# Research

## Density Propagation via Point Cloud Iteration

In this work, we developed a new method to solve the Fokker-Planck or Kolmogorov's Forward equation which is a partial differential equation (PDE) that governs the time evolution of the probability density function of a continuous time stochastic non-linear system. Instead of using traditional techniques like Monte Carlo and/or Function Approximation which suffer from the so called "curse-of-dimensionality", we exploit the gradient flow strucuture of this PDE in space of probability density functions. More details can be found here .

I also presented these results at CITRIS/CPAR Control Theory and Automation Symposium,1st NorCal Workshop. Here is my poster.

## Density Control via Schrodinger Bridge

Under Construction .