Tan Phuong Dong Le

About

I develop computational methods that combine applied mathematics, scientific computing, and machine learning for solving problems arising from PDEs, variational inequalities, free-boundary problems, and data-driven modeling.

I am Tan Phuong Dong Le, also known as Phuong Dong Le, a Doctor of Philosophy in Applied Mathematics from the University of Waterloo. My doctoral research was supervised by Dr. Hans De Sterck and Dr. Giang Tran, and focuses on mesh-free variational methods using radial basis function networks for elliptic partial differential equations, obstacle problems, and free-boundary value problems.

I am broadly interested in scientific machine learning, scalable approximation methods, kernel-based numerical methods, Bayesian inverse problems, graph representation learning, and computational mathematics.

Research Interests

My research connects rigorous applied mathematics with modern computational and machine-learning methods.

Scientific Machine Learning

Machine-learning-based approximation methods for scientific computing, variational problems, and high-dimensional PDEs.

Numerical PDEs

Mesh-free and variational methods for elliptic PDEs, obstacle problems, and free-boundary value problems.

Kernel Methods

Radial basis function networks, random feature methods, and stabilized solvers for ill-conditioned approximation systems.

Inverse Problems

Optimization and Bayesian approaches for parameter estimation, uncertainty quantification, and scientific data assimilation.

Graph Learning

Graph representation learning, graph neural networks, spectral graph methods, and scientific graph learning.

Topological Data Analysis

Persistent homology and geometric methods for analyzing structured data, networks, and biological sequences.

Selected Publications

Selected thesis-related work and publications in applied mathematics, computational methods, graph-based modeling, and data analysis.

Mesh-Free Variational Methods for Free-Boundary Problems via Radial Basis Function Networks

Tan Phuong Dong Le, Hans De Sterck, Giang Tran. PhD thesis-related manuscript.

Random Feature Solvers for High-Dimensional Variational Problems

Tan Phuong Dong Le, Hans De Sterck, Giang Tran. Manuscript in preparation.

Chaos Geometry and Persistent Homology for DNA

Phuong Dong Le. IEEE CSCI, 2022.

Graph-Theoretical Approach to DNA Sequences

Phuong Dong Le. Communications in Statistics, 2022.

Adaptive Geometry for Signed Networks

Phuong Dong Le. Science and Information Conference, Springer, 2022.

Projects and Repositories

Public code and research software related to numerical PDEs, RBF networks, variational methods, and scientific machine learning.

Variational Formulation RBF Networks

A NumPy-based toolkit for mesh-free approximation of partial differential equations using radial basis function networks, weak constraints, and truncated SVD stabilization.

Python NumPy RBF PDEs Variational Methods

View Showcase →

Graph Representation Learning

Notes and future implementations for graph neural networks, graph embeddings, spectral graph methods, and scientific graph learning.

GNNs Spectral Methods Graph Learning Scientific Learning

View GitHub →

Teaching

I have teaching experience in applied mathematics, differential equations, numerical methods, vector calculus, and scientific computing at the University of Waterloo.

I am interested in teaching mathematical modeling, numerical analysis, scientific computing, machine learning, and graph representation learning.