I am interested in mathematical foundations of artificial neural networks and applying them to solve scientific problems. I am interested in neural network with architecture that incorporates mathematical structure specific to the problem. Some of the examples of that are Physics-informed neural networks, group equivariant neural network, HNN, etc.

PhD Thesis

I completed my PhD thesis under the the supervision of Dr. Eduardo Martinez-Pedroza in the area of Geometric Group Theory. I worked at the intersection of Group Theory and Topology. Group theory is the mathematical abstraction to study symmetry and topology is study of spaces.