Current Appointments & Affiliations
Ruth F. DeVarney Distinguished Professor of Mathematics
·
2022 - Present
Mathematics,
Trinity College of Arts & Sciences
Professor of Mathematics
·
2020 - Present
Mathematics,
Trinity College of Arts & Sciences
Chair of the Department of Mathematics
·
2024 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
How Much Can One Learn a Partial Differential Equation from Its Solution?
Journal Article Foundations of Computational Mathematics · October 1, 2024 In this work, we study the problem of learning a partial differential equation (PDE) from its solution data. PDEs of various types are used to illustrate how much the solution data can reveal the PDE operator depending on the underlying operator and initia ... Full text CiteA data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems
Journal Article Statistics and Computing · August 1, 2023 In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in solving large-scale B ... Full text CiteOn Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network
Conference Proceedings of Machine Learning Research · January 1, 2023 This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expr ... CiteRecent Grants
Learning Partial Differential Equation (PDE) and Beyond
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2026RTG: Training Tomorrow's Workforce in Analysis and Applications
Inst. Training Prgm or CMECo-Principal Investigator · Awarded by National Science Foundation · 2021 - 2026Computational Forward and Inverse Radiative Transfer
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2020 - 2024View All Grants
Education, Training & Certifications
University of California, Los Angeles ·
1996
Ph.D.