About me

I am a postdoctoral researcher at mathematical science department, Korea Advanced Institute of Science and Technology (KAIST).

Eureka moment. That has been my core motivation for studying mathematics until now. Accordingly, I have been researching to identify unknown solutions of partial differential equations (PDEs) from known data, hoping to occasionally encounter eureka moments. Specifically, my research topics are: 1) machine learning methodology for fast and general-purpose PDE solvers; and 2) the mathematical modeling and simulation of ocean wave dynamics. For more details, refer to my CV and research statement

Machine learning methodology for fast and general-purpose PDE solvers

My first research topic is dedicated to developing unsupervised operator learning networks for generating the rapid and accurate solution of parametric PDEs, including the 3D Navier-Stokes equations. Once trained by the structure of a target PDE, rather than by reference solutions to the PDE, the operator learning networks are capable of assigning the corresponding solutions to given PDE data in nearly real-time. Accordingly, this capability is useful for generating massive datasets to train physical artificial intelligences within a digital twin environment. Furthermore, this framework allows for real-time ensemble computing across various scenarios, enabling efficient, probabilistic forecasting in weather and climate modeling.

The mathematical modeling and simulation of extreme ocean-wave dynamics

The second topic involves the mathematical modeling and simulation of ocean wave dynamics, specifically focusing on highly non-linear phenomena like rogue waves. Building upon the Euler equations, I have introduced approximate PDE hierarchy and performed simulations using the approximate PDEs to realize rogue wave dynamics. This computational work is expected to serves as a key clue for justifying the relations among ocean wave models, and constructing robust, real-time forecasting and warning systems.