Research

My research interests are Mathematics of Data Science, Graph-based Learning and Clustering, Approximation Theory, Data-driven Metrics for High-dimensional Unsupervised Learning, Machine Learning and their intersections. These are the research topics I have been worked on previously.

• Compressed sensing and its application to signal recovery and image reconstruction

• Graph-based learning and clustering

• Graph Ricci curvature and its applications to data science

• Approximation for high dimensional functions via Kolmogorov Superposition Theorem

• Physics Informed Neural Networks for solving Poisson-Boltzmann equation

• Matrix cross approximation 

• Out-of-distribution detection