Scholar must take up all the ability of the time, all the contributions of the past, all the hopes of the future, s/he must be university of knowledge.      ---- R.W. Emerson.

As a postdoctoral fellow at the Institute of Mathematical Sciences Chennai, I primarily focused on nonlinear analysis and dynamical systems. As a doctoral student at the Indian Institute of Technology Mandi, I worked on dynamical systems with impulsive effects and their application to control problems and ecological systems.  

My independent research program takes both my doctoral and postdoctoral studies one step further to learning system dynamics and control at the interface of optimization, statistical learning, and dynamical system. This often requires conceptual, innovative, and technical understandings that breakthrough along three different dimensions:

Dynamical systems & control: Modelling forced or unforced evolution, in a state space, & establishing its stability, control. Theoretical & data driven system dynamics in statistical learning framework, computing stability & control to estimate perception, prediction & planning in an autonomous control.

Statistical learning: Designing a predictive function in statistical learning framework with discriminative modelling (e.g. regression) or generative modelling (e.g. multi-modality with CVAE) by minimizing a loss function. A transforming a learning problem as an optimization problem.

Optimization: First order & second order adaptive descent algorithms, interior point method for convex problems. Convexification or relaxation or breaking symmetry or uncertainty in non-convex problem & transforming geometrical or physical intuition & of the problem into a scalable optimization algorithm. 

Ongoing works:  

1. Autonomous control system, 2.  Learning algorithm of nonlinear dynamical systems, 3. A perturbed based apdative optimization algorithm of non-convex optimization.