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Traditionally, mathematical models have been widely used to understand complex behaviors or dynamics in science and engineering, even economics and social science. However, identifying a proper mathematical system for certain phenomena requires deep prior knowledge about related theories and advanced mathematics; development has been lagging behind. Nowadays, thanks to the advances in machine learning techniques and data-driven modeling, we are able to effectively identify mathematical models (e.g., ordinary/partial differential equations (ODE/PDE)) from data directly without (or a little) prior knowledge. In this talk, Dr. Lee will present some machine learning techniques of data-driven ODE/PDEs from microscopic data with various examples. Through these examples, I illustrate the concept of the black-box model and the (partially physics informed) gray box model to identify/explain model ODE/PDE. Moreover, he will introduce the correction model of the existing theory-grounded models to enhance prediction accuracy. Such data-driven models can be applied to various research topics from science/engineering to economics. Hence, this presentation will suggest a new direction for a future curriculum for data-driven modeling in our department (and STEM field). |