In recent years, the surge in computational power and the exponential increase in data availability have propelled machine learning (ML) to the forefront of scientific inquiry and computational methodology. This paradigm shift has significantly influenced scientific computing, offering novel perspectives and techniques that extend beyond traditional models. This lecture explores a new direction in research and applications where ML not only complements but also enhances traditional computational approaches. Key topics include the integration of machine learning with numerical methods for tackling multi-scale problems and a detailed convergence analysis from both machine learning and numerical analysis perspectives, focusing on error estimation. By leveraging these advanced techniques, we can address complex partial differential equations (PDEs) more efficiently and accurately, opening up new possibilities for solving some of the most challenging problems in scientific computing.

 

 

ZOOM Address : https://snu-ac-kr.zoom.us/j/5196459524 (ZOOM ID : 5196459524)