomes
The student will learn the following ideas and its relation to information science:
1. Basic ideas of equilibrium statistical mechanics such as canonical distribution, partition function, free energy, Ising models, and phase transition phenomena.
2. Basic theory and implication of Markov-chain Monte-Carlo methods.
3. Mean-field approximation and its applications to various fields such as combinatorial optimizations.
Keywords
Statistical mechanics, partition function, Markov-chain Monte-Carlo methods, belief propagation
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Lectures will be given based on course materials.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Introduction | Introduction of statistical physics and its relations to other fields. Learn basic concepts of statistical mechanics. |
| Class 2 | Ising Models and Phase Transition | Learn mean-field approximation and phase transition phenomena. |
| Class 3 | Markov Chain Monte Carlo Methods (1) | Learn basics of Markov chain Monte Carlo methods. |
| Class 4 | Markov Chain Monte Carlo Methods (2) | Learn representative Gibbs sampling and Metropolis-Hastings algorithm. |
| Class 5 | Advanced Markov Chain Monte Carlo Methods | Learn simulated annealing and exchange Monte Carlo method (parallel tempering). |
| Class 6 | Random Graphs | Learn graphs, random graph ensembles, and their phase transition phenomena. |
| Class 7 | Belief Propagation on Trees | Learn exact belief propagation (message passing) on trees. |
| Class 8 | Loopy Belief Propagation | Learn loopy belief propagation on loopy graphs. |
| Class 9 | Analysis of Loopy Belief Propagation | Learn cavity method and analysis of phase transition of loopy belief propagation. |
| Class 10 | Relation to Information Theory | Learn channel capacity and low-density parity-check codes. |
| Class 11 | Relation to Error-Correcting Codes | Learn belief propagation decoder for low-density parity-check codes. |
| Class 12 | Relation to Combinatorial Optimization | Learn combinatorial optimization problem and its relation to statistical physics. |
| Class 13 | Relation to Machine Learning | Learn relation to Bayesian inference. |
| Class 14 | Summary | Summarize the course. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Course material will be available.
Reference books, course materials, etc.
M. Mézard and A. Montanari, “Information, Physics, and Computation,” Oxford University Press, 2009.
Assessment criteria and methods
Evaluated by report submissions.
Related courses
- MCS.T212 ： Fundamentals of Probability
- MCS.T403 ： Statistical Learning Theory
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students must have basic knowledge of (classical) probability theory and statistics. Students do not need to have knowledge of physics including statistical mechanics.
