Research

Density Propagation via Point Cloud Iteration

Fig.1 Comparison of the analytical and proximal solutions of the FPK PDE for 1D Ornstein Uhlenbeck Process.

Fig.2 Convergence of transient PDFs to the stationary distribution for 2D Nonlinear Non-Gaussian System.

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 .