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
Accurate numerical simulation of electrodiffusion and water movement in brain tissue.
– Mathematical Medicine and Biology
(2021)
38,
516
(doi: 10.1093/imammb/dqab016)
Data-driven discovery of Green's functions with human-understandable
deep learning
(2021)
An optimal complexity spectral method for Navier--Stokes simulations in
the ball
(2021)
Bifurcation analysis of two-dimensional Rayleigh--Bénard convection
using deflation
(2021)
Accurate numerical simulation of electrodiffusion and water movement in
brain tissue
(2021)
Learning elliptic partial differential equations with randomized linear
algebra
(2021)
Deflation-based identification of nonlinear excitations of the three-dimensional Gross-Pitaevskii equation
– Physical Review A
(2020)
102,
053307
(doi: 10.1103/physreva.102.053307)
Computing with Functions in the Ball
– SIAM Journal on Scientific Computing
(2020)
42,
c169
(doi: 10.1137/19m1297063)
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