## MINDS Research

The research goal of MINDS is to understand the mathematical aspects of fundamental data science and its mathematical principles. MINDS research also includes applications of mathematical data science to industry and society. MINDS data science research for society leads us to humanitarian data science for people and society. To achieve these, MINDS research focuses on the following:

- Mathematical research on the principles of data science
- Mathematical understanding of machine learning and artificial intelligence
- Large-scale Scientific computing
- Humanitarian data science

### Research Areas

- Mathematical data science
- Mathematical structure and stability analysis of big data
- Topological data analysis & topological abstractization of big data
- Data based algorithm of machine learning and artificial intelligence
- Large-scale scientific computing & generation of big data
- Partial differential equations and machine learning & PDE-inspired machine learning
- Probability theory, uncertainty quantification, parameter estimation of data
- Data-driven mathematical biology, network theory
- Mathematical analysis of language acquisition data and machine learning algorithm

#### Applications

- Topological data analysis and its applications in the areas of biomedical problems (diagnosis & prediction)
- Topological analysis of big data such as gravitational wave time-series data
- Big data analysis and its stability analysis
- Analysis and prediction of big data from finance and social problems
- Topological analysis of Korean music data
- Machine learning & artificial intelligence approaches to the solution of partial differential equations
- AI-driven simulation of fluid dynamic equations and its applications in industry and bio-medicines
- Anomaly detection in social network and time-series data
- Climate analysis and weather prediction via machine learning and artificial intelligence
- Large-scale scientific computing such as computational fluid dynamics and weather predictions
- Physics-informed, physics-driven artificial intelligence
- Uncertainty analysis of big data and parameter estimation
- Social data analysis and humanitarian data Science

## Faculty Research

- Jae-Hun Jung – Data science, topological data analysis, high order numerical analysis and scientific computing, numerical PDEs, machine learning and artificial intelligence
- Hyungju Hwang – Partical differential equations, machine learning approaches to PDEs, data science, block-chain, social data analysis
- Yun Sung Choi – Functional analysis
- Donhyun You – Computational fluid dynamics, machine learning and artificial intelligence, AI simulation of computational fluid dynamics, fluid analysis
- Minseok Choi – Numerical analysis and scientific computing, uncertainty analysis and parameter estimation, Physics-informed neural network (PINN), machine learning and artificial intelligence for numerical PDEs
- Jae Ryong Kweon – Numerical analysis, corner singularity, finite element analysis, numerical analysis of Navier-Stokes equations
- Sungsup Choi – Statistics, financial mathematics, risk analysis, financial data analysis
- Jong-seong Kug – Mechanism for climate changes, ocean-atmosphere interaction and EL Nino, machine learning and artificial intelligence approaches to geophysical problems
- Kunwoo Kim – Probability, stochastic analysis
- Donghyun Lee – Partial differential equations analysis, applied PDEs, fluid mechanics analysis, kinetic theory
- Minwoo Chae – Statistic, data science, mathematical analysis of machine learning algorithms
- Bo Gwang Jeon – Topology and geometry of 3-manifolds
- Jinsu Kim – Probability, mathematical biology, network science
- Jay Min Lee – Matrix analysis, cognitive image processing, scientific computing, inverse problem