Our research projects are motivated by connections between practical applications such as scientific computing, machine learning, and data science. The current studies have been focused on several interrelated and interdisciplinary directions:

First, meta-learning techniques are used to significantly improve the computational speed and efficiency of numerical solutions of partial differential equations over conventional machine learning-based models.

Second, we take advantage of machine learning to develop new techniques that can resolve singular behavior of partial differential equations which are difficult to handle with existing numerical methods.

Third, with the well-studied numerical PDE theory, we develop new machine learning techniques to tackle difficult problems in machine learning.