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
Bifurcation analysis of a two-dimensional magnetic Rayleigh–Bénard problem
– Physica D: Nonlinear Phenomena
(2024)
467,
134270
(doi: 10.1016/j.physd.2024.134270)
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)
A mathematical guide to operator learning
– Handbook of Numerical Analysis
(2024)
25,
83
(doi: 10.1016/bs.hna.2024.05.003)
Multivariate rational approximation of functions with curves of
singularities
(2023)
Elliptic PDE learning is provably data-efficient.
– Proceedings of the National Academy of Sciences
(2023)
120,
e2303904120
(doi: 10.1073/pnas.2303904120)
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