Shivam Arora
navigation

Research

Home Research Projects Blog
 
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.
I completed my PhD in Mathematics at Memorial University of Newfoundland, St. John's, Canada, under 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.
notion image
Publications
Model-agnostic machine learning of conservation laws from data
Shivam Arora, Alex Bihlo, Rüdiger Brecht, Pavel Holba
arxiv.org
Topological groups with a compact open subgroup, Relative hyperbolicity and Coherence
Shivam Arora, Eduardo Martinez-Pedroza
arxiv.org
Fixed Point Sets in Diagrammatically Reducible Complexes
Shivam Arora, Eduardo Martinez-Pedroza
Submitted
arxiv.org
Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups
Shivam Arora, Ilaria Castellanoano, Ged Corob Cook, Eduardo Martinez Pedroza
Journal of Topology and Analysis
arxiv.org
Subgroups of word hyperbolic groups in rational dimension 2
Shivam Arora, Eduardo Martinez-Pedroza
Groups, Geometry, and Dynamics
arxiv.org
z-Classes in finite groups of conjugate type (n,1)
Shivam Arora, Krishnendu Gongopadhyay
Proceedings - Mathematical Sciences
arxiv.org
Invariant Physics-Informed Neural Networks for Ordinary Differential Equations
Shivam Arora, Alex Bihlo, Francis Valiquette
arxiv.org

PhD Thesis

I completed my PhD thesis under the the supervision of Dr. Eduardo Martinez-Pedroza in the area of Geometric Group Theory.
badge