革新知能統合研究センター

内容:
We are planning a Mathematical Seminar at the open space of the Nihonbashi Office on Friday 6/28.
These talks will be in English.

1.
Speaker : Ippei Obayashi
AIP Topological Data Analysis Team
Time：13:00-14:30

Title: Persistent homology – Introduction and applications

Abstract: In this talk, I will present our recent researches about persistent homology. Persistent homology is the homology theory based on the idea of persistence and is develeped for data analysis from the viewpoint of topology. Persistent homology can characterize the shape of data quantitatively and effectively.
The contents of the talk is as follows:
* Introduction to persistent homology
* Persisitent homology and machine learning
* Applications to materials science

2.
Speaker: Naoya Takeishi
AIP Structured Learning Team
Time：15:00-16:30

Title: The Koopman Operator on Dynamical Systems with and for Machine Learning

Abstract: Analyzing dynamical systems is essential for scientific understanding of natural and social phenomena and engineering purposes such as signal processing, control, and machine learning. In general, however,
the governing equation of dynamics is often unknown a priori, and even if it is known, it is challenging to analyze nonlinear systems. To handle these issues, the operator-theoretic analysis of dynamical systems, especially using the Koopman operator, has been extensively utilized in this decade.
In this talk, I introduce the use of the Koopman operator for data-driven analyses of dynamical systems in conjunction with the techniques and the applications of machine learning. In the first part, I show some data-driven estimation methods of the spectral decomposition based on the Koopman operator, which utilize the techniques commonly used in machine learning (e.g., Bayesian inference and neural networks) and enable us to overcome the issues of
conventional methods. In the second part, I showcase usages of the Koopman operator to machine learning applications, including change-point detection and discriminant analysis.