Leveraging the Geometry of Optimal Transportation in Parameter Identification and Related Problems

Abstract: Optimal transportation (OT) theory, initially developed for the transportation problem of goods and other materials, has found numerous applications in PDE, fluid dynamics, geometric inequalities, probability theory, economics, and so on. Moreover, the recent explosion of interest in data science and machine learning surged an immense interest in OT-based techniques mainly because OT provides a notion of distance and geometry on the space of probability measures.

In this talk, I will discuss the applications of OT geometry in improving and developing novel computational methods for parameter identification and related problems. In particular, I will discuss parameter identification in dynamical systems and PDE-based optimization problems.

Mathematics

Audience: general audience

( video )

Comments: Talk host: Vardan Voskanyan

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Yerevan Mathematical Colloquium

Series comments: "Yerevan Mathematical Colloquium" invites survey talks aimed at a general mathematical audience, that emphasize proof methods, relations between branches of mathematics, possible applications, and open problems.

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