I like to describe myself as someone trained mathematically with machine learning solutions looking for scientific problems.
I have worked on forecasting and modelling of various ecological and biological phenomenon such as infectious diseases, air quality modelling and wildfire spread dynamics.
My research attempts to address the challenges of limited data with unknown dynamics.
In contrast to my application oriented research, I am also interested in gaining a deeper theoretical understanding of machine learning models which includes (but not limited to) random feature models, diffusion models, etc.
While some of the research listed below is ongoing, few are ideas that I have worked on previously. Regardless, I would be more than willing to pursue any of these areas if any opportunity arises.
Wildfires can cause immense destruction of livelihood, property and lives. In order to improve the understanding of wildfire spread, we are working on mapping wildfire spread risk by harnessing the power of available data in learning a physical PDE model of wildfire spread. [In Media]
Methane from Alberta Oil Sands tailings ponds are slowly becoming a cause for global concern in light of climate change and greenhouse gas emission reduction efforts. This research includes collaborations between mathematicians, lab experimentalists and soil microbiologists. Our research focuses on various aspects of understanding these emissions and its impact on air quality using data from weather monitoring stations and lab experiments. [Paper 1] [Paper 2] [In Media]
Infectious diseases have been and will always be an area of interest for researchers. Since appropriate data availability is often a challenge, we use classical models with machine learning to get short term predictions. [Paper] * [In Media].
*This paper received the '2023/2024 Applied Mathematics Graduate Research Paper Award' at University of Waterloo.
Seismic activity is among the hardest phenomenon to model, making accurate earthquake prediction a near impossible task. However, efforts are still ongoing on trying to build models that can understand earthquake waves. Some well known PDE models can studied in detail that can potentially be used to understand waves and shocks. [Paper]
Diffusion models are one of the foundational ideas behind most of the generative AI models. However, very little is known about their nature of training from a theoretical perspective, especially when deep architectures are used. We use random feature models to train a diffusion model that can potentially be used to derive generalization bounds on the convergence of the model to its true distribution. [MATH4AI workshop paper in AAAI 2026 Conference]
Due to the curse of dimensionality, high dimensional function approximation is often challenging, especially in the data scarcity regime. We develop a sparsity based random feature expansion model and derive their generalization bounds. [Paper]
Coming from an academic family, although my exposure to research has been since the day I was born, my formal introduction to exploratory works started early during my schooling and undergraduate studies.
Find below links to some of my earliest formal articles spanning mathematics and social sciences.
Application of Linear Algebra in Robotics [Click to view]
Toricelli's Trumpet: A Paradox [Click to view]
Role of Religion and Caste System in Women Exploitation: A Study in the Indian Context [Click to view]