I am a Research Fellow in Numerical Analysis.
My research interests lie at the intersection between numerical analysis and deep learning. I primarily focus on the mathematical foundations of deep learning to discover mathematical models (partial differential equations) from data, and the development of novel and theoretically justified numerical techniques.
I am a member of the Scientific Artificial Intelligence (SciAI) Center supported by the Office of Naval Research (ONR).
Publications
Randomized Nyström approximation of non-negative self-adjoint
operators
(2024)
LLMs learn governing principles of dynamical systems, revealing an
in-context neural scaling law
(2024)
Multivariate rational approximation of functions with curves of
singularities
(2023)
Elliptic PDE learning is provably data-efficient
– Proceedings of the National Academy of Sciences of the United States of America
(2023)
120,
e2303904120
(doi: 10.1073/pnas.2303904120)
Principled interpolation of Green’s functions learned from data
– Computer Methods in Applied Mechanics and Engineering
(2023)
409,
115971
(doi: 10.1016/j.cma.2023.115971)
Two-component three-dimensional atomic Bose-Einstein condensates supporting complex stable patterns
– Physical Review A
(2023)
107,
012813
(doi: 10.1103/PhysRevA.107.012813)
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