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
(2022)
Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable
Patterns
(2022)
Bifurcation analysis of two-dimensional Rayleigh-Benard convection using deflation
– Phys Rev E
(2022)
105,
055106
(doi: 10.1103/PhysRevE.105.055106)
Learning Green's functions associated with time-dependent partial
differential equations
(2022)
Data-driven discovery of Green's functions with human-understandable deep learning
– Scientific Reports
(2022)
12,
4824
(doi: 10.1038/s41598-022-08745-5)
Learning Elliptic Partial Differential Equations with Randomized Linear Algebra
– Foundations of Computational Mathematics
(2022)
23,
709
(doi: 10.1007/s10208-022-09556-w)
Control of Bifurcation Structures using Shape Optimization
– SIAM Journal on Scientific Computing
(2022)
44,
a57
(doi: 10.1137/21m1418708)
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