My research interests are Mathematics of Data Science, Graph-based Learning and Clustering, Manifold Learning, 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.
Approximation for high dimensional functions via Kolmogorov Superposition Theorem
Function Regression on Manifolds via Transformer
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
Physics Informed Neural Networks for solving Poisson-Boltzmann equation
Low rank matrix cross approximationÂ
Out-of-distribution detection